An Oscillator System for UWB QDAcR
M.Sc. Thesis
An Oscillator System for a Quadrature
Downconversion Auto-Correlation
Ultra-Wideband (UWB) Receiver
Student: Gaurav Mishra
Supervisor: Dr. ir. Wouter A. Serdijn
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An Oscillator System for UWB QDAcR
An Oscillator System for a Quadrature
Downconversion Auto-Correlation
Ultra-Wideband (UWB) Receiver
THESIS
Submitted in partial fulfillment of the
requirements for the degree of
MASTER OF SCIENCE
In
Electrical Engineering (Microelectronics)
By
Gaurav Mishra
Student number: 1287834
Department of Microelectronics (ELCA)
Faculty of Electrical Engineering, Mathematics, and Computer Science
Delft University of Technology, The Netherlands
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An Oscillator System for UWB QDAcR
ACKNOWLEDGMENTS
I am extremely grateful and indebted to my advisor and mentor Dr. ir. Wouter A. Serdijn
for granting me an opportunity to pursue research on this topic for my thesis. This work
would never have been possible without his constant encouragement, support,
thoughtfulness and tutelage.
I would like to express my gratitude to Prof. Dr. John R. Long and Dr. ir. G.J.M. Janssen
for being a part of my thesis committee.
I am extremely indebted to Prof. Dr. John R. Long, for his guidance and helping me in
completion of my studies. I am very much grateful towards Drs. E. Janssen of the
Department of Electrical Engineering and Mr. J.B.A. Stals of International Office, for
supporting me financially and morally during my stay at Delft University of Technology.
This work, my sojourn at TU-DELFT and all my endeavours would never have been
possible without the love, encouragement and patronage of my parents and my brotherly
friends Dr. ir. Akshay Visweswaran, ir. Vincent R. Bleeker and ir. Maxim A. Volkov. It
is through them, that I felt to live and dream again and realize it through sheer grit and
perseverance.
Above all I am thankful to RAM for bestowing me with everything I possess in life.
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An Oscillator System for UWB QDAcR
Abstract
The fast development of CMOS IC process technology and the opening up of high
frequency bands by regulatory bodies has aided wireless communication industry with
development and commercialization of long-medium and short range wireless
communication applications, for example GSM, Wireless LAN, Bluetooth and UWB.
Ultra Wideband (UWB) is a promising technology that covers a bandwidth from 3.1GHz
to 10.6GHz, which features distinctive advantages, such as high data rate over short and
medium range, low interference or co-existence with other wireless technologies and
robustness towards multipath fading and possible usage in personal area network (PAN)
and body area network (BAN), targeting especially health care monitoring applications.
Impulse radio UWB or ir-UWB, is one of the UWB technologies, which applies
transmission of short duration (pico-nano second) and carrier less pulses. Several receiver
architectures [1, 2 & 3] based on the principle of correlation has been proposed, with
Quadrature Downconversion Auto-Correlation Receiver (QDAcR) [3] being one of them.
This thesis work builds up further on the generalized QDAcR model of [3], starting with
an advanced time domain analysis of principle of Downconversion in QDAcR and
exploring the dependency of QDAcR on downconverter related stochastic perturbations
such as phase noise, jitter and amplitude perturbations. The use of Stationary Stochastic
Process Theory, Fokker-Planck Equation and Floquet’s Theory resulted in a simplified
equation, incorporating the effect of stochastic perturbations; this equation of
prominence, further can be extrapolated to perturbation analysis of Zero (low) – IF
receivers. A complete system modeling of QDAcR downconverter resulted in vital
specifications for the QDAcR downconverter being the requirement of a 5.6 GHz
quadrature voltage controlled oscillator (QVCO) with a minimum phase noise of 90dBc/Hz at 1MHz offset and with a maximum permissible phase error of 4 degrees.
This relaxed nature of specifications has opened a plethora of trade-offs. The main aim
being the design of low power Quadrature oscillator, a push-pull LC tank voltage
controlled oscillator, consuming 1mW of power and exhibiting figure of merit of
187.1dB with a tuning range of 12.7% was designed. The Bottom Series QVCO, Parallel
Coupled QVCO and Push-Pull –Polyphase QVCOs were compared for their respective
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An Oscillator System for UWB QDAcR
advantages and disadvantages, which resulted in the selection of the Parallel Coupled
QVCO, because of less power consumption and robust design. The Parallel QVCO
consumes a power of 2.4mW, while having a FOM of 186.36dB. The final design
includes the complete QVCO system and differential buffer (Common Source) with
neutralization capacitors having ability to drive variable loads.
References:
1. Heydari, P.; A study of low-power ultra wideband radio transceiver architectures,
Wireless Communications and Networking Conference, 2005 IEEE Issue
Date: 13-17 March 2005 Volume : 2, On page(s): 758 – 763.
2. M. Z. Win and R. A. Scholtz,” Ultra-Wide Bandwidth Time-Hopping SpreadSpectrum Impulse Radio for Wireless Multiple-Access Communications,” IEEE
Trans. Communications, vol. 48, pp. 679-69, April 2000.
3. Simon
Lee,
S.
Bagga
and
W.A. Serdijn,
“A
Quadrature
Downconversion Autocorrelation Receiver Architecture for UWB,” Joint
UWBST and IWUWBS, May 2004.
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An Oscillator System for UWB QDAcR
Table of Contents
1
CHAPTER 1 ............................................................................................................ 11
1.1
Introduction..................................................................................................... 11
1.2
Ultra-Wideband Communication Systems ................................................... 13
1.3
UWB Regulations and Ultra Wideband System’s comparison with
Narrowband Communication system ....................................................................... 15
1.4
Ultra Wideband Transceiver Architectures and Challenges...................... 19
1.5
Thesis Objectives............................................................................................. 22
2
CHAPTER 2 ............................................................................................................ 23
2.1
System Level Design ....................................................................................... 23
2.2
Quadrature Downconversion Autocorrelation Receiver ............................ 24
2.3
Time Domain Analysis of QDAcR................................................................. 26
2.4
Modeling of an Oscillator in QDAcR ............................................................ 38
2.4.1
The Phase Noise Characterization: Basics and Noise Sources ........... 39
2.4.2
The Phase Noise Characterization: Noise Distribution in a Single
Sideband Spectrum................................................................................................. 44
2.4.3
Modeling of Oscillator in time domain (Jitter and Phase Noise
conversion)............................................................................................................... 47
2.5
Conclusion ....................................................................................................... 52
3
CHAPTER 3 ............................................................................................................ 53
3.1
Introduction..................................................................................................... 53
3.2
Designing and Simulation of the Oscillator in MATLAB ........................... 53
3.3
Analysis of QDAcR architecture ................................................................... 56
3.3.1
Frequency Planning in QDAcR architecture ....................................... 61
3.3.2
The Noise Block....................................................................................... 63
3.4
Designing of the Quadrature Downconversion Auto Correlation Receiver
(QDAcR) in MATLAB ............................................................................................... 64
3.5
Conclusion ..................................................................................................... 102
Section II ........................................................................................................................ 104
4
CHAPTER 4 .......................................................................................................... 106
4.1
Overview of Oscillator Fundamentals ........................................................ 106
4.2
Quality Factor (Q-Factor), Impedance Transformation, Single Transistor
Oscillators and Differential Oscillators .................................................................. 109
4.2.1
Differential Topology Oscillators ........................................................ 113
4.3
-Gm (Negative Transconductance) and LC-Tank Design Essentials....... 114
4.3.1
Designing of LC-Tank for Low Power and Low Phase Noise .......... 115
4.4
LC-Tank Design ............................................................................................ 118
4.4.1
Inductor Modeling and Characterization........................................... 118
4.4.2
Defining Process Related Parameters* ............................................... 120
4.4.3
The optimized inductor design methodology ..................................... 121
4.4.4
Varactor Design Methodology ............................................................. 131
4.5
Oscillator Design Methodology.................................................................... 141
4.5.1
Phase Noise in an Oscillator System.................................................... 142
4.5.2
The Oscillator Start-up condition........................................................ 143
4.5.3
Methodology for Oscillator Design...................................................... 144
4.6
Oscillator Design and Comparison ............................................................. 147
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An Oscillator System for UWB QDAcR
4.6.1
Comparison of Different Oscillator Designs....................................... 150
4.7
Layout Design Considerations ..................................................................... 160
4.8
Conclusions.................................................................................................... 161
5
CHAPTER 5 .......................................................................................................... 162
5.1
Methods of Quadrature Signal Generation and Q-VCO Principle.......... 162
5.2
Q-VCO Principle........................................................................................... 163
5.3
Principle of Injection locking....................................................................... 167
5.4
Implementation of Q-VCO using injection locking ................................... 168
5.4.1
Methodology for Quadrature Oscillator Design ................................ 168
5.5
Q-VCO implementation using Complementary VCO, Poly-Phase filter and
output buffers ............................................................................................................ 178
5.5.1
Poly-Phase Filter Design and Implementation................................... 178
5.5.2
The design of Output Buffer ................................................................ 180
5.6
Conclusion ..................................................................................................... 183
6
CHAPTER 6 .......................................................................................................... 184
6.1
Conclusions.................................................................................................... 184
6.2
Future Work.................................................................................................. 185
References...................................................................................................................... 187
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An Oscillator System for UWB QDAcR
Table of Figures
Figure 1.1: The block diagram of ir-UWB receiver with time domain correlation
using a template [2]......................................................................................................... 12
Figure 1.2: Transmitted Reference Auto-Correlator [1]............................................. 12
Figure 1.3: The Block Diagram of ir-UWB Transceiver [2] ....................................... 12
Figure 1.4: A Narrowband Sinusoidal in (a) the time domain and (b) the frequency
domain.............................................................................................................................. 14
Figure 1.5: Gaussian Mono pulse in time and frequency domain............................. 14
Figure 1.6: The UWB emission mask for the indoor & outdoor communication..... 16
Figure 1.7: Distinction between the different communication techniques. ............... 17
Figure 1.8: Comparison of Data throughput and range for IEEE 802 Standards [12]
........................................................................................................................................... 18
Figure 1.9: Coexistence of UWB signals with narrowband and wideband signals in
the RF spectrum.............................................................................................................. 18
Figure 1.10: Time domain Correlator Receiver architecture [2] ............................... 20
Figure 2.1: Quadrature Downconversion Auto-Correlation Receiver Architecture
[l9]..................................................................................................................................... 24
Figure 2.2: UWB Frequency Spectrum before (top) and after (below)
Downconversion [20] ...................................................................................................... 25
Figure 2.3: State-Space diagram of an oscillator in V-I plane.................................... 34
Figure 2.4: Change in Auto-Correlation Vs. Phase Error .......................................... 36
Figure 2.5: The Power Spectrum of an Oscillator and Phase Noise power of the
carrier at certain offset................................................................................................... 40
Figure 2.6: Phase perturbation due to charge injection.............................................. 41
Figure 2.7: The Single Side Band Spectrum of and Oscillator ................................... 44
Figure 2.8: The various types of Jitters present in a oscillating signal ...................... 47
Figure 3.1: The Block Diagram of LO modeled in MATLAB.................................... 54
Figure 3.2: Complete Block Diagram of Micro Noise Source with AWGN Channel55
Figure 3.3: Phase Noise of -100dB @ an offset of 1MHz............................................. 56
Figure 3.4: Unperturbed Oscillator Output along with perturbed I/Q outputs. ...... 56
Figure 3.5: Block Diagram of QDAcR [19] .................................................................. 57
Figure 3.6: Dual-IF Heterodyne Receiver Topology [39]............................................ 58
Figure 3.7: A Direct-Conversion Receiver.................................................................... 58
Figure 3.8: Showing the various interferers present. .................................................. 61
Figure 3.9: Modeling of Noise ........................................................................................ 63
Figure 3.10: Modeling of Noise Block in MALAB ....................................................... 63
Figure 3.11: QDAcR Block Diagram Representation ................................................. 64
Figure 3.12: The Transient levels of Gaussian Pulse ................................................... 67
Figure 3.13: The PSD levels of Gaussian Pulse ............................................................ 67
Figure 3.14: The PSD levels at σ t =.205e-09................................................................... 68
Figure 3.15: Transient response of the Gaussian for σ t =.205e-09 .............................. 68
Figure 3.16: The PSD levels of Gaussian Mono Pulse ................................................. 69
Figure 3.17: The Transient levels of Gaussian Mono Pulse ........................................ 69
Figure 3.18: The PSD levels of Gaussian Doublet Pulse.............................................. 70
Figure 3.19: The Transient levels of Gaussian Doublet Pulse .................................... 70
Figure 3.20: Block Diagram for the Wavelet Modeling .............................................. 71
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An Oscillator System for UWB QDAcR
Figure 3.21: The Transient levels of Daubechie’s Wavelet. ........................................ 72
Figure 3.22: The PSD levels of Daubechie’s Wavelet. ................................................. 72
Figure 3.23: The PSD levels of a Morlet Wavelet Function........................................ 73
Figure 3.24: The transient levels of a Morlet Wavelet Function. ............................... 73
Figure 3.25: The PSD Levels of a Sinc Wavelet Function........................................... 74
Figure 3.26: The transient Levels of a Sinc Wavelet Function ................................... 75
Figure 3.27: The Block Diagram for the Implementation of the Interferers ............ 76
Figure 3.28 Matlab Noise Model Output showing the main interferers and the
Thermal Noise Floor ....................................................................................................... 77
Figure 3.29: The Phase Distortion vs. Auto Correlation Graph................................. 79
Figure 3.30: The Total Noise PSD levels for UWB (In-Band and Out-Band both) .. 81
Figure 3.31: The Total Noise PSD levels after the Filtration for UWB (In-Band and
Out-Band both) ............................................................................................................... 82
Figure 3.32: The Total Noise PSD levels for UWB (In-Band and Out-Band both) .. 82
Figure 3.33: The Total Noise PSD levels after the Filtration for UWB (In-Band and
Out-Band both) ............................................................................................................... 83
Figure 3.34 The Total Noise PSD levels after the Filtration for UWB (In-Band and
Out-Band both) ............................................................................................................... 84
Figure 3.35: UWB Spectrum after bandpass filter ...................................................... 85
Figure 3.36: Phase Noise requirements Vs. Correlation Coefficient for Gaussian
Pulse ................................................................................................................................. 88
Figure 3.37: The Spectrum Before Downconversion................................................... 89
Figure 3.38: The Downconverted Spectrum................................................................. 89
Figure 3.39: Showing the transient response of the downconverter I/Q signals....... 90
Figure 3.40: Phase Noise requirement Vs. Correlation Coefficient for Gaussian
Mono Pulse ...................................................................................................................... 91
Figure 3.41: The Signal Spectrum for Gaussian Mono Pulse before Downconversion
........................................................................................................................................... 92
Figure 3.42: The Signal Spectrum for Gaussian Mono Pulse after Downconversion
........................................................................................................................................... 92
Figure 3.43: Phase Noise requirement Vs. Correlation Coefficient for Gaussian
Doublet Pulse................................................................................................................... 93
Figure 3.44: Phase Noise requirement Vs. Correlation Coefficient for Morlet
Wavelet............................................................................................................................. 94
Figure 3.45: The Signal Spectrum for Morlet Wavelet Function before
Downconversion .............................................................................................................. 95
Figure 3.46: The Signal Spectrum for Morlet Wavelet Function after
Downconversion .............................................................................................................. 95
Figure 3.47: Phase Noise requirement Vs. Correlation Coefficient for Daubechies’
Wavelet............................................................................................................................. 96
Figure 3.48: Phase Noise requirement Vs. Correlation Coefficient for SINC Pulse 97
Figure 3.49: The Signal Spectrum for SINC function before Downconversion........ 98
Figure 3.50: The Signal Spectrum for SINC function after Downconversion .......... 98
Figure 3.51: The Phase Noise vs. Correlation Coefficient for different pulses ......... 99
Figure 3.52: Modeling of Low Noise Amplifier Block in MALAB........................... 101
Figure 3.53: Correlation vs. Noise Figure of LNA..................................................... 102
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An Oscillator System for UWB QDAcR
Figure 4.1: Oscillator Block Diagram ......................................................................... 107
Figure 4.2: RC Network Transformation................................................................... 110
Figure 4.3: RL Network Transformation ................................................................... 110
Figure 4.4: Single Transistor implementation of an oscillator (a) Direct Feedback,
(b) With Impedance Transformer............................................................................... 111
Figure 4.5: (a) Hartley Oscillator, (b) Colpitts Oscillator and (c) Single Ended
Oscillator using a Source Follower as a positive Active Feedback........................... 112
Figure 4.6: (a) PMOS cross-coupled differential oscillator with current sink and (b)
NMOS cross-coupled differential oscillator with current source............................. 113
Figure 4.7: Negative Transconductance transformation. ......................................... 114
Figure 4.8: (a) Compact lumped-element π -model of an inductor and (b) Single
Port Excitation of equivalent inductor model. ........................................................... 119
Figure 4.9: Test Bench for Inductor Simulation ........................................................ 123
Figure 4.10: Showing the fault in the model predicted inductance value................ 124
Figure 4.11:(a) Q-Factor for the set of Hollow Inductors. ........................................ 126
Figure 4.12: (a) Ratio of Effective Inductance to Parasitic Capacitance................. 128
Figure 4.13: Peak Real (Z11) Vs. Inductance at Oscillation. .................................... 129
Figure 4.14: The Basic Layout of the symindp inductor of value 2.1nH ................. 131
Figure 4.15: Variation of Capacitance for change in Bulk-Gate Voltage................ 134
Figure 4.16: Effective Capacitance Vs. Tuning Voltage Sweep................................ 136
Figure 4.17: Varactor Capacitance Vs. Tuning Voltage for different gate bias
voltages........................................................................................................................... 138
Figure 4.18: Tuning Range offered by the characterized varactor.......................... 139
Figure 4.19: The change in parasitic resistance over the tuning range. .................. 140
Figure 4.20: The LC-tank reactance sweep over frequency. .................................... 141
Figure 4.21: Starting Condition for an Oscillator...................................................... 144
Figure 4.22: (a) Diagram of a PMOS Differential Oscillator, (b) NMOS Differential
Oscillator........................................................................................................................ 149
Figure 4.23: (a) Tuning Range NMOS Diff-Pair Oscillator...................................... 151
Figure 4.24: (a) Phase noise of NMOS Diff-Pair Oscillator @ 1MHz offset ........... 153
Figure 4.25: (a) Peak to Peak Differential Voltage output of NMOS Oscillator..... 155
Figure 4.26: (a) Tuning Range comparison of push-pull oscillator for all the process
corners............................................................................................................................ 157
Figure 4.27: (a) Tuning range comparison of push-pull oscillator for all SS-F & FFF process corners........................................................................................................... 159
Figure 5.1: Two Quadrature Coupled Oscillators. .................................................... 165
Figure 5.2: BS-QVCO (Half Circuit) .......................................................................... 170
Figure 5.3: The Mirror half circuit of P-QVCO ........................................................ 172
Figure 5.4: (a) Phase Noise comparison between P-QVCO and BS-QVCO ........... 174
Figure 5.5: Process Corner Analysis of P-QVCO for tuning range ......................... 176
Figure 5.6: Process Corner Analysis of P-QVCO for phase noise. .......................... 177
Figure 5.7: Process Corner Analysis of P-QVCO for Quadrature Swing ............... 177
Figure 5.8: Implementation of Q-VCO with Poly-Phase Filter............................... 178
Figure 5.9: RC-CR Network (Poly-Phase) [39].......................................................... 179
Figure 5.10: Circuit Design for Poly-Phase Filter Q-VCO. ...................................... 180
Figure 5.11: Phase Noise Vs. Neutralization Cap ...................................................... 182
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An Oscillator System for UWB QDAcR
Figure 5.12: Output Swing Comparison for Oscillator, Buffer and Poly-Phase
outputs............................................................................................................................ 182
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An Oscillator System for UWB QDAcR
1 CHAPTER 1
Introduction: Ultra Wideband Systems & Technology and Thesis Objectives
1.1 Introduction
The advent and development of wireless communication systems and integrated circuit technology have
revolutionized the contemporary life by combining the two main aspects firstly the access to all the
required information at any time and anywhere and secondly the feasibility to perceive information in a
friendlier manner that is portability, flexibility and scalability. There are a many subsystem and standards
of communication within Wireless Communication Systems. A few of them of are as follows:
1. Cellular/Mobile Telephony (Technology: FDM, TDMA, CDMA and Bands: GSM, IS-95, IS 136 and
UMTS etc.)
2. Wireless Local Area Networks (WLANs: 802.11a, 802.11b, 802.11g)
3. Satellite Systems (Ku, K and Ka bands)
4. Bluetooth (ISM Band)
5. Ultra Wideband Radio (3.1GHz. -10.6GHz. ; Impulse radio, MB-OFDM UWB)
The latest being Ultra-Wideband Radio (UWB), is center of attention among the emerging communication
technologies, it is still in developing stage and promises significant advantages over other communication
technologies. The main advantages are transmission of high data rate over short-medium distances (10m100m) with low power consumption and due to spread spectrum characteristics of UWB communication
technology, it is less susceptible to multipath fading and more or less immune to electromagnetic
interference (EMI) [1]. The system design issues for UWB technology have been addressed using two
methods (1) Single Band Radio (Impulse Radio - IR), in which the system operates on the entire bandwidth
as a single-wide band [2,3,4,5] and (2) Multiband OFDM Alliance for UWB (MBOA-UWB). In this the
entire bandwidth is divided in to 14 sub-bands of 528MHz bandwidth each with highest data speed of
480Mb/s. [6] and the system design treats each band as in the case of narrowband communication
technology.
There have been proposed different types of single-band transceiver architectures at system level, which
provide novel solutions and which are mainly based upon the Correlation technique or Energy detection.
The correlation is achieved either by the template mixing and integrating as shown in Figure 1 or by “the
transmitted reference scheme receiver or “autocorrelation receiver” as proposed by [7] as shown in Figure
2. The example of single-band UWB transceiver is shown in Figure 3
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An Oscillator System for UWB QDAcR
Figure 1.1: The block diagram of ir-UWB receiver with time domain correlation using a template [2]
Figure 1.2: Transmitted Reference Auto-Correlator [1]
Figure 1.3: The Block Diagram of ir-UWB Transceiver [2]
However, these proposed architectures are mostly at system level design and have not yet been translated
into a complete circuit level system or into a fully operational IC. There has been reported very little work
regarding parametric extraction, which serves as the basis of translating system level RF-building blocks to
the actual circuit design. Most of these system designs consist of black box models of explicitly designed
subsystems, which are interconnected and presented in the form of fully functional system design, without
taking into account the jitter analysis, mismatching, noise and nonlinear coupling that happens between the
various subsystems at the circuit level. Few circuit level designs have been reported for ir-UWB receiver’s
RF-building blocks, which are mainly partial and inexplicit in nature and do not answer the main questions
regarding the performance of the complete system fabricated into the IC-chip.
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An Oscillator System for UWB QDAcR
At system level an excellent and in depth research has been reported about the basic RF-building blocks
required in ir-UWB receivers; however, there is a scarcity of information about the solutions for possible
bottlenecks that can seriously degrade the receiver’s performance at circuit level. The advantages of low
power consumption and simple processing circuitry posed by ir-UWB receiver are results of ‘AutoCorrelation’ technique, which in turn is totally dependent upon the mixing and matching of pulses; for
these ir-UWB receivers a severe bottleneck is the ‘Timing Jitter’ and its implications on performance of the
receiver. The existence and production of ‘Jitter’ in IC’s circuitry is a natural phenomenon due to presence
of the noise, device fabrication and mismatching in the devices. The ‘jitter’ induced by the circuitry can be
translated into circuit noise and therefore by designing the circuits, which meet the specific requirements, a
possible solution for the severe bottleneck like timing jitter is found and as a result an optimized and
coherent design for a fully functional IC can be derived.
In this work implications of the ‘jitter’ (produced predominantly in the downconverter) on performance of
the ir-UWB based Quadrature Downconversion Autocorrelation Receiver (QDAcR) [8] at system level are
being investigated and the findings lead to a very important result, which defines the constraints and
parameterizes the downconverter in QDAcR, which acts as an integral and important part of UWB signal
processing in analog domain. The importance of the result signifies the circuit design of QDAcR
downconverter for optimal performance. The result outcome also provides an insight into the design
perspective for Wideband Communication technologies like UWB, in which stringent requirements of
narrowband communication technologies are eased and low power, simple and efficient circuit designs can
be used and researched further. Also, the use of different types of (nano-pico seconds duration) pulses as
carrier has been reported, whilst the Gaussian mono or Gaussian double being the most widely used carrier
for information transfer in the UWB system; in this work, the QDAcR system is tested for different kind of
pulses, which fulfills the UWB band in frequency domain, and the outcome is summarized as the choice of
pulse which best suits the optimum performance of the QDAcR.
1.2 Ultra-Wideband Communication Systems
Ultra-wideband communications is a radio frequency technology that uses extremely narrow RF pulses to
communicate between a set of transmitters and receivers. It is distinct from conventional sinusoidal
narrowband wireless technology in which transmission is done on different frequencies, in UWB the signal
is spread over wide range of frequencies. Historically, UWB communication technology was first used by
Guglielmo Marconi in 1901 to transmit Morse code sequences across the Atlantic Ocean using a spark gap
transmitter. The UWB communication technology gained impetus in military applications such as impulse
radar and UWB technology was restricted for just military purposes from 1960s-1990s [9].
The Figure 4 show a UWB pulse in time domain and in frequency domain and a comparison with a
sinusoidal narrowband pulse in time and frequency domain.
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An Oscillator System for UWB QDAcR
Figure 1.4: A Narrowband Sinusoidal in (a) the time domain and (b) the frequency domain.
In UWB the pulse train of extremely short duration (nano second – pico second) is used for communication
as the information carrier in time domain and this generates a very wide spectrum across different
frequencies in frequency domain. “The spectrum of such a pulse sequence (usually Gaussian) has a single
broad main lobe with a low spectral roll-off [10]” and offers advantages like robustness to jamming, coexistence with current radio services. There are many wideband signals that qualify for UWB
communication systems and a few of them are Gaussian, Gaussian Mono (First Derivative of Gaussian),
Gaussian Second Derivative, Morlet, Sinc, chirp or Daubechies wavelet. The Figure 5 below shows a
Gaussian Mono signal a pulse of 500picosecond in time domain and wide spectrum with a single main lobe
at fc = 2GHz. and with a low spectral roll-off in frequency domain.
Figure 1.5: Gaussian Mono pulse in time and frequency domain
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An Oscillator System for UWB QDAcR
1.3 UWB Regulations and Ultra Wideband System’s comparison
with Narrowband Communication system
In UWB communication technology a pulse train is used as information carrier and in comparison to
narrowband technologies, UWB communication technology has very low average transmission power. The
transmission power in UWB technology is in the order of microwatts whereas it is many-folds higher in
magnitude for narrowband communication systems. The reason for extremely low average transmission
power in UWB communication technology is that in UWB the short pulses (nano seconds – pico seconds)
are used and such sort pulses have very low duty cycle. Also a low average transmission power translates
into a longer battery life for UWB communication system devices. According to the FCC regulations
regarding the use of UWB, states that UWB signal must have at least a bandwidth of 500MHz for operation
at frequency 3.1GHz to 10.6GHz ‘OR’ a fractional bandwidth which is at least or larger than the 20% of
the center frequency at all times of transmission. The fractional bandwidth is a measure of bandwidth
between the points which are at -10dB distance from the central frequency [11]. As seen from Figure 4.
The-10dB points are located at f H =1.2 GHz and f H = 2.8GHz with a central frequency f c = 2GHz.
Therefore, for this signal to qualify as UWB signal, the fractional bandwidth Bf > 0.2fc. Calculating the
fractional
Bf =
bandwidth
in
accordance
with
the
FCC
rules,
it
follows
( fH − fL )
2 .8 − 1 .2
× 100 =
× 100 = 80 %
fC
2
; which confirms that the signal is an UWB signal.
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that
An Oscillator System for UWB QDAcR
The classification of the signal on the basis of fractional bandwidth is as follows.
Narrowband
B f < 1%
Wideband
1% < B f < 20%
Ultra Wideband
B f > 20%
The maximum allowed power spectral density (PSD) levels for UWB systems are limited to 41.3dBm/MHz for both indoor as well as outdoor operations; this protects other contemporary wireless
systems having interference from the UWB systems, as these PSD levels for UWB system are equivalent to
the PSD levels of systems like television and computer monitor etc. Figure 6 shows the emission levels
prescribed by the FCC for the UWB communication systems under indoor conditions. The difference
between the indoor and outdoor emission limits for UWB systems is that the spectral mask for outdoor
devices is 10dB lower than that of indoor devices between frequencies 1.6GHz and 3.1GHz. The Figure 6
shows the emission levels prescribed by the FCC for the UWB communication systems under outdoor
conditions
Figure 1.6: The UWB emission mask for the indoor & outdoor communication.
The spread spectrum is also a wideband communication technique, with advantages like low PSD levels,
resistance to jamming, resistance to fading and multiple access capability. All of these advantages are
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An Oscillator System for UWB QDAcR
similar to the merits of UWB systems; however there is a significant difference between both techniques
and this is in the method of achieving the large bandwidth
As mentioned in [10] ir-UWB communication system uses the pulse in-itself as carrier. In narrow band
system sinusoidal is used as carrier in the same way the pico-second Gaussian or other pulses acts as a
carrier for transmitting the data in the ir-UWB systems. “However in a properly designed UWB system the
carrier is indistinguishable from the other spectral components of the UWB signal [10]”. The UWB pulses
provide several GHz of bandwidth while in spread spectrum a few MHz of bandwidth is achieved. Figure 7
shows the distinction between the narrowband, wideband and ultra wideband communication systems. The
UWB technology poses several advantages over the narrowband communication systems. The main
advantages are high data rate, ability to co-exist with narrowband systems and high performance in
multipath channels
Figure 1.7: Distinction between the different communication techniques.
The data rate transfer in any system can be described using the well-known Shannon – Hartley’s Equation,
which is C
= B log 2 (1 + SNR) ; where C = Channel Capacity, B = Bandwidth of the system and SNR =
Signal to Noise Power Ratio. The channel capacity ‘C’ is the data rate or maximum data that can be
transmitted per second over the communication channel and as we see from the Equation that channel
capacity ‘C’ is directly proportional to the Bandwidth of the system and effective signal to noise ratio
‘SNR’. Therefore, the channel capacity can be improved by increasing the bandwidth or effective SNR of
the communication system. In UWB systems the highest allowed PSD allowed by FCC is -41.3dBm/MHz,
which translates to very small value of SNR ( SNRUWB ≈ 0dB ). In comparison to the narrowband
communication systems the UWB system poses a poor SNR value, however it can be seen from the
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An Oscillator System for UWB QDAcR
Shannon’s Equation that ‘C’ is proportional to the Logarithmic of the SNR; therefore UWB system
provides high channel capacity or data rate only by using very wide bandwidth which is usually 7.5GHz. A
comparison of data rate for various IEEE Standards is shown in the Figure 8 below.
Figure 1.8: Comparison of Data throughput and range for IEEE 802 Standards [12]
It can be discerned from the above Figure 1.8 that data rate decreases for the UWB (IEEE 802.15.3a) for
high ranges, this is due to the fact that UWB communications uses pulses or carrier frequency waves (like
Gaussian, Gaussian Mono, Morlet etc.), which have very low Power Spectral Density (PSD) levels and in
some cases the PSD levels are below the noise floor. Therefore, it is hard to detect UWB carriers for higher
ranges and data rate drops significantly. The low PSD levels allow UWB system to co-exist with other
contemporary narrowband communication systems; in Figure 9 it is shown that the UWB PSD levels
resides a few dB above the noise floor if considered for entire 7.5GHz bandwidth, also shown are the PSD
levels of the main Narrowband interferes in this band.
Figure 1.9: Coexistence of UWB signals with narrowband and wideband signals in the RF spectrum
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An Oscillator System for UWB QDAcR
The UWB systems perform with high efficiency in multipath systems; where multipath is generated due to
the signal reflection/refraction with some object. In narrowband communication systems the multipath can
degrade the signal strength due to out of phase addition of LOS (line of sight; non interfering signals) and
NLOS (non-line of sight; interfering signals). The short duration UWB pulses are less susceptible to the
multipath effect, because the time period of UWB pulses is of order of nano or pico seconds. Therefore the
reflected pulses have very low chances of colliding, adding, overlapping and/or superposition with the LOS
pulses and as a result having no or extremely less signal strength degradation. By choosing proper
modulation technique signal strength degradation can be ceased further, the commonly used modulation
techniques for ir-UWB systems are Pulse Position Modulation (PPM), On-Off Keying (OOK), Pulse
Amplitude Modulation (PAM) and Bi-Phase Modulation (BPM). Besides these UWB systems poses many
other significant advantages like low interception and detection by other system i.e. low chances of
eavesdropping because of low PSD signal levels.
1.4 Ultra Wideband Transceiver Architectures and Challenges
The transceiver architecture for the UWB communication technology can be broadly classified into two
categories, based on the transceiver architecture topologies. These primarily differentiate in the way of
treatment of the complete bandwidth offered by the UWB communication technology. These two
methodologies as previously stated are:
1. Multiband OFDM Alliance for UWB (MBOA-UWB): In MBO-UWB system the entire 7.5 GHz
bandwidth is divided in to 14 bands of 528MHz bandwidth each and in total covering the entire frequency
range of 3168 MHz to 10560MHz [13]. The use of OFDM and multiband hopping technique ensures high
data rates and ease from the problem of high speed Analog to Digital Converter and pulse distortion. The
main advantage of MBOA-UWB technique is that it can handle the problem of interference in a far better
manner than ir-UWB technique. As in MBO-UWB system there is not data transmission in 5GHz-6GHz
band, which alienates the main in-band interferer HIPER LAN and its modulated components from
degrading the receiver’s performance. However, as MBOA-UWB employs narrowband communication
architecture this imposes very stringent circuit level design requirements. The main problems encountered
in this architecture are design of band switching circuit which involves band select and high gain LNA and
high phase noise requirements for LO and accurate frequency synthesizer that should synthesize
frequencies for multiband operation with (a low jitter) high phase noise [13,14]. The typical design
parameters of a MBOA-UWB transceiver are given in [13, 15]. A well designed and thorough architecture
of multiple band UWB receiver is given in [16]. The problem of spurs also effect the performance of the
receiver, therefore a high linearity is essential for mixers, which translates into high power consumption,
low conversion gain and small output swing. The multiband OFDM architecture does provide a solution to
complete design and a fully functional IC for UWB system; however, it requires highly complex circuitry,
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An Oscillator System for UWB QDAcR
high power consumption and stringent design requirements. In addition, one of the severities attached to
MBOA-UWB is use of power amplifier (PA) in the transmitter part, which not only increases the power
consumption but adds to the non-linearity and noise issues as well. Besides these disadvantages, the design
of MBOA-UWB system prefers Bipolar technology over CMOS [16] to tackle issues of spurs, phase and
gain mismatch and conversion gain, which can be expensive and not compatible with prevailing CMOS IC
technology for mass production.
2. Impulse Radio UWB system (ir-UWB or Single band Radio): In ir-UWB system, the entire bandwidth is
treated as a single band and processed upon by using the correlation and sampling techniques. The ir-UWB
system is supposed to provide advantages like low power consumption and immunity towards the
electromagnetic interferences. However, these advantages are very much dependent upon the efficiency of
system design for ir-UWB transceiver architecture. The very basic architecture for ir-UWB transceiver
proposed is shown in Figure 3 [2]. In order for this design to work an ADC (analog to digital converter)
should sample and digitize the complete bandwidth of 7.5GHz at the Nyquist rate of minimum
15Gsamples/sec, this high sampling speed will lead to design of an ADC that consumes excessive power
and results in the loss of one of the primary advantages of low power consumption for ir-UWB systems.
The solution to this problem caused by the high sampling rate is presented in [2] in form of the (1) TimeInterleaved Architecture, (2) Frequency-Domain Channelizing and (3) signal processing in analog domain,
the first two topologies do reduce the complexity of ADC design by reducing the sampling speed, but still
suffer from higher power consumption and large die area due to Band Pass Filter. The generalized
architecture of receiver design is presented in Figure 10 [2] in which either time domain correlation or
down-conversion is done, this decimates the sampling frequency and provides with a viable solution for irUWB receiver architecture.
Figure 1.10: Time domain Correlator Receiver architecture [2]
However, ir-UWB correlation receivers do suffer from severe bottleneck of jitter and template
mismatching, other important issue regarding the performance of the ir-UWB receivers is narrowband
interference that can potentially jam the ir-UWB system due to the presence of high power narrowband
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An Oscillator System for UWB QDAcR
interferes, which are presented by the existing narrowband communication standards of
WLAN or
Hiperlan and IEEE802.11a.
Another challenge is channel estimation, as we know that in ir-UWB correlation receivers the received
signal is correlated with the predefined template. Therefore for proper matching with the received signal
knowledge of channel parameters is of foremost importance while deciding about the template. As it is
mentioned previously that UWB pulses are prone to shape distortion, therefore channel estimation becomes
more complex and more important for the UWB communication systems.
To counter the problem of template mismatching and time synchronization a novel solution for ir-UWB
receiver system is presented in the form of QDAcR [8], which is based upon the delay hopped transmitted
reference scheme (DHTR) proposed by [7], in DHTR the correlation takes place between the two pulses
per symbol, which are transmitted with a delay of ‘ τ d ’ as shown in Figure 2, the first pulse, which acts as
reference pulse is delayed by the same time delay of ‘ τ d ’ and multiplied with the second pulse, which acts
as a modulated one and the correlation is achieved by integrating the mixed pulse over one delay length [8].
This technique of autocorrelation is very much advantageous as it does reduce the system design
complexity arising from pulse distortion and mismatching with template. However, it also suffers from
timing synchronization that is, mismatch in the delay time between the transmitter and receiver parts; the
reliability and efficiency of QDAcR is closely dependent upon the design of the delay [8]. The major factor
that easies the complexity of the design constraints is by processing the bandwidth in analog domain [2],
likewise downconversion reduces the circuit design complexities and maintains the ir-UWB system
inherited advantages. The use of analog signal processing and DHTR or autocorrelation technique in
system design proposes the most feasible and optimized design for a complete ir-UWB receiver;
Quadrature Downconversion Autocorrelation Receiver (QDAcR) is such an example. In QDAcR the
bandwidth is downconverted and processed as to reduce the circuit complexity and save power by reducing
the sampling speed of ADC, also the selection of Local Oscillator frequency makes it possible to clear the
bandwidth of existing interferes [8]. However, to realize QDAcR into a fully functional IC, in depth system
analysis of QDAcR should be performed and the first step is to find the parameters of the conventional RF
building blocks, while taking into account the system and design constraints produced by the RF building
blocks and the composite implication of all of these factors on the performance of the QDAcR.
In this chapter the theory of ultra wideband systems and the main system level design issues were dealt in a
concise but comprehensive manner. The main focus of this chapter was to provide an insight into the
developments in the field of UWB system design and gathering the background knowledge of the
advantages as well as the bottlenecks and design issues, with comparison based on the literature research
between the two prominent styles of system architectures that are ir-UWB and MBOA-UWB. Also, a
comparison between the ultra wideband and narrowband communication system is presented, which
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An Oscillator System for UWB QDAcR
highlights the different advantages inherited by UWB system over the Narrowband communication system
due to its definition. In brief in this chapter an overview of existing UWB system designs, their advantages
and serious flaws were discussed, which lay down path to objective of this thesis.
1.5 Thesis Objectives
The thesis titled “An Oscillator system for a Quadrature Downconversion Auto-Correlation Ultra
Wideband (UWB) Receiver ,” is produced to reflect the work done as Master’s Degree Project. The thesis
work can be predominantly divided in to two sub fields. Firstly, the system level study, design and
extraction of the required specifications and parameters for the circuit level design. Second field was to
translate these specifications into circuits.
Primary focus of the work was concentrated towards the system level design and parametric extraction;
which starts with a study of previously done ‘Quadrature Auto-correlation Downconversion Receiver [8] at
the system level design using matlab; however, the previous system design was proposed at the generic
level that is laying down the concept of QDAcR and implementing it in matlab as system design without
taking into consideration the problem of jitter, interferer and specs for the RF building blocks. The next and
the most important step was to design the complete system in order to find the desired phase noise that can
be induced by the local oscillator while meeting the correlation requirements. As an enhancement of this
result was to test the design for various impulse inputs and find for which pulse, the design can have
highest degree of correlation with the least amount of phase noise
The next step was to work on circuit design for the Quadrature Oscillator Q-VCO; in this first step was to
decide upon the oscillator topology while meeting the specifications and utilizing the importance of the
outcome from the system level design. This was followed by the investigation of different Q-VCO
topologies, in order to find a suitable oscillator design topology, which not just meet the specifications but
should provide a robust circuit design. First step involved, the choice of oscillator topology followed by the
optimization for a low power design. The designed LO is then used as an essential element in designing of
Q-VCO, the complete design involves the design of output buffer, able to drive the variable load.
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An Oscillator System for UWB QDAcR
2 CHAPTER 2
Methods and Techniques for System Level Design of QDAcR Downconverter
In this chapter the quantitative methods and techniques used for modeling and assessing the implications of
the ‘jitter’, induced by the local oscillator in the downconverter are presented in detail. First up a brief
overview of the previously done work on QDAcR is presented, this is followed by the most important part
of devising a complete mathematical analysis of basic QDAcR. This analysis helps us in understanding the
implication of phase noise on QDAcR performance. The exercise of quantitative analysis provides in end
with a relationship between phase noise and timing jitter. This relationship serves as the very basis of
advanced system level modeling of QDAcR
2.1 System Level Design
The importance of the downconverter in QDAcR has been highlighted in earlier chapter; the severe
bottlenecks that are present in QDAcR are firstly, the design of downconverter that gives optimal
autocorrelation and secondly, design of time delay circuit; the solution of the latter is published in [8, 17 &
18]. In this section the complete system modeling of the QDAcR is presented. Starting with a brief
explanation of the existing model succeeding it with an in-depth Time domain modeling of the QDAcR,
this analysis in certain conditions can also be extrapolated to general receiver theory. In time domain
modeling for the first time the stochastic nature of the signal and their overall effect is considered, this
leads to the relationship which signifies the role of phase noise (presented as phase perturbation) in the
QDAcR to be specific and can be generalized onto other receivers. The following section presents in brief
about the noises present in the system and the constituents of the phase noise, further in this section the
reasoning of using 1 f 2 region as the prime region for noticing the phase noise in context with the QDAcR
specific design is presented.
In the next section the Time-Jitter analysis of an oscillator and the relationship between the jitter and phase
noise is re-visited, this relationship already exists, but in this section the relationship is derived by
characterizing phase perturbation and timing jitter as two similarly distributed variables, which are
correlated and this effect leads to the description of “accumulating jitter” and/or “cyclostationary” property
of the phase noise. This relationship is used to model the oscillator in MATLAB.
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An Oscillator System for UWB QDAcR
2.2 Quadrature Downconversion Autocorrelation Receiver
In this section, a brief overview of the QDAcR is presented; the Quadrature Downconversion
Autocorrelation Receiver or QDAcR [8] is based on the Delay Hopped Transmitted Reference scheme as
proposed in [7]. By use of ‘autocorrelation’ architecture, the problem of template mismatching is
circumvented. Other major problem of high speed signal processing is curtailed by using the
downconverter, which down converts or wraps the entire frequency band of 7.5GHz to a smaller band
around dc, which can be processed by the ADC (analog to digital converter). Furthermore, this frequency
wrapping or downconversion gives the advantage to clear off strong narrowband interferes like WLAN,
HiperLAN and 802.11a/n by choosing the appropriate Local Oscillator frequency and followed by filtering
the band, these interferes can potentially jam the QDAcR. The block diagram of the QDAcR is given in the
Figure 2.1.
Figure 2.1: Quadrature Downconversion Auto-Correlation Receiver Architecture [l9]
As shown in the Figure 2.1 above, the system design of QDAcR consists of four main stages, 1. Antenna
and LNA (Gain Stage) 2. Downconversion (Frequency Wrapping) Stage, which consists of an Ideal
Oscillator with Quadrature outputs and Ideal Multiplier 3. The Filtering Stage that has Band pass filters
employed to clear off interferes and 4. The Autocorrelation Stage, which consist of time delay, Ideal
Multiplier and an Integrator. In [8] the system analysis of QDAcR under the ideal conditions is presented,
in which the 3.1GHz to 10.6GHz UWB band is downconverted. The oscillation frequency of the ideal
Local Oscillator (LO) is chosen to be 5.5GHz, so that the potentially jamming interferes present around
5.15GHz and 2.4GHz, are downconverted to (5.5-5.1) GHz = .350GHz = 350MHz and 2.4GHz interfere is
converted to (5.5-2.4) GHz = 3.1GHz. The 36% of UWB bandwidth is also lost in frequency wrapping. The
Figure 2.2 shows the principle of band downconversion and also shows downconverted frequency band.
-24-
An Oscillator System for UWB QDAcR
Figure 2.2: UWB Frequency Spectrum before (top) and after (below) Downconversion [20]
The band-pass filters are used for the rejection of the interference is presented in [21]; after
downconversion, the interferes appear at below 350MHz and above 2.4GHz, for the steepest slope an eight
order elliptic band-pass filter with corner frequencies at 350MHz and 2.6GHz, is designed as an
interference rejection filter [21].
In [8] the time domain analysis of the QDAcR is given, which explains the autocorrelation principle of
QDAcR. In which the downconverted Quadrature components are delayed and multiplied intrinsically and
then added. The time domain analysis also signifies the implications of the time delay on the performance
of the receiver and the stringent design condition it poses, besides this the final mathematical relation,
which signifies the importance of the time delay is given by the Equation Y = −
A2 (t ')
cos(ωoscτ d ) (2.1)
4
where ‘Y’ is the output of the mixed signals before integration and this equation shows the dependency of
the autocorrelation coefficient on the time delay or the performance of the receiver is directly related to the
oscillators angular frequency ‘ ωosc ’ and the time delay ‘ τ d ’. Further, the results of the error analysis in
time domain on QDAcR confirms this, in which the analysis for ‘ α ’ (the amplitude mismatch), ‘ β ’ (the
mismatch between the delay time ‘ τ d ’ in transmitter and receiver), and ‘ φe ’ (the phase error between the
Quadrature outputs of the oscillator) is presented [8]. The results of the error analysis are summarized in [8]
and analyzes sow that how important is ‘ β ’ that is the error in the delay time ‘ τ d ’ is for the proper
performance of QDAcR. It also shows that for a mismatch of 20 - 30 picoseconds the autocorrelation is
dropped from 85% to around 65%; therefore, designing of the perfect delay is very important for the
performance of the QDAcR.
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An Oscillator System for UWB QDAcR
2.3 Time Domain Analysis of QDAcR
The time domain analysis and system level simulation done in [8] does not take into account the jitter and
noise analysis and other non-idealities that are present in a real downconverter and other circuits.
Therefore, an up gradation in present system design is required so that the system analysis result can
provide with the accurate and real parameters for circuit level designing of QDAcR. First step in this
direction is to establish mathematically the dependence of the autocorrelation factor on the random
aberrances (such as jitter or phase noise, phase error etc.) contributed by RF building blocks used in the
downconverter. The mathematical model is necessary because the results of quantitative modeling will
make the base for the matlab modeling and also provide the interdependency between various parameters.
The output (voltage signal) of an ideal local oscillator can be defined by the Equation 2.2 as given below,
where ‘ Aout (t ) = Vout (t ) ’ is LO output at time ‘ t ’, where ‘ Alo = V0 ’ is the maximum signal (voltage ‘ V0 ’)
swing amplitude of LO, the angular oscillation frequency is ‘ ωo ’ and a constant phase reference of‘ φ0 (t ) ’.
Aout (t ) = Alo cos(ωo t + φ0 (t ))
(2.2)
However in a practical oscillator there exist non-idealities due to the fluctuations in phase and the
amplitude owing to power supply, non-ideal active devices, passives etc. The Equation for the output now
can be defined as shown in Equation 2.3, where phase is expressed as the function of time ‘ t ’ and denoted
by ‘ φ (t ) = φ0 (t ) +△φ (t ) ’ and the perturbation in phase as ‘ △φ (t ) ’ and the perturbation in the LO
amplitude is denoted by ‘ α (t ) ’. The perturbations present in the phase and the amplitude of the LO are
random in nature [22]. The in-phase (I) output of LO is given in Equation below as:
Aout (t ) = Alo (1 + α (t )).cos(ωo t + φ (t ))
(2.3)
Taking the signal carrier as defined in [8] for the pulse-based signals having a finite band-pass spectrum,
therefore characterizing the pulse signal with a Gaussian envelope, with ‘ ωc ’ being the angular center
frequency and ϕ (t ) as the phase; the real signal carrier is given by the Equation 2.4.
g (t ) = A(t ) cos(ωc t + ϕ (t ))
(2.4)
In QDAcR, the carrier signal is mixed with the outputs of a Quadrature Local Oscillator, which are
described as in-phase component (I) and quadrature (Q) component, therefore if an in-phase (I) component
of an oscillator is given by Equation 2.3 then the Quadrature (Q) is given by Equation 2.5 as shown below;
where ‘ φe ’ is the phase error between the Quadrature outputs of the oscillator.
Aout (t ) = Alo (1 + α (t )).sin(ωo t + φ (t ) ± φe )
(2.5)
Now considering two identical and consecutive pulses of equal sign, which are transmitted at an interval of
‘ τ d ’. Initially, the first pulse signal is transmitted, which is downconverted and filtered in the receiver.
After downconverting the first pulse-based signal in the time domain and filtering the outputs, for in-phase
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An Oscillator System for UWB QDAcR
path the downconverted output is given by
M 1 (t ) as shown by Equation 2.6. As mentioned in [22] the
random perturbations in phase and amplitude of LO are stochastic and instantaneous; therefore, for a
particular oscillation cycle that multiplies with the first pulse signal at any instance ‘t’ , the actual
instantaneous phase ‘
φ (t ) ’ (sum of constant phase and excess phase) for the particular mixing oscillator
cycle is given by φ1 (t ) = φ0 +△φ1 (t ) and amplitude perturbation by α1 (t ) .
M I (t ) = A(t ). Alo (1 + α1 (t )).cos(ωc t + ϕ (t )).cos(ωo t + φ1 (t ))
(2.6)
1
Further simplifying the Equation 2.6 using the identity cos( a ).cos(b) = [cos(a + b) + cos(a − b)] , therefore,
2
the mixed and filtered component given by Equation 2.7;
1
[ A(t ). Alo (1 + α1 (t ))].cos((ωc − ωo )t + ϕ (t ) − φ1 (t ))
2
(2.7)
Delaying the first pulse by time ‘ τ d ’, the Equation 2.7 is now given as Equation 2.8; where
t ' = t −τ d ;
there are no changes in the expected values of amplitude perturbation and excess phase as their values were
decided at the instance of oscillator cycle generation, by the non-idealities present in the form of active
device noise and other affecting parameters. There is always noise associated with any active circuit
component; therefore, an ideal delay element in the QDAcR does not affect the value of phase and
amplitude perturbations. Therefore the Equation for a delayed and filtered signal can be written as equation
2.8
1
[ A(t '). Alo (1 + α1 (t ))].cos((ωc − ωo )t '+ ϕ (t ) − φ1 (t ))
2
(2.8)
Now considering the second pulse, which was delayed in the transmitter by time ‘ τ d ’; mixing this pulse
with the oscillator cycle at time any instance of time ‘t’; the mixed output is given by the Equation 2.9
M I (t ') = A(t '). Alo (1 + α 2 (t )).cos(ωc t '+ ϕ (t )).cos(ωo t + φ2 (t ))
Where
(2.9)
t ' = t − τ d and for the second pulse signal the values of ‘ φ2 (t ) ’ and ‘ α 2 (t ) ’ are defined for a
particular oscillator cycle at an instance of time ‘t’ when mixing of RF-UWB Impulse signal is done with
oscillator signal. The perturbations as defined earlier are produced by the non-idealities present in the real
downconverter. Simplifying the Equation 2.9 and neglecting the summing components of ‘ ωc & ωo ’, which
are filtered and as the response through the band-pass filter, we have the final outcome, which is given by
the Equation 2.10
1
[ A(t '). Alo (1 + α 2 (t ))].cos((ωc − ωo )t '− ωoτ d + ϕ (t ) − φ2 (t ))
2
(2.10)
Now multiplying the Equations 2.8 and 2.10, we have the multiplied in-phase output required for the
autocorrelation; the multiplication of two mixed and delayed pulses is given in Equation 2.11 below.
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An Oscillator System for UWB QDAcR
A(t ') 2 . Alo (1 + α1 (t )). Alo (1 + α 2 (t ))
{[cos((ωc − ωo )t '− ωoτ d + ϕ (t ) − φ2 (t ))].[cos((ωc − ωo )t '+ ϕ (t ) − φ1 (t ))]}
4
(2.11)
1
Simplifying the Equation 2.11 by using the identity cos( a ).cos(b) = [cos(a + b) + cos(a − b)] , we have
2
output as given in Equation 2.12
A(t ')2 . Alo (1 + α1 (t )).Alo (1+ α2 (t ))
{cos(2(ωc − ωo )t '− ωoτ d + 2ϕ(t) − φ2 (t) − φ1 (t)) + cos(φ1 (t ) − φ2 (t ) − ωoτ d )}
8
(2.12)
The above shown Equation 2.12 gives the total mixed (LO x RF-UWB Impulse Signal), filtered and
delayed (delayed and multiply) IN-Phase component of QDAcR.
In order to see the dependence of QDAcR on the non-idealities presented by the downconverter, a complete
time domain analysis is necessary. The time domain analysis of the Quadrature path is done similarly in the
same fashion as of the In-Phase path.
The quadrature mixed component‘ M Q ’ is given by Equation 2.14; which shows the mixing of RF-UWB
Impulse signal with an LO signal. The RF-UWB signal is given by Equation 2.13
g (t ) = A(t ) cos(ωc t + ϕ (t ))
(2.13)
The quadrature mixed component is given below by Equation 2.14, where ‘ φ3 (t ) ’ and ‘ α 3 (t ) ’ are the
expected values of the total phase and amplitude change for a particular quadrature oscillator cycle, which
is multiplied to the first signal pulse in order to downconvert.
M Q = A(t ) Alo (1 + α 3 (t )).cos(ωc t + ϕ (t )).sin(ωo t + φ3 (t ) ± φe )
(2.14)
1
The Equation 2.14 is further simplified using the identity cos(a).sin(b) = [sin(a + b) − sin( a − b)] . The
2
simplified mixed and filtered quadrature component is given by Equation 2.15 as shown below.
1
− [ A(t ). Alo (1 + α 3 (t ))].sin((ωc − ωo )t + ϕ (t ) − φ3 (t ) ± φe )
2
(2.15)
Now delaying this quadrature filtered and mixed component by time ‘ τ d ’ and substitute t ' = t − τ d in
Equation 2.15, the Equation 2.16 is obtained.
1
− [ A(t '). Alo (1 + α 3 (t ))].sin((ωc − ωo )t '+ ϕ (t ) − φ3 (t ) ± φe )
2
(2.16)
The time domain analysis for the second pulse which is being sent by a delay of time ‘ τ d ’ from the
transmitter, mixed with quadrature LO signal at any instance of time ‘t’, filtered and simplified is given by
the Equation 2.17 as shown below. Where‘ φ4 (t ) ’ and ‘ α 4 (t ) ’ are the expected values of the total phase
and amplitude change for a particular quadrature oscillator cycle, which is mixed with the second signal
pulse.
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An Oscillator System for UWB QDAcR
1
− [ A(t '). Alo (1 + α 4 (t ))].sin((ωc − ωo )t '− ωoτ d + ϕ (t ) − φ4 (t ) ± φe )
2
(2.17)
The two mixed and filtered pulse responses in Equations 2.16 and 2.17 are multiplied as for the process of
the autocorrelation; therefore the final Quadrature path response is obtained by simplifying using the
identity sin( a ).sin(b) =
1
[cos(a − b) − cos(a + b)] and the simplified answer iis given by the
2
Equation 2.18.
A(t ')2.Alo (1+α3 (t)).Alo (1+α4 (t))
{sin((ωc −ωo )t '−ωτd +ϕ(t) −φ4 (t) ±φe ).sin((ωc −ωo )t '+ϕ(t) −φ3(t) ±φe )}
o
4
⇕
A(t ')2.Alo (1+α3 (t)).Alo (1+α4 (t))
{cos(φ3 (t) −φ4 (t) −ωτd ∓ 2φemax ) − cos(2(ωc −ωo )t '−ωτd + 2ϕ(t) −φ4 (t) −φ3 (t) ± 2φemax )}
o
o
8
(2.18)
Now for the complete output of the QDAcR the in-phase and quadrature phase responses are added up.
Therefore the final auto-correlated output of the QDAcR is given by adding the Equations 2.12 and 2.18,
which is given by the Equation 2.19.
A(t ') .A (1+α1 (t)).Alo (1+α2 (t))
lo
2
8
{cos(2(ωc −ωo )t '−ωτd +2 (t) −φ2 (t) −φ1 (t)) + cos(φ1 (t) −φ2 (t) −ωτd )}
ϕ
o
o
+
A(t ') .A (1+α3 (t)).A (1+α4 (t))
lo
lo
2
8
{cos(φ3 (t) −φ4 (t) −ωτd ∓ 2φe ) −cos(2(ωc −ωo )t '−ωτd +2ϕ(t) −φ4 (t) −φ3 (t) ± 2φe )}
o
o
max
max
(2.19)
The above Equation holds quite a significance as it shows on which variables and in what manner the
autocorrelation in the QDAcR is dependent upon, the perfect or near perfect level of autocorrelation is vital
for QDAcR in order to perform with distinctive advantages posed by ir-UWB system over MBOA-UWB
system as explained previously in Chapter 1. Also, by the analysis of the Equation 2.19, a first insight into
the circuit design of downconverter is provided.
In Equation 2.19, the autocorrelation is dependent upon the time delay ‘ τ d ’ as is shown in [8, 23].
However, the delay is considered to be an ideal one, but in real circuit this is not a fact. Therefore the
perturbation in the Equation 2.19 can be modeled appropriately as a composite perturbation and the effects
of the perturbations in amplitude and phase of the carrier (Pulse) due to the delay can be taken into account.
In the time domain analysis presented in this work, the effect of perturbations in an Oscillator and the effect
of phase error (which is also treated as a stochastic variable) between the in-phase and quadrature outputs
is primarily investigated. The Equation 2.19 also signifies the importance of the oscillator design for proper
-29-
An Oscillator System for UWB QDAcR
autocorrelation in order to reduce the BER (Bit to Error Ratio); which is a crucial parameter while
assessing the ir-UWB receiver’s or any receiver’s performance.
The Equation 2.19 can be further simplified using a few approximations, these are as follows.
The perturbations due to uncorrelated noise, which follow the stationary stochastic process that is the
random variables ( xn1 ,....., xnk ) and ( xn1+ n ,....., xnk + n ) for every k ≥ 1 in some sample space have same
joint distribution; therefore all the uncorrelated noise perturbations characterized by stationary stochastic
process have same distribution and mean is time independent; this approximation is in accordance with [24]
in which the random perturbations in an oscillator due to uncorrelated noise that is white noise (stationary)
and modulated white noise(cyclostationary) can be characterized by the Gaussian distribution in time. This
follows that in Equation 2.19, the phase noise stochastic perturbations φ1 (t ) & φ2 (t ) are uncorrelated and
have same Gaussian distribution and the same applies on the phase noise perturbations given
by φ3 (t ) & φ4 (t ) . This can be mathematically proved; we know that the (auto) correlation between two
random variables ‘X’ and ‘Y or X*(in case of autocorrelation, for the autocorrelation random variables are
associated
with
C X , X * (t1 , t2 )or ρ X ,Y =
a
repetitive
process
E[( X − µ X ).(Y − µY )]
σ XσY
e.g.
An
Oscillator)
and
is
given
by
where ρ X ,Y is the coefficient of correlation and C X , X * (t1 , t2 ) is the
coefficient of autocorrelation, σ X & σ Y are the standard deviations and µ X & µY are the means and the
operator ‘E’ defines the expected value of a random variable. Let consider a oscillation cycle which is
given by Equation 2.2, considering the LO output at instances ‘ t1 & t2 ’ which are given by the following
Equations Alo (t1 ) = A0 (ω0 t1 + φ (t1 )) & Alo (t2 ) = A0 (ω0 t2 + φ (t2 )) ,
where
φ (t1 ) = φ1 (t ) = φ0 + ∆φ (t1 )
and
φ (t2 ) = φ2 (t ) = φ0 + ∆φ (t 2 ) , since the phase perturbations have joint Gaussian distribution, therefore the sum
and differences of instantaneous phases are also Gaussian and can be described as shown in Equation 2.20.
φ (t2 ) − φ (t1 ) = ∆φ (t2 ) − ∆φ (t1 ) = ∆φt
(2.20)
&
φ (t2 ) + φ (t1 ) = 2φ0 + ∆φ (t2 ) + ∆φ (t1 ) = 2φ (t1 ) + ∆φt
Since the Probability density function (PDF) is Gaussian, the process can be described as the ‘Wiener
Process’ as shown in [25], which defines mean to be ‘zero’, therefore the autocorrelation is given by
Equation 2.21
C (t1 , t2 ) = E[ Alo (t1 ). Alo (t2 )] = A02 .E[cos(ω0 t1 + φ (t1 )).cos(ω0 t2 + φ (t2 ))]
(2.21)
1
Solving the Equation 2.21 using the identity cos( a ).cos(b) = [cos(a + b) + cos(a − b)] , the simplified
2
Equation is given as 2.22
C (t1 , t 2 ) =
2
A0
{ E[cos(ω0 (t2 − t1 ) + ∆φ (t ))] + E[cos(ω0 (t2 + t1 ) + 2φ (t1 ) + ∆φ (t ))]}
2
-30-
(2.22)
An Oscillator System for UWB QDAcR
Now solving the Equation 2.22 for the expected value operator ‘E’; breaking the Equation 2.22 into two
∞
parts for simplified solution. The expected values is defined by E = ∫ X . f ( X ).dX
−∞
(2.23)
Where ‘ f ( X ) ’ is the PDF and for the Gaussian process it is given by Equation 2.24 as
PDF= f (∆φ (t )) =
∆φ 2 (t )
exp −
2σ 2
σ ∆φ (t ) . 2π
∆φ
1
(2.24)
E[cos(ω0 (t2 − t1 ) + ∆φ (t ))] = E[cos(ω0 (t2 − t1 )) cos ∆φ (t ) − sin((ω0 (t2 − t1 )) sin ∆φ (t )]
(2.25)
Solving for the expected value ‘E [ ]’ in Equation 2.25, by using the Equations 2.23 and 2.24. The solution
is shown in the subsequent steps.
E[cos(ω0 (t2 − t1 )) cos ∆φ (t )] = cos(ω0 (t2 − t1 )).E[cos ∆φ (t )]
E[cos ∆φ (t )] =
∞
∫ cos ∆φ (t ).
−∞
(2.26)
σ 2 ∆φ ( t )
∆φ 2 (t )
exp −
.d (∆φ (t )) = exp −
2σ 2
2
σ ∆φ (t ) . 2π
∆φ
1
σ 2 ∆φ ( t )
Therefore simplified form of Equation 2.26 is given by exp −
2
(2.27)
.cos(ω0 (t2 − t1 )) (2.28)
Solving for the other half of Equation 2.25, first simplifying as shown in 2.29
− E[sin((ω0 (t2 − t1 ))sin ∆φ (t )] = − sin((ω0 (t2 − t1 )).E[sin ∆φ (t )]
E[sin ∆φ (t )]] =
∞
∫ sin ∆φ (t ). σ
−∞
∆φ 2 (t )
exp − 2
2σ
∆φ ( t )
∆φ ( t ) . 2π
1
.d (∆φ (t )) → 0
(2.29)
(2.30)
The simplified form of Equation 2.25 is given by Equation 2.31
σ 2 ∆φ ( t )
E[cos(ω0 (t2 − t1 ) + ∆φ (t ))] = exp −
2
.cos(ω0 (t2 − t1 ))
(2.31)
Now simplifying the other half of the main autocorrelation Equation, which is Equation 2.22; first finding
the expected values of E[cos(ω0 (t2 + t1 ) + 2φ (t1 ) + ∆φ (t ))] . The simplification is shown in the subsequent
steps.
E[cos(ω0 (t2 + t1 ) + 2φ (t1 ) + ∆φ (t ))] = E[cos(ω0 (t2 + t1 )).cos(2φ (t1 ) + ∆φ (t )) − sin(ω0 (t2 + t1 )).sin(2φ (t1 ) + ∆φ (t ))]
⇓
cos(ω0 (t2 + t1 )).E[cos(2φ (t1 ) + ∆φ (t ))] − sin(ω0 (t2 + t1 )).E[sin(2φ (t1 ) + ∆φ (t ))]
⇓
cos(ω0 (t2 + t1 )).{E[cos(2φ (t1 )).cos(∆φ (t )) − sin(2φ (t1 )).sin(∆φ (t ))]}
−
sin(ω0 (t2 + t1 )).{E[sin(2φ (t1 )).cos ∆φ (t )) + cos(2φ (t1 )).sin(∆φ (t ))]}
(2.32)
Now further simplifying Equation 2.32 by using the results of Equations 2.27 and 2.30, the solution of 2.32
is given in the following steps.
-31-
An Oscillator System for UWB QDAcR
σ 2 ∆φ ( t )
exp −
2
{cos(ω0 (t2 + t1 )).E[cos(2φ (t1 ))]. − sin(ω0 (t2 + t1 )) E[sin(2φ (t1 ))]}
(2.33)
Now solving the Equation 2.33 for the expected value operator ‘E’; breaking the Equation 2.33 into two
parts for simplified solution.
‘ φ (t1 ) ’Is defined as net phase of the oscillation cycle at instance‘ t1 ’ and t1 ∈ [t0,t2 ); t0 → −∞ ,
therefore φ (t1 ) can be expressed as the phase change in the time period ‘ t2 − t0 ’ or the value of φ (t1 ) can be
approximated as φ (t1 ) = ∆φ (t2 ) − ∆φ (t0 ) = ∆φ (t ); t → −∞ OR E[cos(2φ (t1 ))] = E[cos(2∆φ (t )]
E[cos(2∆φ (t )] =
∞
∫ cos(2∆φ (t )). σ
−∞
4∆φ 2 (t ))
exp −
.d (∆φ (t ))
2σ 2
∆φ ( t )
∆φ ( t ) . 2π
1
(2.34)
Solving Equation 2.34 the same way as Equation 2.27, the solution is
E[cos(2∆φ (t )] =
∞
∫ cos(2∆φ (t )). σ
−∞
4∆φ 2 (t ))
1
2
exp −
.d (∆φ (t )) = exp(−2σ ∆φ ( t ) ) (2.35)
2σ 2
2
∆φ ( t )
∆φ ( t ) . 2π
1
2
In the final solution of Equation 2.35, the variance σ ∆φ (t ) → ∞ when lower limit of ‘ t → −∞ ’. As explained
in the reasoning of formulation of Equation 2.34 that the value of ‘ t ’is upper bound with max(t ) → t2 ,
2
which defines the range of phase perturbation‘ ∆φ (t ) ’. The variance‘ σ ∆φ (t ) ’of the perturbation is directly
1
2
2
proportionate to the time or σ ∆φ (t ) ∝ t ; t → −∞ therefore the final solution exp(−2σ ∆φ (t ) ) → 0 .
2
Similarly E[sin(2φ (t1 ))] can be approximated with E[sin(2∆φ (t )] and as solved in Equation 2.30 the
solution is given by E[sin(2φ (t1 ))] = E[sin(2∆φ (t )] = 0
(2.36)
The Equation 2.33 in the simplified form can be written as shown in 2.37
σ 2 ∆φ (t )
lim exp −
2
σ ∆φ ( t ) →∞
2
1
2
{cos(ω0 (t2 + t1 )). exp(−2σ ∆φ (t ) )} = 0
2
(2.37)
The final solution of Equation 2.21 in a simplified is shown in Equation 2.38 below.
C (t1 , t 2 ) =
2
σ 2 ∆φ (t )
A0
(exp −
2
2
σ 2 ∆φ ( t )
A2
.cos(ω0 (t2 − t1 )) = 0 .cos(ω0 (t2 − t1 )).exp −
2
2
(2.38)
The above Equation 2.38 is of prime importance, if we consider the process of autocorrelation and
correlation. Firstly, for the case if we consider the correlation then Alo (t1 ) & Alo (t2 ) has to be considered
distinctive, that is two different oscillation cycles initiated at time instances t1 & t2 , therefore the correlation
can only exist in time period t ; ∀t ∈ (t2 , ∞] , however if the results of Equation 2.32 and 2.38 are analyzed it
shows that correlation factor ρ X ,Y (t ) → 0; ∀t ∈ (t2 , ∞] , this result also coincides with the result in [24],
which says that phase noise perturbations have a Gaussian PDF and are uncorrelated. Second case, if we
consider just autocorrelation then Alo (t1 ) & Alo (t2 ) are considered the response of a single oscillation cycle
-32-
An Oscillator System for UWB QDAcR
at two different instances t1 & t2 then there exists a definite autocorrelation given by the solution of Equation
2.38. Therefore the approximation made earlier that φ1 (t ) & φ2 (t ) (and φ3 (t ) & φ4 (t ) ) are uncorrelated is
proved mathematically correct. The same result as in Equation 2.38 can be inferred from [25] and section
VIII (Equation 33) of [24]; which signifies that there does not exist any correlation between the two
distinctive oscillation cycles, that is the oscillation cycles originated at different time instants do not have
any correlation as the phase noise process is characterized as Markovian process or mathematically
R( i ,k ) (t ,τ ) = 0; if i ≠ k . However, there exist a definite autocorrelation as proved by Equation 2.38 and the
similar results presented in correlation analysis in Equation 34 in [24], which mathematically gives the
autocorrelation
as R( i , k ) (t , τ ) =
of
∞
∑X
i = −∞
i
an
oscillation
cycle
at
two
distinctive
time
instances
1
X i* exp( − jiωoτ ).exp( − ωo2 i 2 .c. τ ) ; for every i = k . Also, the other main result
2
conclusion from the above analysis is that excessive phase keeps on adding in the form of the correlation,
which is present in the Oscillatory cycle.
Further deductions form the above obtained results are as follows. The perturbations present in the
oscillator’s phase are of random nature and the value of perturbation associated with a particular oscillation
cycle at any two given instances, that is for time ' t ' and‘ t + τ d ’ are different. If the in-phase (I) and
quadrature components (Q) are derived from a single source and or correlated sources (in the case back
gate connected / Injection locked Q-VCO), then there will be a definitive correlation between the phase and
amplitude perturbations of in-phase and quadrature LO outputs for a given oscillation cycle at any time
instance ‘t’, but no correlation between the in-phase and quadrature components generated at two
distinctive time instances for e.g. I and Q responses at time ' t ' and‘ t + τ d ’.
The in-phase and quadrature outputs are correlated if and only if generated at the same instance of time ‘t’
and therefore, we can apply the equality of random variable theorem, which states that if the two random
variables are equal if and only if the probability of their being different approaches zero, that is
P( xn1 ≠ xn 2 ) = 0 ⇒ 0 < corr ( xn1 , xn 2 ) ≤ 1 ⇔ xn1 = λ xn 2 (incase of linear dependence between the two
random variables). Where P is the probability function, corr ( xn1 , xn 2 ) gives the correlation between the
random variables
xn1 and xn 2 and where λ is some constant. Therefore for a cycle that at any given
instance ‘ t ’, providing the in-phase component and the quadrature component, the perturbations for one
particular cycle will be correlated and linearly dependent. That is, for a single source generation or a
correlated source generation the valid approximation will be φ1 ( t ) = λφ φ3 ( t ) and φ2 ( t ) = λφ φ4 ( t ) ,
where ‘ λφ ’ is linear scalar constant defining the correlation between the respective phase change for inphase and quadrature components of an oscillator and as specified before φe is the expected stochastic
-33-
An Oscillator System for UWB QDAcR
value of the phase error between the In-Phase and Quadrature components. If any further perturbation in
the phase induced in quadrature output, due to the mechanism of generation of the quadrature output signal
is to be considered and integrated, then it can be expressed can be approximated with the random
variable φe , then it can be estimated that φ1 ( t ) = φ3 ( t ) ; λφ ≃ 1 and φ2 ( t ) = φ4 ( t ) ; λφ ≃ 1 ; Therefore
the expected values of the random perturbations in in-phase and quadrature phase components are equal
that is E f (φ1 , φ2 ) = E f (φ3 , φ4 ) .
2. Amplitude Perturbations Approximations: As described in [26], the response of a perturbed oscillator
can be best described using the state-space or phase plane diagrams. Figure 2.3 below represents the state
space of an oscillator in V-I plane, the response of the unperturbed oscillator is given by the perfect closed
limit cycle, which represents a stable oscillator with a perfect periodicity. If at any instance‘ t0 ’ the
oscillator is perturbed from its perfect periodic state, there occurs a change in amplitude which marked by
α ( t0 ) and change in the phase is ∆φ ( t0 ) .
t1
t0
α ( t0 )
Vc
t0
Limit Cycle
∆φ(t0)
t1
t2
t2
t3
t3
∆φ(t4)
Il
t4
t4
Figure 2.3: State-Space diagram of an oscillator in V-I plane
In Hajimiri-Lee Model [22] the change in amplitude is characterized by the amplitude impulse sensitivity
function given by ‘ Λ (ω0 t ) ’ and mathematically the change is given by α (t ) = Λ(ω0 t )
∆V (t )
,
V0
where ∆V ( t ) = V0 − V ( t ) is the change in voltage due to instant perturbation, the modeling presented in [22]
is based on heuristic and empirical treatment of the problem rather than quantitative and analytic. The
amplitude impulse response‘ hA (t ,τ ) ’is given by Equation (4.36) in [22] which is reproduced here as
Equation 2.39. Where ‘ d (t − τ ) ’ is exponentially decaying function and signify the excess amplitude, the
decaying function is given by Equation 2.40 [Equation 4.44 in 22].
-34-
An Oscillator System for UWB QDAcR
Λ (ωo t )
d (t − τ )
qmax
hA (t ,τ ) =
d (t − τ ) = e
−ωoτ
Q
(2.39)
.u (t − τ )
(2.40)
The same result as shown in Equation 2.42 below can be obtained by using the Floquet vectors theory for
solving the differential algebraic Equation, describing the nonlinear oscillatory system [24]. The final
solution for the perturbation in the amplitude is given by Equation 20 in [24], on analysis of this Equation it
can be clearly verified that change is amplitude is directly dependent on integrand of Floquet periodic
exponents over the time period ‘ t ’ and is given by Equation 2.41, where ‘ µi (t ) ’is the Floquet exponent
and exp( µi (t )) is called the characteristic multiplier. It can be deduced form the Equation 2.41 that the
resultant change in the amplitude, which is given by ‘ α (t ) ’ decays exponentially with time and that the
amplitude tends to rest back at the normal levels as the time increases. This mathematical analysis also
bolsters the approximation made in this section in which the overall effect of amplitude perturbations on
the phase noise characteristics is proved to be mathematically negligible.
n
t
i =1
0
α (t ) ∝ ∑ µi (tˆ) ∫ exp( µi (tˆ − r )).dr
(2.41)
Using the approximations presented in statements 1 and 2 in order to simplify Equation 2.19
By Equation 2.39, 2.40 and 2.41 it is clear that the amplitude change α (t ) → 0 when t → τ & τ = (0, ∞] ,
therefore first approximating for amplitude perturbations effect in 2.19 by taking the response of QDAcR
over a time period ‘ t ’
2
2
A(t ') .A lo
8
{cos(2(ωc − ωo )t '− ωτ d
o
+ 2ϕ(t) −φ (t) −φ (t)) + cos(φ (t) −φ (t) − ωτ
2
1
1
2
o d
)}
+
2
2
A(t ') .A lo
{cos(φ3 (t) − φ4 (t) − ωτd ∓ 2φe ) − cos(2(ωc − ωo )t '− ωτ d + 2ϕ(t) − φ4 (t) − φ3 (t) ± 2φe )}
o
o
max
8
max
(2.42)
Now further simplifying the Equation 2.42 using the analysis of statement 2, we have Equation 2.43 as the
solution
2
2
A(t ') .A lo
8
{cos(2(ωc − ωo )t '− ωτ d
o
+ 2ϕ(t) −φ (t) −φ (t)) + cos(φ (t) −φ (t) − ωτ
2
1
1
2
o d
)}
+
2
2
A(t ') .A lo
8
{cos(φ1 (t) − φ2 (t) − ωτ d ∓ 2φe ) − cos(2(ωc − ωo )t '− ωτd + 2ϕ(t) − φ2 (t) − φ1 (t) ± 2φe )}
o
o
max
max
(2.43)
-35-
An Oscillator System for UWB QDAcR
3. Approximations for the Phase Error: In this section the effect of phase error is heuristically calculated on
the total autocorrelation of the QDAcR, as it can be calculated from 2.42 that at any instance the expected
value of phase error can be quantized between the limits or mathematically as given by Equation 2.44
E φe (t ) = (0, ±2φe )
(2.44)
The cause of phase error in the In-phase and Quadrature components is primarily associated with the
process variations in the passives and devices manufacturing, which is stochastic in nature, for QDAcR the
effect of phase error on the autocorrelation coefficient can be modeled heuristically, using the MATLAB
modeling of QDAcR and inducing the phase error between the In-Phase and Quadrature components the
change in the autocorrelation factor is measured. The graph plotted below shows the change in
autocorrelation versus the phase error.
Figure 2.4: Change in Auto-Correlation Vs. Phase Error
As it can be analyzed from the above graph that the maximum phase error of ‘ φe (t ) ≃ 17.5 − 18 ’ is
possible in order to have desirable autocorrelation factor in range of 100% − 80% , therefore in the worst
case scenario the value of ‘ φ max ’ possible is ∼ 8.75 . The Equation can therefore be simplified further if by
e
process and circuit design the possible maximum phase error can be fixed below 8.5 .
-36-
An Oscillator System for UWB QDAcR
Now using the results obtained by the heuristic analysis in order to simplify the main time domain QDAcR
Equation given by 2.41; let take K =
A(t ') 2 . A2lo
8
(2.45)
Therefore the Equation 2.43 can be re-written as shown in Equation 2.46 below.
{
}
K [cos(φ1 (t ) − φ2 (t ) − ωoτ d )] + cos(φ1 (t ) − φ2 (t ) − ωoτ d ∓ 2φemax )
+
(2.46)
{
}
K [cos(2(ωc − ωo )t '− ωoτ d − φ2 (t ) − φ1 (t )) − cos(2(ωc − ωo )t '− ωoτ d − φ1 (t ) − φ2 (t ) ± 2φemax )]
The Equation 2.46 can be further simplified, if we limit the value of ‘
φe
’ that is the phase error should
be as less as possible, as given by Equation 2.47, in which lim and therefore we have Equation 2.47,
2φe → 0
ψ = 2(ωc − ωo )t '− ωoτ d − φ2 (t ) − φ1 (t )
where &
;
Φ = φ1 (t ) − φ2 (t ) − ωoτ d
lim K
2φe → 0
+
lim K
2φe → 0
{c o s ( Φ ) +
{[ c o s (ψ
c o s ( Φ ∓ 2 φ em ax )
}
) − c o s (ψ ± 2 φ e m a x ) ]
}
⇕
li m K
2φ
e
→ 0
{c o s ( Φ ) +
c o s( Φ ). c o s 2φ e
m ax
± s i n ( Φ ). s in 2 φ
e m ax
}
+
li m K
2φ
e
→ 0
{c o s (ψ
⇕ li m 2 φ e
2K
→ 0 ⇒ c o s( 2φ ) → 1 & sin ( 2φ ) → 0
e
e
{c o s ( Φ ) }
≤ 2φ
⇕ 0
2K
) − c o s (ψ ) c o s ( 2 φ e ) − s i n (ψ ) s i n ( 2 φ e ) }
{[ c o s ( φ
em ax
1
≤ 8 .5
( t ) − φ 2 ( t ) − ω oτ
d
) ]}
⇔ 2K
[c o s ( ω o τ d
+ φ 2 (t ) − φ1 (t )) ]
⇓
2
A ( t ') . A
4
2
lo
. [c o s ( ω o τ
d
+ φ 2 (t ) − φ1 (t )) ]
( 2 .4 7 )
The final solution of time domain analysis of QDAcR, whilst considering the approximations
(mathematically proven) and process non-idealities present in the downconverter is derived in Equation
2.47. The solution shows the dependence of the autocorrelation on the time dependent phase present in the
system due to the oscillator and the time delay.
-37-
An Oscillator System for UWB QDAcR
The Equations 2.46 and it’s extremely simplified version, which is Equation 2.47, both provides distinctive
merits over the all previous analysis presented so far, which are as follows:
1. The time domain analysis proves that the autocorrelation factor, which is of prime importance in
QDAcR, is directly dependent upon the phase perturbations of an Oscillator, which is further characterized
as the oscillator phase noise. The time domain analysis in itself provides the analysis for general homodyne
and as well as heterodyne receiver architectures as a subset. The time domain analysis is not just limited to
the QDAcR.
2. An accurate mathematical treatment of time domain analysis is presented; which, firstly characterize the
nature of the perturbations that is ‘Stochastic’ and then rightly assess the effect of these perturbations. The
mathematical model provides the scalability of characterizing the overall effect of noise, mismatch and
process variations (which can be characterized as stochastic perturbations) for the mixer. E.g. if we wish to
characterize the effect mismatching in the mixing, then by defining the effect of mismatch as one of the
random variable in the solution Equation. At system level we can directly see the effect by plotting the
results vs. the Expected or range bound (heuristic) value of the process stochastic variable.
3. A first insight into the circuit level design, firstly the empirical processing of phase error provides the
answer as which circuit design method should be used in order to generate the In-Phase and Quadrature
components and the amount of phase error that can be incorporated in the receiver in order to attain the
desired auto-correlation levels.
4. This model can be easily extrapolated onto the Combined Auto-correlation Receiver (CAcR) architecture
which is proposed in [23]. The final Equation at which we will arrive will be the same
2.4 Modeling of an Oscillator in QDAcR
The time domain analysis of QDAcR results in Equation 2.19 and 2.47, that shows the dependence of the
autocorrelation on the phase and amplitude of a LO, that is dependence on ‘ φ (t ) ’ and ‘ α (t ) ’. In order to
model an oscillator with all the non-idealities, the effects of the phase‘ φ (t ) ’ and amplitude change‘ α (t ) ’
should be modeled. The frequency domain uncertainties of LO are represented by random phase and
change in the amplitude, due to the phase modulation (PM) and amplitude modulation (AM) present in the
oscillator in frequency domain and as a measure of the oscillator performance these uncertainties are
expressed as the spread of noise power spectrum around the central frequency / fundamental harmonic.
While in time domain the uncertainties in an oscillator are combined denoted by the ‘Timing Jitter’ or
simply called as ‘Jitter’. In circuit design the performance of the Local Oscillator is characterized by the
phase noise, which is in the frequency domain, in order to model the LO, that is characterizing the sources
of uncertainties and the effects of uncertainties in the frequency domain one must first understand the
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An Oscillator System for UWB QDAcR
dependence and transformation between the time domain and the frequency domain, that is the relationship
between the ‘Jitter’ and the ‘Phase Noise’.
2.4.1 The Phase Noise Characterization: Basics and Noise Sources
The performance of an oscillator is characterized by the amount of power spread at a certain offset
frequency around the carrier frequency or the fundamental tone (if carrier wave form is not sinusoidal) of
the oscillator output and is measured in a bandwidth of 1 Hertz; As low the power spread, as close the
performance will match the performance of an ideal oscillator. The power spread is measured through
analyzing the RF spectrum of the oscillator; the spectrum is symmetric about the carrier frequency [27].
The voltage output of an oscillator is given by the Equation 2.48.
Vout (t ) = Vo (1 + α (t )).cos(ωo t + φ (t ))
(2.48)
Where ‘ Vout (t ) ’ is the output voltage at any time instance ‘t’ and ‘ Vo ’ is the maximum voltage swing
possible for the LO output. The spread around the carrier frequency (the sidebands) is caused by the
fluctuations in phase and amplitude, which are represented by ‘ φ (t ) ’ and ‘ α (t ) ’.
The power spectrum
around the central frequency is resultant of the perturbations in the phase and the amplitude of the oscillator
output, therefore the total power spectral density of the spectrum around oscillation frequency can be
denoted as the sum of the noise power due to the phase and amplitude perturbations that is the noise power
due to phase modulation (PM) and amplitude modulation (AM).
The measure of the performance of the oscillator is done in terms of the measure of single sideband noise
spectrum power density at a certain offset frequency (and bandwidth of 1Hz.) from the carrier frequency
and it is termed as ‘Phase Noise’, expressed in dBc\Hertz or L {∆ω} , Figure 2.5 shows the characterization
of the phase noise.
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An Oscillator System for UWB QDAcR
Figure 2.5: The Power Spectrum of an Oscillator and Phase Noise power of the carrier at certain
offset.
The power under the spread power spectrum as shown in the Figure 2.5 represents the total power, that is,
power that includes the effect of both amplitude as well as phase uncertainties. The total effect of
perturbations is given by the Equation 2.49;
P
(ω + ∆ω ,1Hz.)
Ltotal {∆ω} = 10.log sideband o
Pcarrier
(2.49)
Where ‘ Ltotal {∆ω} ’ is the total of the effect of phase and amplitude fluctuations, which is measured at an
offset angular frequency of ‘ ∆ω ’, ‘ Psideband (ωo + ∆ω ,1Hz.) ’ gives the SSB (single sideband) power at the
offset frequency and ‘ Pcarrier ’ represents the total power under the power spectrum [22].
The effect of amplitude noise can be reduced by amplitude limiting mechanism such as automatic gain
control circuit to control amplifier gain or the finite supply voltage [27] and intrinsic nonlinearity of the
device [22]. The amplitude restoring mechanism can be explained by the LTV impulse response model,
which is described in [22]. As stated in [22] that if an ideal parallel LC tank oscillating at voltage amplitude
Vout (t ) = V0 across the capacitor, is injected with an impulse of current and as a result there is sudden change
(increase) in the voltage through the capacitor that is given by ∆V (t ) =
∆q
, where ∆q is the total charge
Ctotal
injected by the current impulse and the total capacitance is given by Ctotal . There will be only Voltage
amplitude change given by ∆V (t ) if the current impulse is applied at the peak of voltage across the
capacitor and only phase change given by ∆φ (t ) if the current impulse is applied at zero crossing. At any
instance ‘t’ the change in the amplitude and phase is shown by the Figure…the amplitude limiting
mechanism of AGC and nonlinearity of devices can be treated closely to the change in the amplitude,
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An Oscillator System for UWB QDAcR
which is proportional to the amplitude impulse function Λ (ω0 t ) and mathematically the change is given
by α (t ) = Λ (ω0 t )
∆ V (t )
α (t ) → 0 when t → ∞ and φ (t ) → ∆φ (t ) as t → ∞ .
V0
α(t)
∆V(t)=Kα( )
α(
∆φ(t)
∆φ
Vc
Il
Figure 2.6: Phase perturbation due to charge injection
The change in the phase due to the perturbation induced by current impulse is given by the Equation 2.50
∆φ (t ) = Γ (ω0τ )
∆V
∆q
= Γ (ω0τ )
VMAX
qmax
(2.50)
Where the change in phase ‘ ∆φ (t ) ’ is related to the
In [24] the overall effect of the perturbation in the amplitude is explained by considering it as an orbital
deviation component of an oscillator. The nonlinear perturbation analysis provides the result that the orbital
deviation is small at any give instance of time and further it confirms and adheres to the postulated
amplitude stabilization given in [22]. Therefore for practical reasons we can consider Ltotal {∆ω} = L {∆ω} ,
that is the total noise power present in the SSB spectrum can be equated with the noise power produced due
to the phase modulation, which is commonly known as phase noise. The typical single sideband power
spectrum for the phase noise in terms of L {∆ω} is shown in the Figure 2.5 The phase noise is given by the
Equation 2.51; which is commonly known as Leeson’s Equation of phase noise; this Equation is to model
phase noise, which is based on a linear time invariant (LTI) analysis of tuned tank oscillator[28],
2 FkT
L {∆ω} = 10.log
P
s
2
ω1 3
ω
f
o
• 1+
• 1 +
2QL ∆ω
∆ω
(2.51)
Where‘ F ’is device excess noise number, ‘k’ is Boltzmann’s constant, ‘T’ the absolute temperature, Ps is
average power dissipated in the tank, ωo and ∆ω are the oscillation and the offset frequency and
quality factor of the loaded tank.
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QL is the
An Oscillator System for UWB QDAcR
The sources of noise in an oscillator can be broadly classified in two categories; firstly, the noise produced
by the active devices used in the Oscillator and secondly, by the resonator. On the basis of mechanism the
noise present in an Oscillator can be further classified into (1) Thermal noise (2) Shot Noise and (3) Flicker
Noise (1/f noise).
1.Thermal Noise: The noise caused by the Brownian motion of thermally agitated charge carriers in a
conductor, which represents the randomly varying current and consequently the random voltage (via Ohm’s
Law) [30], it is also commonly known as ‘White Noise’ or Johnson Noise’. The available noise power is
given by the Equation PNA = kT ∆f where ‘ k ’ is Boltzmann’s constant, absolute temperature is given by
‘ T ’ and ‘ ∆f ’is the frequency bandwidth. The thermal noise has a constant energy per hertz or per
required bandwidth. The thermal noise can be associated with the passive circuit components like resistor,
where it is given by the Equation
2
2
vn = 4kTR∆f or in terms of the current by in =
2
vn
= 4kTG ∆f
R2
where R is the resistance value and G the conductance, the white noise is also associated with the real time
inductors and capacitors (if we consider parasitic resistance). In active devices (MOSFET) the thermal
noise is present in the form of drain current noise due to the resistive nature of the drain-source channel;
however, in short channel NMOS the drain current noise is far exceeding from the normal values devised
by long channel theory; it is due to the role played by the thermal noise produced by the substrate, the
substrate can be modeled in terms of simple resistive [29] or as done in [30] as a RC circuit, therefore the
excess current noise measured is due to the substrate current noise. The thermal noise can be further
associated to the gate noise in MOSFET due to resistive poly gate [29], which is negligible at low
frequencies, however can dominate at radio frequencies[30]; the thermal noise is present as a base
resistance noise in BJT, which is a major source of thermal noise in BJT and the noise voltage across the
2
base resistance rb is given as vb = 4kTrb ∆f , the ‘thermal noise’ can be characterized as the ‘Gaussian
Noise’ as amplitude of the thermal noise follows a Gaussian distribution [30].
2. Shot Noise: The shot noise can be described as the noise produced by the direct current flowing through
a junction that acts as a potential barrier; the randomness is caused by the hopping of the electrons over the
potential barrier arriving at the random time. This randomness in the arrival time gives rise to white noise
nature of the shot noise, which gets worst with the increase in average current through the junction or
2
increase in the bandwidth. The ‘Shot Noise’ is given by the Equation in = 2qI DC ∆f , where
noise current, q is electronic charge,
in is the rms
I DC is the DC current and ∆f is the noise bandwidth [30]. The shot
noise is a major contributor in the overall noise of bipolar junction transistor, collector current shot noise is
given by ic2 = 2qI c ∆f and the shot noise due to the base current, which can become dominant at the radio
frequencies and is given by ib2 = 2qI B ∆f however, it is the partial but major component in the total base
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An Oscillator System for UWB QDAcR
noise present in a BJT. The amplitude of the shot noise also follows the Gaussian distribution, as it is
similar to the white noise or thermal noise. In MOSFET the shot noise is present in the form of gate leakage
2
current which is given by noise gate current ig = 2qI g ∆f , it becomes significant at radio frequencies or
when driven by a high source impedance; besides the shot noise both MOSFET and BJT gate/base consists
of flicker and burst noise.
3. Flicker Noise: This noise is also known as the ‘1/f’ or ‘pink’ or ‘colored’ noise; the flicker noise has the
spectral density which increases with decrease in the frequency, therefore mathematically it is given
as 1/ f n , where the index‘ n ’ attains value in the region 0 < n ≤ 4 as described in [31] and it is associated
with the roughness distribution of a signal. Furthermore, as illustrated in [31] that in an one-dimensional
system for n = [1, 2, 4] the periodic behaviour of flicker noise is seen and for n → 1 the flicker noise
behaviour can be associated with the physical phenomenon of voltage fluctuation in a resistor when current
is flowing through it. Therefore, the flicker noise in an electrical circuitry can be appropriately described by
the following Equation, specified in [30] as N 2 =
K
∆f , where N is the rms noise, that can be either
fn
voltage or current, K is an empirical parameter it is biased dependent and device specific and ‘n’ is an
exponent close to the unity [30] and in [32] the exponent n = 1 ± 0.2. There have been reported several
mechanism for the generation of flicker noise in [32] and [29], also among the all semiconductor devise the
MOS exhibits the highest amount of flicker noise due to their surface conduction mechanism [29]. In [30] it
is stated that flicker noise is a major noise source in MOSFET, as it is most sensitive to the surface
phenomenon or the roughness of the surface. One of the measures for the flicker noise is done my
measuring the corner frequency of the device that is the frequency where the flicker noise component
power spectral density (PSD) is equal to the PSD levels of total of thermal and shot noise under the ceteris
paribus conditions. The MOSFET devices (surface devices) are highly sensitive to the surface phenomenon
because of the way they are fabricated, which translates into the fact that the corner frequency in
MOSFETs is many times higher than the corner frequency of BJT, which are considered to be bulk devices
by
the
2
by ind =
way
of
fabrication;
in
MOSFET
the
mean-square 1 f drain
noise
is
given
g2
K
K
i m 2 i∆f ≈ n iωt2 iWLi∆f , where W is the width of the MOS, L is the channel length
n
f WLCox
f
and ωt is the MOS cut-off frequency. The 1 f noise in NMOS is typically 50times larger than for PMOS
devices [29, 30]; in MOS devices the 1 f noise corners occurs generally between kilohertz to megahertz
and even in gigahertz range, while in bipolar from few tens of hertz to hundreds of hertz [30]. The flicker
noise is present in the resistor if there is DC current flowing through it and this the cause of excess noise
found in resistor apart from thermal noise [30]. The flicker noise is given by 1/ f n , can be characterized by
different distributions for different values of the noise index ‘ n ’ as shown in [31]. The region
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An Oscillator System for UWB QDAcR
corresponding to the electrical flicker noise and point of interest is when n → 1 , for values of n ≤ 1 the
2
flicker noise can be characterized by the Gaussian distribution and as‘ n ’ deviates there is noticed a
difference from normal Gaussian distribution. The power spectrum density of flicker noise is characterized
by the multiple Lorentzian spectra [33]; the singularity arises in the spectrum for n = 1 , therefore the
spectrum is given by Equation 18 in [33]. The other type of noise source, which exhibits the sensitivity
similar to the 1 f noise, is burst noise or popcorn noise and as stated in [33] for the flicker noise the burst
noise also mostly exhibits a multiple Lorentzian spectrum and the spectral density of burst noise is
mathematically given by equation 31 in [34] as Sburst ( f ) = K
‘ f ’ and ‘
in
f
1+
fc
2
where ‘K’ is a device constant ,
f c ’ are the central and 3dB cut-off frequencies of the Lorentzian Spectrum, ‘ i ’ the device
current and ‘ n, 0.5 ≤ n ≤ 2 ’ is the exponent for the colored noise.
2.4.2 The Phase Noise Characterization: Noise Distribution in a
Single Sideband Spectrum
The single sideband phase noise spectrum of an oscillator can be best plotted as shown in the Figure 2.7
Figure 2.7: The Single Side Band Spectrum of and Oscillator
As it is shown in the Figure 2.7 that ssb phase noise spectrum consists of mainly three frequency region
marked by 1 f 3 , 1 f 2 and 1 f 0 these regions are characterized by type of noise source they represent, in
depth study dealing with the characterization of the noises present in an oscillator has been done and the
types of noises influencing each region can be characterized as follows.
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An Oscillator System for UWB QDAcR
1. The most important region in single sideband phase noise spectrum plot i.e. L {∆ω} Vs. ∆ω Plot is
the 1 f 2 noise region; it represents all the white noise (white and modulated white noise) generated in the
oscillator. The characterization of the 1 f 2 noise is very well presented in [24] and it is termed as ‘the
unifying theory’, which characterizes all the uncorrelated white noise sources and their effect on the
oscillator performance. The phase change is stochastically characterized in the time domain by calculating
the time-varying probability density function (PDF) of the phase change, this characterization results that
the phase change ‘ ∆φ (t ) ’ becomes asymptotically with time a Gaussian random variable, with a constant
mean ( µ ) and linearly increasing time dependent variance σ 2 (t ) and σ 2 (t ) = ct , where ‘ c ’ is a scalar
constant. In the spectrum analysis of the oscillator output, the unifying theory states that the phase
deviation ∆φ (t ) changes the power spectral density in the frequency domain; however, the total power of
the periodic oscillator signal remains conserved. In frequency domain the PSD of an ideal oscillating signal
can be replicated by the Dirac Delta function‘ δ ( x) ’, where the PSD levels take the shape of an impulse
function at central frequency and harmonics, the effect of phase deviation in the frequency domain is that it
spreads the spectral power given by δ ( x ) functions at all harmonics; however the total spectrum power
remains the same [24]. The phase noise due to total white noise that is the total 1 f 2 noise spectrum in a
single sideband phase noise plot can be shown as in Figure 2.7; the 1 f 2 region is marked by
the −20dB / dec. noise slope. The phase noise is given by the Equation 2.52, for the approximation that
0 ≤ ∆ω ≪ ωo and small values of ‘ c ’.
ω 2c
L {∆ω} ≅ 10.log 4 2 o
ωo c
+ ∆ω 2
4
(2.52)
The unifying theory [24] even deals with the shortcomings of the Leeson’s LTI phase noise model which is
given in Equation 2.51. If we consider Equation 2.51 and look for behaviour of the SSB phase noise
spectrum the offset frequencies approaching the carrier frequency that is ∆ω → 0 , the solution of Equation
2.51 provides with an infinite noise power density at the carrier which is not accurate. The Equation 2.52
can be equated to the Lorentzian spectrum as shown in Equation 2.53, where‘
f o ’is the oscillation
frequency and‘ ∆f ’ is offset frequency at which the phase noise is measured.
ω 2c
L {∆ω} ≅ 10.log 4 2 o
ωo c
+ ∆ω 2
4
π f o2 c
1
⇔ L {∆f } ≅ 10.log⋅
2
2
2
π (π f o c) + ∆f
(2.53)
Furthermore, it can be proved quantitatively that the total power of the phase noise spectrum is conserved
and that phase perturbation causes the spread around the harmonics. As the integral of the Equation 2.53
which exhibits the Lorentzian spectrum has a finite value of ‘1’ between minus infinity to the plus infinity
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An Oscillator System for UWB QDAcR
∞
that is
∫ L{∆ω} = 1 .
In [35] the power spectral density of noise component due to white noise or the
−∞
spectrum shown by 1 f 2 region, is characterized by high frequency variations in the feedback loop and is
given by the Lorentzian function; the feedback loop consists of a frequency select resonator, which filters
the undesired noise components and the selective output is provided back to the input of the active device
that acts as an amplifier [27].
2. The frequency modulated flicker noise or 1 f noise component is represented by 1 f 3 region as marked
in the Figure 2.7. There have been several attempts to characterize the effect of flicker noise in an oscillator
spectrum; the credible studies are [34, 35, 22]. In [34] the 1 f noise is treated as a special case of the
colored noise, where the colored and correlated noise is characterized stochastically, representing it by a
one-dimensional Gaussian distributed process with the approximation that the bandwidth of the colored
noise source is significantly smaller than the oscillation frequency, to simplify the modeling the colored
noise sources are assumed to be auto-correlated only, that is uncorrelated with each other. The [34] treats
1 f noise as a stationary stochastic process, which attains a finite value at f = 0 and deviates from the
characterized Lorentzian spectrum below the cut-off frequency ‘ γ c ’; the spectrum is defined as a function
of the 3-db bandwidth ‘ γ ’ and the process operation frequency ‘ f ’. The spectrum of the 1 f noise is
given by S N
1 f
∞
1
γc
γ 2 + (2π f ) 2
as in Equation (38) in [34], which is S N1 f = 4 ∫
d γ and signifies that the spectral
density contribution due to 1 f noise is pronounced at the low frequencies near the fundamental frequency
of the oscillator and the value of spectrum at f = 0 is given by S N1 f (0) =
4
γc
. The behaviour, which in
Figure 2.7 is marked by 1 f 3 and is given by -30dB/dec slope and the cutoff frequency if marked by the
point where 1 f 3 and 1 f 2 regions meet, this point as stated previously is commonly called as 1 f corner
(it is not same as the1 f corner frequency of the device). However, in the calculation of phase noise
spectrum due to 1 f noise, the approximations in defining the flicker noise spectra are taken; firstly, that is
the1 f noise is a stationary stochastic process, which is bounded in an interval of time, that is classified as
‘Relaxation time’ in [33], this allows to define the continuous spectra 1 f noise over a certain bandwidth
defined by the relaxation time interval [33] and which is same as the limits from cut-off frequency to
infinity as stated in Equation (38) [34] and Secondly that in the single side band phase noise spectra the
power due to 1 f noise is concentrated at the low frequencies [34].
3. The device flicker noise or 1 f noise component: As we have noticed that as the channel length is
decreasing the device own 1 f increase and for NMOS and other contemporary technologies it extends to
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An Oscillator System for UWB QDAcR
few Megahertz. Therefore, the unmodulated component of the device flicker noise is dominant and it’s
effect is seen at the lower frequencies. As shown in Figure 2.7 the device flicker noise does provide a roll
off with 10dB/decade and is effective at low frequencies level.
2.4.3 Modeling of Oscillator in time domain (Jitter and Phase Noise
conversion)
The effect of uncertainties in an Oscillator can be illustrated in terms of ‘Jitter or Clock Timing Jitter’ in the
time domain, which corresponds to the ‘Phase Noise’ in frequency domain. The Jitter can be broadly
described as the difference between the zero-crossing / transition times of a signal and the absolute value of
the signal time period over a specified time interval; therefore ‘Jitter’ can be classified as the deviation in
the period of a signal over the certain time interval. The Figure 2.8 represents the jitter present in a signal of
T + T2 +T3 .... + Tn-1 +Tn 1
mean time period ‘ T0 ’& T0 = 1
= f 0 , where f 0 is the fundamental and unperturbed
n
oscillation frequency. The various types of jitter are given by ∆T1 , ∆T2 , ∆Tn & ∆Tn+1 .
T1 =T0 ± ∆T1
T2 =T0 ± ∆T2
∆T
n
∆ Tn+ 1
Figure 2.8: The various types of Jitters present in a oscillating signal
In case of an Oscillator these variations occur in each and every cycle and are caused by noise, which in
time domain is translated to ‘jitter’ or can be termed as noise induced jitter. The jitter produced by the noise
in any system is a random variable and can be characterized stochastically in a similar fashion as the noise
in an oscillator. The phase noise dependent jitter can also be classed as an Ergodic Process which also
follows the Gaussian distribution.
The jitter in an Oscillatory system is generally characterized as 1) Absolute Jitter and 2) Cycle Jitter and 3)
Cycle to Cycle Jitter on basis of time of observation.
1. Absolute Jitter: The term absolute jitter is associated with the jitter that has been accumulated over a
period of time. As shown in the Figure 2.8 the jitter values ∆Tn & ∆Tn+1 are the values associated
with n th & n+1th cycles respectively. The jitter ∆Tn in the n th cycle acts as a source for the jitter ∆Tn+1 present
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An Oscillator System for UWB QDAcR
in the n+1th cycle, similarly accumulated effect of jitters present in all the previous cycles can be seen in the
corresponding oscillation cycle. This shows that jitter once induced in the system can not be get rid off and
it keeps on adding due to the non-idealities present in the circuit. Therefore, absolute jitter is also termed as
long term jitter and the numerical value of the absolute jitter ∆Tabs is given by the Equation 2.54 below.
K
∆Tabs, K th = ∑ ∆Tn
(2.54)
n =1
The jitter induced by the phase noise in a circuit is a stochastic quantity, taking in to the account the above
2
Equation 2.54, the standard deviation‘ σ abs (t ) ’ and the variance‘ σ abs (t ) ’ present in absolute jitter are given
by the Equation 2.55 below. The absolute jitter is of importance in describing the jitter induced in a phase
lock loop, because the total jitter translates into the total phase error produced in a certain time ‘t’ and
corrected by the phase lock loop.
K
K
n =1
n =1
2
σ abs (t ) = ∑ Tn − T0 & σ abs (t ) = (∑ Tn − T0 ) 2
(2.55)
2. Cyclic Jitter: Cycle Jitter is commonly known as rms (root mean squared) cycle jitter, this rms cycle
jitter is a measure of the magnitude of the perturbation in one particular period when compared with the
mean period ( T0 ). Mathematically it is given by the Equation 2.56 below. Where‘ ∆Tc ’ is the rms cycle
jitter present in the K th cycle. The standard deviation‘ σ c (t ) ’ and the variance‘ σ c2 (t ) ’ present in rms cycle
jitter are given by equation 2.57
∆Tc = lim
K →∞
σ c (t ) = lim
K →∞
1 K
∑ ∆Tn2
K n =1
(2.56)
1 K
1 K
lim
∑ (Tn -T0 )2 & σ c2 (t ) = K →∞ K ∑ (Tn −T0 )2
K n =1
n =1
(2.57)
3. Cycle to Cycle Jitter: The cycle to cycle jitter is defined as the time period difference between the two
consecutive cycles, the difference between the two consecutive cycles provides the magnitude as well as
the actual effects the short term perturbations, as a result of white noise and uncorrelated Gaussian
distributed noise sources, which is seen as 1 f 2 noise power in the frequency spectrum. Therefore,
mathematically cycle to cycle jitter can be written as given by Equation 2.58
∆Tcc = lim
K →∞
1 K
1 K
2
lim
∑ (∆Tn+1 − ∆Tn )2 ⇒ K →∞ K ∑ (∆Tn+1 + ∆Tn2 − 2∆Tn+1.∆Tn ) ⇒ 2.∆Tc
K n =1
n =1
-48-
(2.58)
An Oscillator System for UWB QDAcR
In the Equation 2.58 the product terms are neglected and the relationship between cycle and cycle to cycle
jitter is obtained. Similarly, the variance and standard deviation can be obtained as shown in Equation. 2.59
2
σ cc = lim
K →∞
1 K
1 K
lim
∑ ((Tn+1 − T0 ) − (Tn -T0 ))2 ⇒ K →∞ K ∑ (Tn+1 − T0 )2 + (Tn -T0 )2
K n =1
n =1
(2.59)
Neglecting the product terms in the Equation 2.59. The above Equation can be considered as the sum of
cyclic variances in two consecutive cycles, therefore mathematically it can be expressed as shown in
Equation 2.60
2
σ cc (t ) = 2.σ c2 (t )
(2.60)
The stochastic nature of the jitter can be explained by defining the mathematical relationship between the
jitter and phase noise. Considering very first Equation of an oscillatory motion given by Equation 2.3 and
in this neglecting the amplitude perturbations, therefore the new Equation can be re-written as
Aout (t ) = Alo .cos(ωo t + φ (t ))
(2.61)
Considering the small change in the angular frequency‘ ∆ω (t ) ’because of the small phase
perturbation ∆φ (t ) and neglecting the amplitude perturbations that is considering Aout (t ) = Alo ; then the
excess phase can be related to excess angular frequency as in Equation 2.63
Aout (t + ∆ t ) = Alo .
lim
∆ ( ω ,φ ( t ), t ) → 0
cos((ω 0 + ∆ ω )t + φ (t ) + ∆ φ (t ))
⇓
Alo .
lim
∆ ( ω ,φ ( t ), t ) → 0
( cos(ω 0 t + φ (t )) cos( ∆ ω t + ∆ φ (t )) − sin(ω 0 t + φ (t )) sin( ∆ ω t + ∆ φ (t )) )
⇓
(2.62)
Aout (t + ∆ t ) = Alo .
⇓
lim
∆ ( ω ,φ ( t ), t ) → 0
cos(ω 0 t + φ (t )).cos( ∆ ω t + ∆ φ (t ))
Aout (t + ∆ t )
→1
Aout (t )
1=
lim
∆ ( ω ,φ ( t ), t ) → 0
∆ω (t ) = −
cos( ∆ ω t + ∆ φ (t )) ⇒ ∆ ω t + ∆ φ (t ) = 2 nπ
t
d
φ (t ) ⇒ φ (t ) = ∫ ∆ω (τ ).dτ + φ (0)
0
dt
(2.63)
By using the above mentioned Equation…the time varying excess phase ∆φn (t ) associated with the
n th period which is directly related to the jitter produced in the n th period is expressed mathematically as
∆Tn = ∆φn (t )
T0
2π
Similarly, the cycle jitter can be expressed in terms of cyclic phase perturbation ‘ ∆φc (t ) ’,
where ∆φc (t ) = lim
K →∞
∆Tc = ∆φc (t )
1 K
∑ ∆φn2 (t ) , therefore
K n =1
T0
T0
⇒ ∆Tcc = ∆φc (t )
2π
2 2.π
(2.64)
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An Oscillator System for UWB QDAcR
Similarly, the variances in time and frequency domain have the mathematical relationship as defined by
Equation 2.65 below.
T φT
1
1 K
1 K
σ c ∆φ ( t )
σ c2 (t ) = lim ∑ ( ∆φn (t ) 0 − 0 0 ) 2 ⇒ 2 lim ∑ (∆φn (t ) −φ0 ) 2 =
K →∞ K
K →∞ K
2π 2π ω0
ω02
n =1
n =1
2
2
σ cc (t ) =
2.σ c2 ∆φ ( t )
ω02
⇒ σ c2 ∆φ ( t ) =
2
σ cc (t ).ω02
(2.65)
(2.66)
2
Extending the deduced results of section 2.3 to the above Equations numbered 2.66,
as the phase
perturbation follows the Gaussian distribution and it is proved that the jitter and phase perturbation are
linearly dependent. Then by the theorem that if two random variables are linearly dependent and one of
them follows Gaussian distribution then other random variable can also be characterized by Gaussian
distribution, which is mathematically expressed as for two random variables ‘ xk & xm ’ and considering
‘ xk ’ to be Gaussian distributed
Theorem (corollary): If a1 .xk = a2 .xm for any linear constants‘ a1 & a2 ’; while xk is having Gaussian
distribution then it implies that random variable ‘ xm ’ can also be characterized by Gaussian distribution.
This theorem serves as a corollary to theorem 7.2 in [24]. Therefore, the extrapolated results show that the
timing jitter produced in an oscillator does have Gaussian distribution. In the same fashion it can be
deduced that the production of timing jitter is an Ergodic process, which in turn justifies the accumulation
of the time jitter and corresponding stationary stochastic behavior of phase deviation.
For the time domain modeling of the phase noise, next step is to calculate the relationship between the
timing jitter and the phase noise. Firstly, describing the power spectrum density for determining the phase
noise. As described in the section 2.4.1 and 2.4.2 the phase noise is given by Equation 2.49.
Mathematically it can be derived by starting with the interchangeable relationship between the
autocorrelation and the spectral power density, which is given by Weiner-Khinchin theorem, shown as
Equation below
∞
C (τ ) = ∫ S (ω )e jωτ df
−∞
⇕
(2.67)
∞
S (ω ) = ∫ C (τ )e
−∞
− jωτ
dτ
Using the Einstein diffusivity Equation as described in Equations numbered 13 and 29 in [26] in Equation
numbered 2.38, the correlation can be defined in terms of the diffusion coefficient ‘D’ as given by Equation
2.68 below.
C (τ ) =
(
A02
.cos(ω0τ ).exp − Dφt . τ
2
)
(2.68)
Now using the Weiner-Khinchin theorem as given by Equation (), the PSD is given by Equation 2.69 below
S (ω ) = ∫
∞
−∞
(
)
A02
.cos(ω0τ ).exp − Dφt . τ .exp − jωτ dτ
2
(2.69)
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An Oscillator System for UWB QDAcR
The solution of the Equation 2.69 is a well known one and given in [25, 26, 28], therefore the value of PSD
is
Dφt
A02
.
2 (ω − ω0 )2 + Dφ2t
S (ω ) =
(2.70)
The single side band spectrum density is given by ‘ S ss (ω ) ’ and it is mathematically given as
S ss (ω ) = 2.S (ω ) = A02 .
Dφt
(2.71)
(ω − ω0 ) 2 + Dφ2t
The total PSD by white noise sources ( 1 f 2 ) as given by Equation 37 in [24], therefore ‘ Ptot ’ can be
approximated as shown in Equation 2.72 below
∞
Ptot = ∫ Sss (ω ).d ω = 2. A02
(2.72)
0
Therefore, the phase noise having the Lorentzian distribution as given in 2.49 at an offset frequency ∆ω can
be expressed as given by Equation 2.73.below
2 Dφt
Ltotal {∆ω} = 10log
∆ω 2 + Dφ2
t
(2.73)
Applying the approximation that as applied in Equation 2.52 that is ∆ω ≫ Dφt , the phase noise is given by
the Equation 2.74
2 Dφt
Ltotal {∆ω} ≅ 10log
2
∆ω
Ltotal {∆ω}
2 Dφt
⇒ 10 10 =
∆ω 2
(2.74)
For defining the phase noise in time domain by using the Equations number 2, 29 & 30 from [26], we
define σ c2 ∆φn (t ) =
2
k
n∆φn ( t )
∑ ( Dφ ) .t
k =0
t
k
(2.75)
k
nt
tk
→ T0 , combining the above Equation with
k =1 k
Ensemble over a finite time period, which means that ∑
Equation 2.74 & 2.75, the very important relationship between the cycle to cycle jitter variance and the
phase noise is given by the Equation number 2.76
Ltotal {∆ω}
10
10
=
3
ω 3 .σ 2 (t )
ω 3 .σ 2 (t )
ω0
2
σ cc (t ) ⇒ Ltotal {∆ω} = 10log 0 cc 2 = 10log 0 c 2 (2.76)
2
4π .∆ω
4π .∆ω
2π .∆ω
The above Equation 2.76 holds importance as it serves the basis for the modeling of the micro noise source
in QDAcR in time domain. The result deduced in the above Equation is a well known one and is in
complete uniformity with other similar results [24, 36, 37, 38]; however this proof presented here defines
the relationship between the jitter and phase noise, while characterizing them as dependent stochastic
variables and describing the mathematical relationship between the Cycle to Cycle jitter and phase noise.
This relationship depicts and conforms fully to the Phase Noise stochastic mathematical characterization
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An Oscillator System for UWB QDAcR
and the relationship between the Timing Jitter and phase noise is used for modeling in MATLAB for the
purpose of modeling a real oscillator for QDAcR.
The Equation models the phase noise produced by the white uncorrelated/ correlated (modulated) noise
sources in an Oscillator, which is given by 1 f 2 region in the oscillator power spectrum. As explained in
the section 2.4.2 that for the wideband systems and the system where the intermodulated signals as well
spurs either can be filtered or do not put stringent phase noise condition on the system the spectral density
can be estimated by white noise (un-correlated/correlated) spectral power density model only; therefore the
effect of 1 f 3 region in the Oscillator power spectrum can be discounted for the purpose of system
modeling and in particular for the QDAcR.
Therefore, for the ir-UWB QDAcR system the total phase noise is modeled as the total amount of phase
noise generated by the white noise sources and given by 1 f 2 region in the oscillator power spectrum.
Approximation of the total phase noise using simply 1 f 2 region indeed is a good estimation technique for
the wideband systems, which suits best to the wideband ‘Zero IF’ and even multiple band switching
wideband ‘(Super) Heterodyne’ receiver architectures.
2.5 Conclusion
In this chapter, we presented an in-depth mathematical analysis of phase noise with respect to QDAcR. The
rigorous analysis is based on non-linear time variant system theory, which is extended to stationary
stochastic process like white noise. We derived a complex model, which captures the noise/jitter related
non-idealities of QDAcR and the same analysis can be extrapolated to other zero-IF or homodyne receiver
architecture systems by adjusting the limiting quantities. The study of phase noise as physical process and
its stochastic behaviour helped us in better understanding of phase noise and time jitter relationship. This
well-known relationship serves as building block for time domain oscillator model, which will be used to
find the specifications related to QDAcR downconverter.
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An Oscillator System for UWB QDAcR
3 CHAPTER 3
System Analysis and Modeling of QDAcR
3.1 Introduction
In this chapter, we further build upon the derivations and results deduced from the pervious chapter.
Starting with modeling of a real oscillator with all phase as well as amplitude perturbation incorporated. It
is followed by understanding of QDAcR architecture and its limitations pertaining to total phase error,
linearity and noise issues. As a solution a new architecture of QDAcR with added filters is proposed, this
change not just eases the operational constraints but also increases the bandwidth usage to 76% of FCC
allowed mask. The next section contains the complete modeling of QDAcR in MATLAB, the different
pulse shapes were exploited for their interference resistance and as for which pulse highest correlation can
be achieved for same phase noise. This leads to an extremely important result as how much phase noise is
required in order to have desirable autocorrelation. Also, the analysis of LNA noise factor dependence on
autocorrelation is presented.
3.2 Designing and Simulation of the Oscillator in MATLAB
The mathematical model of an Oscillator in the frequency and time domain is being presented in section
2.4, in this section the mathematical model of phase noise in time domain is being implemented in
MATLAB and SIMULINK. The phase noise model in the time domain is based on the relationship
between time jitter and phase noise, which is illustrated in the Equation 2.76. The oscillator is modeled as
an integrated Gaussian distributed macro noise source. The block diagram of Oscillator phase noise model
in Matlab is presented in the Figure 3.1. The Oscillator model consists of the following building blocks.
1. The Source / Oscillator: This block consists of Sinusoid signal generator, generating a continuous
sinusoidal signal at a specified frequency of ‘ ω0 ’with amplitude of ‘ A0 ’ and constant phase of ‘ φ0 (t ) ’.
Mathematically it is given by Aout (t ) = Alo cos(ωo t + φ0 (t )) .
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An Oscillator System for UWB QDAcR
Figure 3.1: The Block Diagram of LO modeled in MATLAB
2. The integrated Micro Noise source block is represented as AWGN Channel, which stands for additive
white Gaussian Noise channel. This represents the combined (integrated) noise effect of the white
modulated/un-modulated noise sources present in an Oscillator. The AWGN represents for the random
Gaussian noisy channel, when the signal is passed through the AWGN Channel the randomness is
introduced in the oscillator signal, this randomness can be seen as the perturbation in the phase as well as
the amplitude of the oscillator signal, as proved earlier settling of the amplitude perturbation the block can
be estimated with Gaussianly distributed phase perturbation only.
The amount of perturbation which finally translates into the phase noise induced in the QDAcR Oscillator
spectrum is controlled from the AWGN Block by varying the variance parameter based on the relationship
given by the Equation 2.76. The Gaussian distributed variance is Cyclic Jitter as described in the section
2.4.3, as it can be seen from the block diagram in Figure 3.1 above that the difference between the
perturbed and the fundamental signal at instance ‘t’ is measured, which totally coincides with the definition
of the cyclic jitter. In calculations the cyclic jitter is replaced by the cycle-to-cycle jitter as it is true
representation of the perturbations related to one particular cycle. The random perturbation is translated
into the signal as a phase modulation.
The architecture of the AWGN channel is shown in the Figure 3.2 below, the function ‘ G (t ) ’ is a function
of the random signal generated by random signal block (generation of a random sequence) which is
Gaussianly distributed, with mean = 0 and variance = 1. The function ‘ G (t ) ’ which acts as an asymptotic
envelope as described in (Max).
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An Oscillator System for UWB QDAcR
( x n 1 , ....., x n k )
µ = 0; σ
2
=1
G (t )
σ c2 (t )
Figure 3.2: Complete Block Diagram of Micro Noise Source with AWGN Channel
Therefore mathematically the output signal of the AWGN channel block can be written as in Equation 3.1,
where‘ G (t ) ’ is AWGN channel function.
∆ω (t ) ≈ G (t ). Alo cos(ωo t + φ (t )) ; Since ∆ω (t ) =
Therefore
d
φ (t ) ,
dt
d
φ (t ) ≈ G (t ). Alo cos(ωo t + φ (t ))
dt
(3.1)
The final product which reflects the time domain signal of realistic oscillator is obtained when the time
domain complex signal (total perturbed phase) is multiplied with an ideal oscillator output. Mathematically
it is given by Equation 3.2.
Aout (t ) = Alo .cos(ωo t + φ (t ))
⇕
(3.2)
Vout (t ) = Vo .cos(ωo t + φ (t ))
The real time output of an oscillator with In-Phase, Quadrature and Ideal responses is shown in the Figure
3.3 below. The Figure 3.3 shows an oscillator with a central frequency of 5.6GHz, amplitude of 1Volts and
phase noise of -100dBc/Hz at an offset frequency of 1MHz. In the succeeding Figure 3.4 the unperturbed
and perturbed Quadrature Oscillator outputs are shown with the running cycle to cycle jitter of 4.7725femto
seconds to produce the phase noise of -120dBc/Hz@1MHz offset, this jitter is induced through the variance
block in the AWGN Channel.
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An Oscillator System for UWB QDAcR
Figure 3.3: Phase Noise of -100dB @ an offset of 1MHz.
Figure 3.4: Unperturbed Oscillator Output along with perturbed I/Q outputs.
3.3 Analysis of QDAcR architecture
One of the main objectives of this thesis has been to look into the pros and cons of the present system
architectures for ir-UWB receivers. The QDAcR architecture proposed in [8, 23] can be characterized as
low-IF receiver architecture and is shown in the Figure below. In UWB the processing of bandwidth of 7.5
GHz. poses severe design constraints, typically there has been no transceiver architecture devised to
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An Oscillator System for UWB QDAcR
process such a wideband, the two most common architectures for the transceiver’s design are “(Super)
Heterodyne or IF architectures and Zero-IF or Low-IF architectures. Both of these architectures possess
specific merits and demerits in accordance with the specific use based on the RF bandwidth, modulation
scheme and system design specifications.
Figure 3.5: Block Diagram of QDAcR [19]
Heterodyne transceivers are predominantly used for narrowband communication systems where the channel
/ entire signal bandwidth measures maximum in Kilohertz or fraction of Megahertz. The heterodyne
receiver gives the advantages of high channel selectivity and receiver sensitivity. The functionality of
heterodyne receiver is explained by taking an example of Dual-IF Heterodyne Receiver Topology [39] as
shown in the Figure 3.6 below. The first step involved in designing the heterodyne receiver is the frequency
planning that is choosing the appropriate Oscillator frequencies (in the case of multiple downconersions),
this calculation of oscillator frequency plays an important role as it decides the frequencies at which the
Image will reside.
The Image is calculated as ωImage = ω LO ± ω IF & ωIF = ωRF ± ωLO ; the proper choice of frequency facilitates
that the “Spurs (the Intermodulated components)” do not fall in the RF, IF or LO frequency bands, as if the
signal strength is higher it can desensitize the receiver. The “Image Reject Filter” is used before the process
of Downconversion and after the LNA as shown in the Figure in order to suppress the Image, the Image
reject filter requires a high “Q”, which largely depends upon the strength as position of the Image as well
any interferer residing in the concerned band. The requirements of moderate to high “Q” for the Channel
Select Filter depends upon the Mixer output, as if high IIP2, IIP3 and conversion gain can relax the
Channel Select Filter’s requirements, also the purity of Oscillator spectrum that is the higher phase noise
also acts as a major factor in easing the Channel Select Filter’s requirements.
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An Oscillator System for UWB QDAcR
However, the heterodyne topology poses advantages like, the use of Image Reject filter not only stops the
image but also provide a higher degree of port-to-port isolation for LO-LNA leakage and thus
circumventing the chances of higher strength spurs getting mixed into the RF path or LO power seepage to
the Antenna and subsequently corrupting the transmitted signal. Other aspects of the IF-Receiver
architecture that poses design concerns are integration of the Image reject filter and LNA’s output
impedance matching. The Image reject filter is usually realized as an off-chip passive component network
[39], which in turn puts the severity on the output impedance of the LNA to match to 50 ohm in order to
transfer the maximum RF signal power and this result in the trade-offs between the power dissipation,
noise-figure, stability and the gain [39]. Here it was described in brief the functionality, advantages and
disadvantages of a “Heterodyne Receiver”.
Figure 3.6: Dual-IF Heterodyne Receiver Topology [39]
The other type of receiver architecture is “Direct-conversion, Zero-IF, Low-IF or Homodyne” receivers in
which the RF signal is directly downconverted to the baseband levels. The LO frequency is chosen such
that it equal to Or approaches to the RF band center frequency, therefore mathematically it can be
RF
illustrated as ωLO ≐ ωCenter , which implies that the ω IF ≐ 0 , a block diagram representation of direct-
Alo cos(ωo t )
conversion receiver is shown in the Figure 3.7 below.
RF
ωo = ωCenter
Alo sin(ωo t )
Figure 3.7: A Direct-Conversion Receiver.
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An Oscillator System for UWB QDAcR
The Zero-IF topology results in reducing the design complexity by avoiding the use of Image reject Surface
Acoustic Wave (SAW) filter, which in turn eases out the severity of output impedance matching on the
LNA. Furthermore, by avoidance of SAW filters, the Zero-IF topology simplifies the possibility of
designing the front end as monolithic process (No off chip components). However, there are other kinds of
receiver topology specific severities that downgrade the performance of the Zero-IF receiver. These are as
follows:
DC Offsets & LO Leakage
Noise (Flicker) Issues
I/Q Mismatches
These direct-conversion receiver’s drawbacks are being analyzed in the perspective of the QDAcR, as
QDAcR architecture as shown in Figure 3.5 falls under the direct-conversion receiver’s category. The
functionality of the QDAcR at system level and circuit level, while taking components discretely is very
well described in [8, 19, 20 and 23]. As one of the primary objectives is to analyze the QDAcR as a fully
integrated receiver at the system level and for this purpose it is of utmost importance to first analyze the
architecture and find the possible bottlenecks and the corresponding solutions.
a) DC Offsets and LO Leakage: The DC offsets can corrupt the RF signal since the downconversion folds
the RF signal band around the DC and the centre frequency is shifted to “Zero”. Therefore, any data folded
around the DC levels could be corrupted in presence of unwanted products at DC or at quite low
frequencies and these unwanted signals are generated due to the phenomena of “Self Mixing” and Interferer
leakage [39]. The self mixing happens as the LO power leakage due to improper isolation between the LOLNA and LO-Mixer input ports, once the leaked signal (power) either enters the LNA or Mixer and it gets
mixed further and downconverted to near DC levels, which in turn corrupts the signal. The main reasons of
LO leakage are capacitive coupling, substrate coupling and bond wire coupling (in case of off-chip LO)
[39]. When a strong interferer (in-band poses more severity than out of band interferer) with its central
frequency close to LO frequency leaks through the LNA input port and in turn it mixes with LO signal and
producing a furthermore strong interferer at the DC levels. DC offsets is a major problem, which severely
degrades the performance of the homodyne receiver.
If we analyze DC offset effect in the context of QDAcR, we notice that the extent of severity is more than
any other normal direct-conversion receiver, because of the presence of primary and in-band interferers
with their center frequency close to the LO frequency. The degradation in the performance is measured as
the resultant of net BER ratio and the effect of interference is quantitatively shown in the [40, 23]. A novel
solution is also reported in [23], which is in form of a band-reject LNA with a simulated notch of 20dB
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An Oscillator System for UWB QDAcR
along with the 7th order transformer orthonormal-C band-reject filter with a 25dB interference rejection and
LNA+Band-Reject Filter in combination with an antenna having a notch of 15dB. The total interference
rejection reported by this combination is in the range of 35-60dB for IEEE802.11a/n WLAN.
The IEEE802.11a/n interferer sweeps across the entire band of 4.915GHz to 5.825GHz, with data
transmission in different channels depending upon the local regulations. Therefore, while doing the system
level analysis, it is considered the entire band of 910MHz ∼ 1GHz bandwidth as interferer band with central
frequency of in the range of 5.35-5.37GHz. Now if we extrapolate the results of [23] then we find that
combination of the antenna +B-Reject Filter +B-Reject LNA, gives the total maximum rejection
(simulated) of 15dB over the entire interferer bandwidth. Undoubtedly, this approach provides a novel
solution but still it lacks in providing the appropriate isolation for interferer leakage as well as LO leakage
(feed-through) to the antenna. The problem of interferer and LO leakage is circumvented with much more
effectiveness in heterodyne receiver topology by the use of Image reject filter in the LO-LNA path, which
increases the port to port isolation, while doing the filtering and second the LO frequency is not equal to the
RF signal center frequency. The solution to problem of DC offsets specifically in context to the QDAcR is
discussed in detail in the section 3.4, where the proposed solution is tested at the system level.
b) Noise (Flicker) Issues: As described in detail in section 2.4.1 the device flicker noise exists from a few
KHz to MHz and the device corner frequency increases with every decrease in the channel length in the
CMOS. Generally the received RF signals are in the order of +10dBm to -120dBm and as the signal is
converted to the DC in direct-conversion receiver, the downconverted band coinciding with the device’s
corner frequency becomes vulnerable of being corrupted. Therefore, a high gain is required in the
receiver’s front end architecture, as it can be seen from the Frii’s Noise Equation (given below) that the
gain ‘G’ is of prime importance in controlling the total noise Figure. The higher the gain, lower is the noise
Figure, and noise defines the minimum detectable receiver for the receiver system.
FTotal = F1 +
F2 − 1 F3 − 1
FN − 1
+
+−−−−−+
G1
G1G2
G1G2 − −GN −1
(3.3)
Therefore in the direct conversion receiver the gain of the front end blocks becomes more important in
order to reduce the overall noise effect of the system, the direct-conversion uses the single stage
downconversion to the baseband level, while in the heterodyne system couple or more downconversion
stage are used. Since each stage introduces some gain as well as noise, however the overall noise-figure is
less in heterodyne than the homodyne receiver.
c) I/Q Mismatches: As explained in the [39] the importance of the quadrature components especially in the
any other modulation scheme other than the amplitude modulation, therefore any mismatches between I
and Q signals corrupt the downconverted signal. The effect of phase error on the QDAcR is being explored
in the previous section and it is seen that the performance drastically deteriorates as the phase error
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An Oscillator System for UWB QDAcR
increases. Also, all the stages in the RF front end (LNA, Mixer, Oscillator etc.) add there own amplitude
and phase errors thus corrupting the signal. Therefore, the phase and amplitude errors arising due to I/Q
mismatches are important factor in the QDAcR performance.
3.3.1 Frequency Planning in QDAcR architecture
The frequency planning is the very first and a necessary step towards determining the receiver’s system
specifications, it gives the view of channel availability and interferer free region. In case of Ultra wideband
it is essential to know all the interferers and mitigate them through the receiver design and the signal
modulation techniques. Since UWB has a bandwidth of 7.5GHz, which makes it prone to wide number of
out of band and in-band interferers, a detailed analysis of all the possible interferers is presented here,
which lays the foundation of system specs as well as the desired receiver architecture. The following Figure
3.8 shows the possible interferes with their maximum possible signal power at the receiver’s end marked by
the various colored lines.
Figure 3.8: Showing the various interferers present.
The desensitization and blocking of the receiver happens when a strong interferer owing to the nonlinearity of the device / system decreases the average gain of the circuit. There are generally three different
types of non-linear effects seen in a circuit, these are as follows.
Harmonics: Any given function, which is Fourier series decomposable, when applied to a nonlinear system,
where the output is expressed as y (t ) = α 0 + α1 x(t ) + α 2 x 2 (t ) + α 3 x3 (t ) + .... show the frequency components
in the output, which are integral multiple of the fundamental frequency. If the amplitude (strength) of these
harmonics is high then by self mixing or through port leakage (as in the case of LO-LNA path) or mixing
with the RF signal, these harmonics create spurs and these spurs can easily desensitize the receiver, these
issues are major source of concern especially in “homodyne or Zero/Low-IF” receivers.
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An Oscillator System for UWB QDAcR
Cross-Modulation: This Non-Linearity arises when in a non-linear system; an amplitude modulated
interferer transfers the modulation to the desired RF signal. It is a third order non-linearity and is proved
mathematically in [39] and this effect the receiver’s dynamic range, with cross modulation corrupting the
RF signal in the channel. The receiver system with high IP3 and high linear mixer output also shows a good
resistance towards the cross-modulation.
Intermodulation: The Intermodulation is a process in which when two RF inputs are applied to the input of
any non-linear system then as a result there are components which are not the harmonics of the input
frequencies [39]. If we take the inputs to be at the frequencies ω1 & ω2 then the main third order
Intermodulated products occur at 2ω1 ± ω2 & 2ω2 ± ω1 frequencies and ratio of fundamental to the third
order non-linearities is described as the third order intercept point and is represented in the form of
IIP3(Input IP3) or OIP3(Output IP3). Similarly, the second order non-linearity is given by the
Intermodulated products occurring at the frequencies ω1 ± ω2 & ω2 ± ω1 . The level of the distortion
(compression in the output with respect to the input) in any circuit due to the third order and second order
Intermodulated products is given by the Figures of merits for circuits called IIP3 and IIP2. The
Intermodulated products falling in the RF band are called in-band interferers which cause more severity
than the out of band interferers that is the Intermodulated products falling outside the RF signal band. The
concept of Intermodulated products with mathematics in detail is explained in [39].
Pertaining to the UWB we can decipher from the above Figure 3.8 the number of interferers possible, the
number of possible third order and second order. With a possible of ‘341’ third order Intermodulated
products falling in the UWB band and a possible number of ‘262’ second order in band Intermodulated
product interferers. Therefore the interferers literary jammed the UWB band; however with proper
selection of the appropriate filter topology and proper QDAcR architecture topology can mitigate the effect
of most of these interferers.
If we see the Intermodulated product (both third and second order) tables we find that if the interferers with
frequency 3.7GHz and below are filtered out then the UWB can be free of almost 90% of the possible in
band interferers. Other most important source of interference is IEEE802.11a/n which sweeps bandwidth of
approximated to 1GHz, with centre frequency hopping around 5.35-5.37 GHz, therefore the oscillation
frequency is chosen in such a way that the major interferers can be downconverted to the DC levels and
then can be easily filtered out. Therefore the present QDAcR architecture definitely requires some
additional changes in order to meet the basic specifications for the in band communication. The possible
solutions are discussed in detail in the next section.
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An Oscillator System for UWB QDAcR
3.3.2 The Noise Block
This block is modeled to calculate the desired Noise Figure of a circuit, to find the desired value in order
achieve the proper level of correlation. The Noise Figure is one of the important parameters for measuring
the system’s performance. The noise Figure ‘NF’ mathematically is given by
NF =
SNRin
; SNRin ≥ SNRout
SNRout
(3.4)
The noise produced in an active circuit is both device parameter and bias dependent, which is hard to model
in matlab without knowing the bias conditions and device in use. Therefore, the active circuit is treated as a
noiseless black box and all the noise is referred to the input of the two port network [39]. In the Figure 3.9
below it is shown that the total increase in the input noise floor is equal to the “Noise Figure” of the that
particular, the variable ‘F’ is the ‘Noise Factor’.
Figure 3.9: Modeling of Noise
In MATLAB the noise source is taken as an Additive White Gaussian Noise Channel (AWGN) which
covers all the thermal and shot noises. The input level of noise Nin is calibrated to the receiver’s thermal
noise floor (minimum noise present in the receiver chain) and the output level of the noise N o is calibrated
as per the desired “Noise Figure”. The block is easily integrated into any of the circuits (for e.g. LNA,
Mixer, Amplifier) and enabling the measurement of the output for the desired Noise Figure.
Figure 3.10: Modeling of Noise Block in MALAB
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An Oscillator System for UWB QDAcR
3.4 Designing of the Quadrature Downconversion Auto
Correlation Receiver (QDAcR) in MATLAB
The QDAcR is modeled is fully in the MATLAB in order to find the complete system specifications under
the realistic circuit operating conditions, while taking care of the possible bottlenecks. For, this purpose
first task is to describe the Matlab model for the QDAcR (old architecture) which is as shown in the Figure
3.11. The different blocks in the model are described in the detail in the following section, first the system
specification are calculated and then the proposed changes at block level are described, which in end lead
τd
τd
to a composite renewed architecture for the QDAcR.
(∑)
(∫)
Figure 3.11: QDAcR Block Diagram Representation
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An Oscillator System for UWB QDAcR
1. The RF Input Block: The foremost task is to define the specifications for the received radio signal, as the
accurate signal modeling serves as the start point for further system calculations. This block replicates the
RF-Input from the antenna as in the case of ir-UWB communication system. The block implements a few
nano-pico second pulses as the received RF-Signal; the strength of the received RF signal for the modeling
and link budget analysis is calculated using the formula as given in [41] and reproduced below. According
to the FCC the maximum emissions level in UWB is -41.3dBm/MHz therefore taking the maximum
transmitted power to be PT = −41.3 + 10 log( f H − f L ) dBm
PR = PT + G T.ANT +L P + G R.ANT dBm
(3.5)
Where PR =Received input power of RF Signal, G T.ANT =Gain Antenna at transmitter side, G R.ANT =Gain
Antenna at the receiver end and L P =Path Loss or the amount by which the signal strength has deteriorated
due to interference, continuous reflection and other effects. The value of path loss is given by the following
Equation as
4π f c
L P = 20 log
+ 20 log( d )[dBm]
c
(3.6)
Where d= Path Length in meters and c=Speed of light. Since the bandwidth of UWB is 7.5GHz, which
ranges from 3.1-10.6GHz and is characterized as IEEE802.15.4a. The UWB centre frequency is given by
the f C =
f L . f H =5.732GHz, where ‘ fC ’ is the geometric mean [41] or if taking arithmetic mean then it is
fL + fH
=6.85GHz. Second approximation is about the path length ‘d’, the main purpose of UWB is to
2
work as short distance radio and it is shown in the Figure 1.8 as the relation between the through put and
distance. Therefore, calculating the received power for d= [5, 10, 20] m. Approximating antenna gains (Rx
& Tx) to be ‘zero’; therefore we have
PR 5 = −64.1367dBm
PR10 = −70.1573dBm
(3.9)
PR 20 = −76.1779dBm
As it can be discerned relatively easily that power received at the Rx end decrease with increase in the path
length and also the through put decreases with increase in distance.
For, the modeling of the input RF-Signal, the worst case scenario is used while considering the 20m path
distance and further calculating the minimum level of signal that can be detected (MDS) and it given by
MDS = −174dBm + 10 log B + NFsys
(3.10)
As the starting point for the calculations, first the value of receiver’s noise-figure has to be calculated. The
thermal noise floor of the UWB receiver is -75.249dBm (considering the total bandwidth of 7.5GHz), this
shows that the desired RF signal is already buried inside the noise-floor. If the receiver’s own noise is
added to this value it further deteriorates the problem posing designing complexities, for the desired
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An Oscillator System for UWB QDAcR
processing of the signal the front end needs to have lowest noise-figure as well as high gain for the
attaining the proper signal levels for the Analog to Digital Converter Input stage. Therefore, a trade off
between the system gains, system noise Figure as well as the total power consumption has to be devised.
Approximation for the receiver’s Noise Figure (NF): first up, the noise contribution from the primary
candidates (most noisy) Mixer and LNA is considered. For this purpose first approximating the mixer’s
specifications as given in [42, 43], the reported noise-figure varies with the frequency, going up as the
frequency increases, therefore sticking to the center frequency of 5.732GHz and doing all the calculations
at this frequency. Therefore as in [43] the NF is averaged to be 17dB, with a conversion gain of around
5.5dB, in [42] the reported noise Figure is about 7dB with a conversion gain of around 2.5dB. The two
mixers, which are quoted as referenced are designed in two different circuit topologies and assumptions.
For the calculation and requirement of the QDAcR, we have to go with a HIGH-Gain Active mixer, which
results in a relatively high noise Figure. Therefore, with some more margins taking noise Figure of mixer to
be ≈ 20dB, the net value of the noise Figure seen at the receiver’s antenna end is given by the Frii’s noise
Equation, by which having a high gain LNA becomes a necessity.
A few good reported UWB LNAs are [p.139 of 23], with the highest gain of 19 ± 2 dB in [23-[121]] and
lowest NF of 2.51 ± 0.47 dB [23-[114]]. Since the gain and the noise figure, which are reported happen to be
technology and circuit design dependent, therefore it is not wise to average any of the required parameters,
however this provides hint to have approximated gain value (the mode value) which is around 16.5dB and a
maximum noise Figure of 4.5dB. Taking these as the approximated values (starting point) the total noise
Figure approximated by the Frii’s Equation is NFsystem = 10dB (2dB Duplexer + 7.96dB from LNA+Mixer).
Therefore the value of maximum detectable signal is -65.25dBm or higher, therefore for distance of
5meters or less UWB proves to be a useful communication in comparison to various existing platforms.
However, designing system for 20meters distance with a maximum signal level of -76.18dBm, to this
adding an extra margin of 10dB for other circuit and process related irregularities such as transmitter
leakage to the receiver, effect of parasitic, signal loss due to jamming etc. therefore for calculation taking
the received signal value to be -86.18dBm. Next step is to define the total receiver gain, which will define
the level of input for the ADC stage. Considering the input levels of ADC in the order of a few hundreds of
mV [atmel], and approximating the value to be around ±250 mV or +1dBm. Therefore the total desirable
receiver gain = 87.2dBm to be a minimum.
There are many different pulses reported as carrier/signal for ir-UWB system, modeling and testing of
some of them is presented here in order to find which pulse performs the best for the QDAcR. Matlab
model of QDAcR is modeled with the different pulses as RF-Signal inputs, these pulses are namely
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An Oscillator System for UWB QDAcR
Gaussian, Gaussian Mono, Gaussian Doublet, Sinc function, Mortlet Wavelet of Gaussian and Daubechie’s
Wavelet of Gaussian.
a) Gaussian Pulse: The Gaussian Pulse is given by g (t ) =
1
2πσ t
e
t − µt
−
2σ 2
t
, where the width of the Gaussian
pulse is given by ‘ σ t ’ and the value of ‘ µt ’ is the mean and it signifies the position of axis of symmetry.
According to [23] Gaussian pulse has good time-frequency resolution however poor spectral efficiency.
The Figures below show the transient and power spectral density of a Gaussian pulse, for σ t =.1e-09 and
time period of 1nsec. The PSD diagram shows the output from
− fs
2
, 0,
fs
2
Gaussian can be changed by changing the σ t .
Figure 3.12: The Transient levels of Gaussian Pulse
Figure 3.13: The PSD levels of Gaussian Pulse
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, the bandwidth of the
An Oscillator System for UWB QDAcR
It can be seen that the signals levels are well below the FCC limits and if the point of pulse origin is shifted
form negative axis to the origin or to 3.1GHz, the Gaussian covers a bandwidth of approximately 11GHz,
which covers the entire desired band from 3.1GHz-10.6GHz. The bandwidth is a function of sigma; it
shows that by choosing the appropriate variance a better spectral efficiency for the desired bandwidth can
be attained. The Figures 3.14 and 3.15 below shows the bandwidth of around 7.5GHz (axis can be shifted
to 3.1GHz by changing the mean of the Gaussian) covering the entire Ultra Wideband and signals levels ≤ 86.2dBm for σ t =.205e-9
Figure 3.14: The PSD levels at σ t =.205e-09
Figure 3.15: Transient response of the Gaussian for σ t =.205e-09
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An Oscillator System for UWB QDAcR
b) Gaussian Mono or First Derivative of the Gaussian Pulse is also widely used as a carrier for the ir-UWB
systems. The PSD and transient response of the Gaussian mono pulse are shown in the Figures 3.16 and
3.17 below. The bandwidth is adjusted to meet the UWB requirement and provide, higher spectral
efficiency by providing a higher roll-off at the ends of band. This can be seen as over the half bandwidth
the Gaussian mono provides the fall of over-60dB, which is 20dB greater than the provided by the
Gaussian or Gaussian Doublet.
Figure 3.16: The PSD levels of Gaussian Mono Pulse
Figure 3.17: The Transient levels of Gaussian Mono Pulse
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An Oscillator System for UWB QDAcR
c) Gaussian Doublet or Second Derivative of the Gaussian Pulse is used as a carrier for the ir-UWB
systems. The PSD and transient response of the Gaussian doublet pulse are shown in the Figures 3.18 and
3.19 below, the bandwidth is adjusted to meet the UWB requirement by varying the σ t and provide, higher
spectral efficiency by providing a higher roll-off at the ends of band in comparison to the simple Gaussian.
Figure 3.18: The PSD levels of Gaussian Doublet Pulse
Figure 3.19: The Transient levels of Gaussian Doublet Pulse
The Daubechie’s, Morlet and Sinc function are modeled in the matlab as the wavelet. The design principle
for the wavelet based filters is explained comprehensively in [23]. The typical flowchart involves the
following stages in respective order [23]. Starting with the Polynomial Approximation, 2) Laplace
Transformation, 3) Rational Approximation, 4) State Space Optimization and 5) Designing of the desired
transfer function on to the silicon. The transfer functions for Daubechie’s and Morlet Wavelet are taken
from [44, 23] and the coefficients of the state spaces elements are changed in order to comply to the
QDAcR system design.
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An Oscillator System for UWB QDAcR
The generalized model used in the Matlab modeling for these wavelets is shown in the Figure 3.20 below.
When the Unit Impulse is multiplied with the Gaussian function, it provides the impulse output which has
Gaussian distribution, this replicates as the Gaussian Envelope for the transfer function and desired wavelet
output is achieved.
1; x = 0
0; x ≠ 0
δ ( x) =
H (s) =
G (t )
p0 + p1 s + p2 s 2 ...... pm s m
q0 + q1 s1 + q2 s 2 + ......qn s n
( x n1 , ....., x nk )
µ = 0;σ
2
= 1
Figure 3.20: Block Diagram for the Wavelet Modeling
d) Daubechie’s Wavelet: The transfer function of the Daubechie’s is taken directly from the [23], the coefficient of state space matrix are found by Matlab command. The co-efficient are multiplied by constants
to have entire bandwidth response. The values are as follows
[A]: [0 2.066e11 0 0 0 0 0 0; -2.66e11 0 3.146e11 0 0 0 0 0; 0 -3.146e11 0 3.399e11 0 0 0 0; 0 0 -3.399e11
0 3.531e11 0 0 0; 0 0 0 -3.531e11 0 4.016e11 0 0; 0 0 0 0 -4.016e11 0 5.297e11 0; 0 0 0 0 0 -5.297e11 0
10.74e11; 0 0 0 0 0 0 -10.74e11 -17.99e11].
[B]: [0; 0; 0; 0; 0; 0; 0; 2.393e11]
[C]: [.9831 .3831 .02877 -.179 0.1166 -.02037 0 0]
[D]: [0]
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An Oscillator System for UWB QDAcR
Figure 3.21: The Transient levels of Daubechie’s Wavelet.
Figure 3.22: The PSD levels of Daubechie’s Wavelet.
e) Morlet Wavelet: The co-efficient of state space matrix [A,B,C,D] are given below. The following
Figures 3.23 and 3.24 show the PSD levels and the transient response of the Morlet Wavelet Function.
[A]: [0 2.649e11 0 0 0 0 0 0 0 0; -2.649e11 0 7.412e10 0 0 0 0 0 0 0; 0 -7.412e10 0 2.669e11 0 0 0 0 0 0; 0
0 -2.669e11 0 1.102e11 0 0 0 0 0; 0 0 0 -1.102e11 0 2.58e11 0 0 0 0; 0 0 0 0 -2.58e11 0 1.575e11 0 0 0; 0 0
0 0 0 -1.575e11 0 2.539e11 0 0; 0 0 0 0 0 0 -2.539e11 0 2.381e11 0; 0 0 0 0 0 0 0 -2.381e11 0 4.24e11; 0 0
0 0 0 0 0 0 -4.24e11 -5.391e11]
[B]: [0; 0; 0; 0; 0; 0; 0; 0; 0; 8.303e9]
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An Oscillator System for UWB QDAcR
[C]: [0.75 -1.34 0.75 0.68 -0.57 0.44 -0.002 -0.1 0.04 0]
[D]: [0]
The Equation of the morlet wavelet filter is given by Equation 3.11 below and it is obtained by multiplying
a Gaussian envelope with the cosine function.
ψ (t ) = cos(5 2(t − 3))e − (t −3)
2
(3.11)
Figure 3.23: The PSD levels of a Morlet Wavelet Function
Figure 3.24: The transient levels of a Morlet Wavelet Function.
f) SINC Wavelet Function: The co-efficient of state space matrix [A,B,C,D] of a Sinc function are given
below. The following Figures show the PSD levels and the transient response of the Sinc Wavelet
Function.
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An Oscillator System for UWB QDAcR
[A]: [0 1.59e11 0 0 0 0 0 0 0 0 0; -1.59e11 0 2.357e11 0 0 0 0 0 0 0 0; 0 -2.357e11 0 3.09e11 0 0 0 0 0 0 0;
0 0 -3.09e11 0 3.567e11 0 0 0 0 0 0; 0 0 0 -3.567e11 0 3.67e11 0 0 0 0 0; 0 0 0 0 -3.67e11 0 3.796e11 0 0 0
0; 0 0 0 0 0 -3.796e11 0 4.301e11 0 0 0; 0 0 0 0 0 0 -4.301e11 0 5.45e11 0 0; 0 0 0 0 0 0 0 -5.45e11 0
8.061e11 0; 0 0 0 0 0 0 0 0 -8.061e11 0 17.72e11; 0 0 0 0 0 0 0 0 0 -17.72e11 -30.53e11]
[B]: [0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 3.118e11]
[C]: [.9909 -.6302 -.1765 .781 -.4091 -.2802 .2825 -.01653 .04606 0 0]
[D]: [0]
The Equation of the Sinc wavelet function is given by Equation 3.12 below as
ψ (t ) =
sin(π t )
πt
(3.12)
Figure 3.25: The PSD Levels of a Sinc Wavelet Function
As it can be discerned from the above Figure that among all the wavelet and normal Gaussian functions
plotted and tested for the RF signal, the Sinc function has the highest spectral efficiency. It can be seen that
the decay of 50-60dB over a bandwidth of 4GHz can be used for the system design advantage for example
where high roll-off is required in the filter response. In [23] it is mentioned that Sinc wavelet has a ‘Brick
Wall’ kind of response, which is ideally suitable for the UWB communication system. The Transient
response of a Sinc function is shown in the Figure 3.26 below.
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An Oscillator System for UWB QDAcR
Figure 3.26: The transient Levels of a Sinc Wavelet Function
2. The Narrow Band Interferers (NBI) and White Noise Block: Through this block the effect of the channel
white noise and the interference induced by the Narrow Band signals such as Wi-Max(2.3GHz-2.7GHz &
3.3GHz-3.7GHz), IEEE 802.11b/g and 802.11a/n standards is being applied to the receiver system design.
As postulated by the [40] that these interferes further corrupts the quality of the desired Radio Frequency
(RF) signal and as a result the final RF signal at the input of the Low Noise Amplifier (LNA) can be
mathematically denoted by the following Equation
r (t ) = s (t ) + n(t ) + i (t )
(3.13)
Where r (t ) , s(t ) , n(t ) and i(t ) denotes the resultant (Corrupted + Noisy) RF input at the LNA, the UWB
signal, the Gaussian white noise and the narrow band interferes respectively. The effect of narrow band
interferes can be modeled as a correlation between the narrow band signal interferes i (t ) and UWB
signal s(t ) , narrow band signal i (t ) and the noise n(t ) and the (auto) correlation between the narrow band
signal i (t ) itself. The following are expressed numerically as µ (is ) , µ (in ) & µ (ii ) respectively, the severity
caused by the narrowband interferes and noise in the ir-UWB receiver’s performance is appropriately
measured in terms of the Bit Error Ratio (BER) as given in [40]. The results deduced in [40] shows
that‘ µ ( in ) ’ or the correlation between the narrow band interferer and the Gaussian random noise,
downgrades the performance of the receiver severely than any other interference/signal//noise correlations
that is µ (is ) or µ ( in ) , the severity effect on the performance of receiver can be characterized as
µ (in ) > µ (is ) > µ (ii ) . This result shows that it is necessary to filter out the narrow band interferes before
performing the auto-correlation of the received signal. The narrow band interferes can be modeled
mathematically as sinusoid signal with a complex envelope function ‘ u (t ) ’, which remains constant for the
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An Oscillator System for UWB QDAcR
{
}
entire UWB symbol duration [23, 40]. Mathematically it is given by i (t ) = 2 Re u (t ).e j 2π fint t ,
where u (t ) = u (t ) e jφu (t ) is a low-pass function for the narrow band interferer function ‘ i (t ) ’, the interferers
can be filtered out by modeling them as real band-pass signals with central frequency ‘ f int ’ and
bandwidth B & B ≪ W , where‘ W ’ is UWB Bandwidth. Considering the NBI sinusoid function i (t ) ,
putting the values for IEEE standards 802.11a/b/g/n in the Equation 3.14.
{
i (t ) = 2 Re u (t ).e j 2π fint t
}
(3.14)
The NBIs are modeled as the impulse response of a filter, the exact function is constructed by defining the
transfer function ‘ H ( s ) ’. The transfer function is calculated according to the algorithm described in [23],
the transfer functions for IEEE802.11a/b are calculated and implemented in MATLAB in order to replicate
the exact NBI responses, the effect of thermal noise / channel white noise floor is added to total noise
output. The Wi-max interferer is also modeled based on the above Equation as a sinusoid. The Figure 3.27
below shows the matlab model of the ‘Interferer - Noise’ Block. The interferers’ output level is quantized
to the -10dBm level for 50ohm impedance (this to analyze the QDAcR in the worst case scenario, as typical
interferer power is between -30dBm to -80dBm levels), the noise floor / receivers’ noise floor is modeled
for entire 7.5GHz bandwidth‘ (∆f ) ’.
Figure 3.27: The Block Diagram for the Implementation of the Interferers
The Figure 3.28 below shows the output of the interferer block; the NBIs are shown, first the zoom picture
of OFDM 802.11b, then 802.11a and the white noise as thermal noise floor.
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An Oscillator System for UWB QDAcR
Figure 3.28 Matlab Noise Model Output showing the main interferers and the Thermal Noise Floor
3. Filtering Stage: As seen in the QDAcR linearity analysis that the UWB system suffers severely from the
interferers and most of the in-band interferers are the Intermodulated products of mainly Wi-Max and
IEEE802.11a/b/g/n communication standards with other 16 possible interferers. Therefore, for the proper
functioning of the QDAcR it is very necessary to filter out the interferers. As discussed before that the
solution proposed in [23] offers a maximum of around 35-40dB rejection for the W-LAN interferer and
then downconverting the entire band by wrapping the spectrum around the baseband and filtering the main
downconverted interferers by using a Band pass filter. However, the existence of Wi-Max interferer and
Intermodulation due to device non-linearity makes it impossible to have an interferer free baseband signal.
In broad terms the published work on QDAcR is a good design proposition, however if we see the possible
interferer table (2nd and 3rd Order interferers), then we find that even after the downconversion and filtering,
most of the baseband spectrum is full of Intermodulated interferers. It is of utmost necessity to filter the
major interferers before they can enter LNA, otherwise it will not only put high linearity requirements on
the LNA but result in complex design and higher power consumption. and importantly a low “Q” with
respect to passives, also in active filters there is a possible chance of direct interferer leakage.
Therefore, here now is proposed a band-pass filter with the system level simulations, showing its
advantages as well as the possible drawbacks. Taking the all the interferers from 450MHz (GSM) to
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An Oscillator System for UWB QDAcR
3.7GHz (Wi-Max) and their possible 2nd order and 3rd order modulated effects. The first approach is to
block all these interferers entering the device and having any Intermodulated products, hence having a
band-pass filter in between the antenna and the LNA. The BPF should have steeper transition and should
offer as high rejection as possible and as flat as possible output over the entire bandwidth. Here it is
required a wideband BPF, choosing the lower passband frequency to be 3.7GHz and upper frequency to be
10.6GHz. It can be seen that by choosing the lower cut-off frequency to be 3.7GHz a UWB signal
bandwidth of around 600MHz is lost, however it is necessary in order to make receiver operable and to be
robust.
The filter needs to stop all the interferes from 0Ghz-3.8GHZ range, providing the maximum rejection
possible, the passband exists from 3.8GHz-10.6GHz, with a wideband notch at 5GHz-6GHz that attenuates
the WLAN interferer as much as possible. It is necessary to attenuate these major interferers entering active
device circuitry in order to circumvent the number of internmodulated products and keep the
downconverted band clean. The possible candidates are only passive filters, which are SAW (surface
Acoustic Wace) filter (off-chip) and Microstrip Filters; use of active filter is ruled out, because of the
requirement of the high levels of band rejection and as low as possible insertion losses, which translates
into a filter with a high ‘Q’ quality factor. Also for large bandwidth response active filters show poor
linearity, noisier (because of the accumulation of device noise) and consume higher power.
.
The effect of phase distortion in QDAcR is modeled using matlab and is depicted in the Figure below. This
graph represents the maximum phase distortion that can be tolerated with in QDAcR, the assumption that is
made during the modeling of the phase distortion is as follows: All the components are ideal, including the
delay block. The consideration of the delay block being ideal is justifiable because of we see the QDAcR
architecture it can be noticed that the correlated UWB pulses are subject to same frontend signal
processing, only distinction being the that one is delayed by the delay block and its replica is delayed in the
transmitter. The discernable information form the graph below is that maximum tolerable single-ended
phase error of 24degrees is permissible for auto-correlation coefficient of 0.85.
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An Oscillator System for UWB QDAcR
Figure 3.29: The Phase Distortion vs. Auto Correlation Graph
The next estimation for the total phase distortion is to subtract the feasible quadrature phase error between
the In-Phase and Quadrature responses from the maximum permissible phase error of 22.8 degrees. As it is
proved in the section 2.3 that the maximum allowable phase error between I/Q responses is 8.75 degrees
and it can be curtailed down by designing a good Q-VCO. Therefore as a design parameter for the circuit
designer fixing the maximum allowable quadrature phase error to be 5 degrees or less, this will result in
fixing in single ended permissible maximum error to be 20degrees. Therefore, the maximum composite
phase error for the Delay block, Mixer, LNA and filter stages is 20degrees.
The next step is to choose the topology for the band pass filter and the candidates are Chebyshev Filter
(Type1 and Type 2): Both kind of chebyshev filters are considered for the system topology, as these both
provide distinctive advantages. Type 1 has the high roll off, however more flatness in the passband is
observed in the Type 2 filter. There exist a ripple in the stopband in the type 2 topology, however by
deciding the lower band and upper band cut-off frequencies carefully; the ripple can be turned out to be
advantageous in improving the spectral efficiency as in the case of multiple-wide band rejection. The phase
distortion or the group delay in the Chebyshev filters is on the higher side in comparison to the Butterworth
and Bessel filters
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An Oscillator System for UWB QDAcR
Elliptic Filter: These filters provide steeper transition from passband to stopband in comparison to the
Chebyshev filters. The phase distortion is the highest in the elliptic filters, when compared to the Bessel,
Butterworth and Chebyshev filters, therefore it will put additional burden on the time delay accuracy
required in the QDAcR.
The next step requires choosing the implementation of the filter using the passives. As mentioned earlier
that the specifications required for the bandpass filter can be matched either by the Microstrip
(Transmission Line) filter or SAW-Passive filters. The choice is a Microstrip (Transmission line) Bandpass
Filter, in which the passives or lumped elements can be implemented using the Microstrip line as stubs or
transmission line resonators etc. The choice of using Microstrip filter is a conducive one as it offers the
lowest insertion loss possible, which helps the low RF signal levels from having much more attenuation,
thus relaxing the power-Gain budget for the subsequent active stages in the circuit. As reported loss of
0.58dB in [45] and of 2dB [46] across the complete 7.5GHz bandwidth in comparison to insertion loss of 89dB over a narrowband [23]
The Microstrip / transmission line filters offer high Rejection in comparison to its other counterpart
topologies, the QDAcR system requires to have highest possible rejection in the stopband, as it is seen in
[45, 46, 47] that a rejection levels of 30-50dB are quite achievable.
Power consumption in Microstrip filters is less and the signal power is delivered to the load much more
efficiently than other implementable filter designs for e.g. the active filters; this is because of the precise
input/output impedance matching to the antenna and LNA.
Use of Microstrip line with RF-MEMS as described in detail in [48] offers the far better solution than the
other implementation methods. It offers a high ‘Q’, high linearity and less power consumption. In the
context of QDAcR the phase distortion plays an important role, the main principle of Auto Correlation
relies on the accuracy of the time delay with respect to the transmitted signal. Therefore, the phase error
which is imparted by any of the frontend stages puts an extra burden on the time delay as well as reduces
the level of the correlation. In transmission lines the delay is less and much more quantifiable than passives
implemented as lumped elements, because lumped element system or even monolithic passives are
susceptible to higher degree of process variation or ambient conditions than the Microstrip line filters.
The Microstrip line or Microstrip line +RF-MEMS turn out to be a suitable solution for implementing the
BPF, however implementing the BPF this way do have some drawbacks. The primary drawback is off the
chip implementation, this brings in the issues of bondwire passives and IC packaging and housing, signal
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An Oscillator System for UWB QDAcR
corruption and other non-linearities and non-uniformities into the context. However, a careful
understanding of these issues while designing the subsequent stage (LNA) is applied then the effect of
these non-uniformities can be mitigated to certain extent. These non-uniformities play similar role in any
other lumped element filter, therefore under the circumstances it can be discerned that the performance and
requirement met of Microstrip line filter suits more than the any other implementation method.
At the system level looking at the specifications requirement Vs the choice of topology, a comparison is
made between the chebyshev and elliptic filters and is modeled in MATLAB.
1. Chebyshev (type2, order 8): In the Figures 3.30 and 3.31 below, we see the PSD of in-band interferes,
which are Wi-Max and IEEE802.11b/g and Bluetooth and IEEE802.11a/n or WLAN. The maximum level
of interferer signal at the antenna is taken to be -10dBm . The filter is modeled for the rejection of 50dB
and it can be seen from the response that in the bandpass filter only a notch of around 15dB (total of 65dB)
in addition to the overall rejection.
Figure 3.30: The Total Noise PSD levels for UWB (In-Band and Out-Band both)
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An Oscillator System for UWB QDAcR
Figure 3.31: The Total Noise PSD levels after the Filtration for UWB (In-Band and Out-Band both)
2. Chebyshev (type1, order 8): Taking the same input conditions as in the previous case, for the interferers;
modeling the filters based on the Chebyshev Type1 function.
Figure 3.32: The Total Noise PSD levels for UWB (In-Band and Out-Band both)
In the Figure 3.33 below the filtered response of Chebyshev-1 is shown, if compare the two responses we
find that the notch has significantly disappeared and also the rejection is 30dB@ Wi-Max and
IEEE802.11b/g and Bluetooth, while due to the implementation of a wideband notch the rejection levels
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An Oscillator System for UWB QDAcR
drop to 50-60dB. This topology also provide the desirable rejection however the simulated value
comparison makes Chebyshev-2 a better choice than the Chebyshev -1
Figure 3.33: The Total Noise PSD levels after the Filtration for UWB (In-Band and Out-Band both)
3. Elliptic Filter (Order 8): Testing and analyzing filter response of an elliptic filter and comparing it with
previous responses. Since the PSD levels of the total interferes (noise) are the same, therefore just the
filtered response of the Elliptic Filter is shown in the Figure 3.34 below. The analyses of the response
shows that Elliptic filter does provide the faster roll-off from stopband to passband than the Chebyshev
filter, however the attenuation obtained is low and typically comparable to Chebyshev-1 response.
Therefore the simulation results show that the appropriate choice of filter would be a Chebyshev-2 type.
The filters in general can be further refined from the basic system level design by using the algorithm
devised for the orthonormal filters using the wavelets [44, 23]. This algorithm focuses on the optimization
of the filter response in frequency domain by windowing the response using the wavelets and finding the
more optimized scalar coefficients. But, the application of this algorithm for the wideband BPF system will
not be as useful as for the narrowband filtered response, despite the fact that the windowed responses can
be scaled up and down using a constant factor. This scaling factor if raised in its value in order to
compensate the entire 7.5GHz bandwidth then it effects the ‘resolution’, that is trade-off within degree of
optimization and the filter response. Therefore, a conventional and optimized Chebyshev-type2 filter is
proposed for the bandpass filter. The primary objective of the proposed BPF is to shield the active front end
from all the interferers (most rejection for interferers till 3.7GHz) and the any development of the
Intermodulated products. Looking from the circuit level aspect, the use of filter between the Antenna and
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An Oscillator System for UWB QDAcR
LNA, will not only solve the major problem of the interferers to a higher degree, but will also provide
isolation for the LO and interferer feedthrough, which is of concern in the
direct downconversion
topology.
Figure 3.34 The Total Noise PSD levels after the Filtration for UWB (In-Band and Out-Band both)
3.1 Band Reject Filter (5GHz-6GHz stop band): In this section a second filter is proposed at the system
level, the proposed band reject filter is to be placed after the LNA. The function of this filter is to provide a
notch or have a stop band in 4.9-5.9GHz frequency range. The topology and requirements for this filter are
very much similar with the propose Band Pass filter, apart from the functionality that here a band reject
filter is proposed.
The other big merit of this design apart from cleaning the UWB signal is to increase the port to port
isolation between the LO and the LNA port. When the stop band reject be implemented than the LO, whose
oscillating frequency is inside this region sees highest rejection or port to port isolation on its feedthrough
path towards the antenna and LNA. Also implementing filter separately will provide further head room to
increase the gain of LNA , with less design complexity and less power consumption also.
The Time and Frequency domain interplay: The uniqueness of ir-UWB relies in the principle that pulses of
nano-pico seconds duration in time domain, when seen in the frequency domain covers a wideband. The
pulses are modulated and shaped specifically in order to meet the FCC mask requirements and cover the
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An Oscillator System for UWB QDAcR
entire bandwidth of 7.5GHz. The area under the PSD curve shows the total energy associated with the
signal and when a signal is processed the total area under the curve changes. The signal processing in the
receiver’s frontend as well as any other electrical circuitry happens in the time domain and its effect is seen
in the frequency domain, after expressing the signal in the form of its Power Spectrum. This interplay
between time and frequency domain can be used advantageously in order to process, shape or code the
information in a signal in an efficient manner. As explained earlier the necessity of filtering received UWB
signal, this step does helps in making the received signal free from the interferers but at the cost of loss of
information.
The selection of lower cut-off frequency for the band-pass filter around 3.7GHz is necessary; however, this
results in the loss of the information between 3.1GHz to 3.8GHz frequency levels. Similarly, the filtering of
IEEE802.11a/n interferer through the band-pass filter, antenna and LNA + Band-reject filter [23] results in
the loss of information between the 5GHz to 6GHz frequency levels. If we see the PSD graph of any of the
pulse used as a signal/carrier in ir-UWB, it is evident that the major concentration of signal power spectrum
is central bound that is concentrated around the UWB band central frequency. Therefore, the major portion
of the coded information, which exists in 5GHz -6GHz frequency range is also filtered out along with the
interferer. The Figure 3.35 below shows the filtered PSD levels and loss of information during filtering of
the interferers.
Figure 3.35: UWB Spectrum after bandpass filter
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An Oscillator System for UWB QDAcR
The one and most rational solution to this problem is to have a proper pulse shaping and modulation
scheme in the time domain, which when plotted in frequency domain shows a possible notch or low PSD
levels in the 5GHz to 6GHz frequency region. This recommendation if implemented will not only help the
information from getting lost but it will also provide a great ease in the filtering of the existing interferers in
the specified bandwidth and also alleviate the problem of the DC-offsets, which significantly degrade the
performance of the QDAcR or Homodyne receivers in particular. As described in section 2.2, the QDAcR
employs the principle of band downconversion by using LO and this principle results in the form of
convolution of all the information present around the LO frequency to the DC levels, which is then lost and
filtered out unprocessed by the subsequent band-pass filter stage.
The composite effect of the bandpass filter after the antenna and a band stop filter after the LNA and proper
pulse shape modeling results in the processing of a higher amount of the stipulated 7.5GHz bandwidth in
comparison to the QDAcR proposed in [8]. Considering the LO frequency to be the same 5.5GHz as given
in [lee-bgga] then the UWB band is downconverted from DC to 5.1GHz. and the WLAN interferer shifted
between DC to 500MHz range. If downconverted band is filtered by another bandpass filter or a highpass
filter with lower rejection frequency to be 500MHz, then we achieve a bandwidth of 4.6GHz to process,
which is a significant increase of 105% more information bandwidth then the previously proposed QDAcR
architecture.
4. The Oscillator Block: In this section, application of previously described MATLAB model of LO is
presented. This section precedes the LNA modeling, as firstly the main objective of this thesis is to model
an oscillator for the QDAcR, find the desired phase noise for various pulses. Followed by narrowing down
on the choice of the pulse for further modeling and transfer the system level specifications into a circuit. In
section 2.4 & 2.5 the mathematical modeling of an oscillator in MATLAB has already been described in
detail and in this section the LO is tested for different pulses, to find out the lowest phase noise
requirements for QDAcR in order to have a desirable Auto-Correlation levels. The desired phase noise is
induced by controlling the timing jitter variance for the AWGN channel, the Phase Noise vs. Auto
Correlation graph is plotted which signifies the importance and requirements of phase noise in QDAcR.
First step in simulation is to zero upon the frequency of the oscillation. This decision is influenced by the
following factors, position of the interferers and their Intermodulated products, the central frequency of the
UWB Bandwidth, which is 5.733GHz and the specifications of the succeeding bandpass filter stage after
downconversion. Looking at the interference table it is visible that the main in-band interferers is WLAN
(considering that all other interferences are filtered by the BPF after the antenna and so are their possible
Intermodulated products) and that the WLAN as well as possible second order products reside in the 5GHz
to 6GHz frequency bandwidth. Therefore, the appropriate frequency turns out to be 5.5GHz which will put
the interferers and Intermodulated products in between DC and 500MHz band. Considering the second
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An Oscillator System for UWB QDAcR
dominant factor of the central frequency which is 5.733GHz, the central frequency is important as the
information band should be downconverted equally on both sides of the DC; otherwise its consequences
will be seen in the circuit designing. As most of the circuits are designed based on the specifications, which
are derived from the modeling of the Single Sideband Spectrum (SSB), also because of unequal distribution
the performance of the QDAcR (Homodyne) receiver will degrade. The difference between the central
frequency and 5.5GHz is 233MHz, in order to divide this difference equally across the DC the LO
frequency should be equal to 5.615GHz.
f LO =
( f mid −band − f c )
2
+ f mid −band , where f mid − band = 5.5GHz & f c = 5.733GHz , therefore f LO = 5.615GHz .
The next step involves finding the appropriate phase noise that QDAcR can tolerate, while having auto
correlation of 85% or more. The significance of phase noise has already been explained in detail in the
previous sections throughout this chapter, from the circuit designer perspective phase noise holds
prominent importance in LO or transceiver circuit design as there exist trade off between the phase noise,
power consumption, the choice of particular oscillator topology and LO circuit complexity. These tradeoffs are explained in more detail in the next chapter; besides this phase noise is a most important factor in
deciding the Figure of merit (FOM) of an oscillator. The phase noise graphs for different pulses are plotted
here under, the phase noise is induced by inducing the jitter, which is controlled by the amount of noise
perturbation that in turn is controlled through the variance introduced in the signal through the AWGN
block. The phase noise model runs for different values of phase noise and noticing the amount of
correlation between the signal levels without any perturbation and with phase noise. The data for different
pulses is tabulated and plotted, at an offset frequency of 1MHz, with modeled NBIs, LNA and proposed
BPF filter stage.
a) Gaussian Pulse: The phase noise specifications for the Gaussian pulse are modeled here. The result is
presented in the tabulated and graph form and it can be seen that the correlation levels of 90% or more is
achievable for the phase noise of Figure 3.36 of -75dBc/Hz @ an offset of 1MHz.
Jitter ( σ c , sec)
Phase Noise (dBc/Hz)
Correlation Coefficient
1e-09
-15.537907
0.45334
5e-10
-21.5585038
0.57471
1e-10
-35.537907
0.66967
5e-11
-41.5585038
0.73108
1e-11
-55.537907
0.8112
5e-12
-61.5585038
0.85178
1e-12
-75.537907
0.9475
5-13
-81.5585038
0.9877
1e-13
-95.537907
0.999999
Table 3.1: Depicting the values of the Phase noise induced and the Correlation levels achieved.
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An Oscillator System for UWB QDAcR
Figure 3.36: Phase Noise requirements Vs. Correlation Coefficient for Gaussian Pulse
The following Figures 3.37 and 3.38 show, the frequency response of the In-Phase signal before and after
downconversion of the signal and the Figure 3.39 shows the transient response of the I/Q downconverted
Signal. The responses are under real condition, it means under the noisy channel and interference filtering.
It is clearly visible from the comparison of the two power spectrums of the signal that the entire band get
downconverted around the LO frequency and shifts to the DC. The In-Phase and Quadrature
downconverted signal is shown in the time domain, also verifies the validity of the modeling and
downconversion.
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An Oscillator System for UWB QDAcR
Figure 3.37: The Spectrum Before Downconversion
Figure 3.38: The Downconverted Spectrum
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An Oscillator System for UWB QDAcR
Figure 3.39: Showing the transient response of the downconverter I/Q signals.
b) Gaussian Mono Pulse: In the following table 3.2 and graph the phase noise requirement for the Gaussian
mono pulse is plotted in Figure 3.40
Jitter ( σ c , sec)
Phase Noise (dBc/Hz)
Correlation Coefficient
1e-09
-15.537907
0.52618
5e-10
-21.5585038
0.6384
1e-10
-35.537907
0.7298
5e-11
-41.5585038
0.7995
1e-11
-55.537907
0.8817
5e-12
-61.5585038
0.93118
1e-12
-75.537907
0.9875
5-13
-81.5585038
0.99973
1e-13
-95.537907
0.99999
Table 3.2: Depicting the values of the Phase noise induced and the Correlation levels achieved.
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An Oscillator System for UWB QDAcR
Figure 3.40: Phase Noise requirement Vs. Correlation Coefficient for Gaussian Mono Pulse
It can be seen that the Gaussian mono requires less phase noise for the same correlation coefficient in
comparison to the Gaussian Pulse. The interferers, signal levels, as well as the LO signal are the same for
all the pulses, which means that the dispersion of the power spectrum of the LO signal will be the same for
all the pulses. therefore, this scenario can be looked upon as that Gaussian mono pulse offers better
correlation than the Gaussian pulse. This is also proves the analogy; that some pulses offer better spectral
efficiency in terms of higher roll off at the desired frequencies than the others. The following Figures 3.41
and 3.42 show the downconversion of the filtered band, first Figure showing the spectrum before the
downconversion and second showing
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An Oscillator System for UWB QDAcR
Figure 3.41: The Signal Spectrum for Gaussian Mono Pulse before Downconversion
Figure 3.42: The Signal Spectrum for Gaussian Mono Pulse after Downconversion
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An Oscillator System for UWB QDAcR
c) Gaussian Doublet Pulse: The Second Derivative of a Gaussian is used as an UWB pulse RF signal in
QDAcR and the phase noise analysis of QDAcR for the Gaussian Doublet is presented here. It can be seen
that Gaussian Doublet too require a less phase noise in comparison to Gaussian pulse for same value of
correlation coefficient, as explained earlier because the spectral efficiency of the doublet is better than the
Gaussian pulse. The table 3.3 and graph in Figure 3.43 below show the data from the modeling of the phase
noise Vs. Correlation for the Gaussian doublet pulse.
Jitter ( σ c , sec)
Phase Noise (dBc/Hz)
Correlation Coefficient
1e-09
-15.537907
0.4992
5e-10
-21.5585038
0.5803
1e-10
-35.537907
0.70412
5e-11
-41.5585038
0.7747
1e-11
-55.537907
0.8704
5e-12
-61.5585038
0.9218
1e-12
-75.537907
0.9738
5-13
-81.5585038
0.9993
1e-13
-95.537907
0.99999
Table 3.3: Depicting the values of the Phase noise induced and the Correlation levels
achieved.
Figure 3.43: Phase Noise requirement Vs. Correlation Coefficient for Gaussian Doublet Pulse
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An Oscillator System for UWB QDAcR
d) Morlet Wavelet Pulse: The phase noise requirement of QDAcR is modeled for the Morlet wavelet of a
Gaussian Pulse. The phase noise graph of Morlet wavelet function as shown in Figure 3.44 is very similar
to the Gaussian Doublet graph, though the spectral efficiency that is the rate of roll off the edges at the cutoff frequencies is not similar to Gaussian doublet. If we notice the spectrum graph carefully in Figures 3.45
and 3.46 then we see that due to the shape of morlet wavelet pulse the notch near the LO frequency, betters
the spectral efficiency after downconversion hence providing higher correlation than the anticipated one.
Jitter ( σ c , sec)
Phase Noise (dBc/Hz)
Correlation Coefficient
1e-09
-15.537907
0.487
5e-10
-21.5585038
0.5883
1e-10
-35.537907
0.7138
5e-11
-41.5585038
0.78203
1e-11
-55.537907
0.8417
5e-12
-61.5585038
0.903
1e-12
-75.537907
0.9714
5-13
-81.5585038
0.9991
1e-13
-95.537907
0.9999
Table 3.4: Depicting the values of the Phase noise induced and the Correlation levels achieved.
Figure 3.44: Phase Noise requirement Vs. Correlation Coefficient for Morlet Wavelet
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An Oscillator System for UWB QDAcR
Figure 3.45: The Signal Spectrum for Morlet Wavelet Function before Downconversion
Figure 3.46: The Signal Spectrum for Morlet Wavelet Function after Downconversion
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An Oscillator System for UWB QDAcR
e) Daubechie’s Wavelet function of Gaussian Pulse: The phase noise analysis of QDAcR for the
Daubechie’s’ wavelet function as RF input signal is shown below in Figure 3.47. If we compare
Daubechie’s’ wavelet with the Gaussian pulse, then it is visible that Daubechie’s’ wavelet resembles
Gaussian with ringing at the higher cut off frequencies. The same similarity we find in the phase noise vs.
correlation graph of these two pulses.
Jitter ( σ c , sec)
Phase Noise (dBc/Hz)
Correlation Coefficient
1e-09
-15.537907
0.4618
5e-10
-21.5585038
0.5792
1e-10
-35.537907
0.67315
5e-11
-41.5585038
0.74308
1e-11
-55.537907
0.8177
5e-12
-61.5585038
0.87802
1e-12
-75.537907
0.95916
5-13
-81.5585038
0.9981
1e-13
-95.537907
0.9999
Table 3.5: Depicting the values of the Phase noise induced and the Correlation levels
achieved.
Figure 3.47: Phase Noise requirement Vs. Correlation Coefficient for Daubechies’ Wavelet
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An Oscillator System for UWB QDAcR
f) SINC Function Pulse: As it is noticed in the RF Input description of the QDAcR that SINC function
poses to be an ideal pulse for the UWB communication, with high spectral efficiency and the same is
reflected in phase noise vs. correlation result. The SINC function achieves the high correlation for the
lower phase noise in comparison with all other pulses. The graph Figure 3.48 below shows the phase noise
vs. correlation for SINC. The RF signal and downconverted spectrum are shown in Figures 3.49 and 3.50.
Jitter ( σ c , sec)
Phase Noise (dBc/Hz)
Correlation Coefficient
1e-09
-15.537907
0.5283
5e-10
-21.5585038
0.6428
1e-10
-35.537907
0.74331
5e-11
-41.5585038
0.8526
1e-11
-55.537907
0.89771
5e-12
-61.5585038
0.9376
1e-12
-75.537907
0.989
5-13
-81.5585038
0.99998
1e-13
-95.537907
0.99999
Table 3.6: Depicting the values of the Phase noise induced and the Correlation levels
achieved.
Figure 3.48: Phase Noise requirement Vs. Correlation Coefficient for SINC Pulse
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An Oscillator System for UWB QDAcR
Figure 3.49: The Signal Spectrum for SINC function before Downconversion
Figure 3.50: The Signal Spectrum for SINC function after Downconversion
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An Oscillator System for UWB QDAcR
The graph as Figure 3.51 shown below summarizes the phase noise vs. correlation plots for different pulses
into a single plot. It is visible from the graph below that SINC and Gaussian Mono are the best pulses in the
group of pulses which is being tested as ir-UWB RF input signal. This result totally coincides with the
findings in the RF input signal section and has been explained, as the spectral efficiency of pulses, which
helps them correlate better than other pulses.
Phase Noise Vs. Correlation for different pulse
1.05
1
0.95
0.9
Correlation Coefficient
0.85
0.8
0.75
0.7
0.65
0.6
Gaussian
Gaussian Mono
0.55
Gaussian Doublet
0.5
Morlet Wavelet
Daubechies' Wavelet
0.45
SINC Function Pulse
0.4
-15.5379 -21.5585 -35.5379 -41.5585 -55.5379 -61.5585 -75.5379 -81.5585 -95.5379
Phase Noise (dBc/HZ) @ 1MHz
Figure 3.51: The Phase Noise vs. Correlation Coefficient for different pulses
The significance of the Figure 3.51 is that, it gives an insight into the phase noise requirement of an irUWB Oscillator, which is of utmost importance in designing ir-UWB downconverter. The result holds its
uniqueness because the result obtained is a resultant of through quantitative analysis and complete system
level modeling. The approach is fundamental because it takes whole QDAcR system in consideration and
modeled for a very much realistic scenario. The phase noise specifications for QDAcR are reported for the
first time and among the first in ir-UWB transceiver category.
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An Oscillator System for UWB QDAcR
As mentioned earlier that phase noise specification set the base for circuit designer to choose the correct
topology, trade-offs in order to optimize the circuit design, therefore the obtained results are necessary as
well as form the base for circuit design of ir-UWB oscillator and henceforth downconverter.
5. The Low Noise Amplifier Block (LNA): For the purpose of complete QDAcR modeling, LNA is also
modeled in MTLAB. LNA is modeled for the optimization of the desired gain at the minimized noise
Figure levels simultaneously for the maximum auto-correlation levels. The prime parameters that govern
the functioning of LNA are stability, input/output matching, low noise Figure, linearity and high gain.
Every parameter is important and there exist certain trade-offs, which designer has to take care of in order
to have an optimum solution. The stability and maximum stable gain, are largely device dependent
parameters therefore S-parameters of the device has to be known at the system level in order to model.
Second, major parameter that is also partially device dependent (bias) and dependent on the strength and
position of the interferers is ‘Linearity’. The importance having a high linear system and high gain stages at
the same time is a necessity of ir-UWB receivers and QDAcR in particular has been discussed earlier in
previous sections; therefore our main focus in LNA modeling is to optimize Gain and Noise Figure for
correlation level of 85% or more.
Here a generic model of LNA for ir-UWB (QDAcR) is proposed, with the following assumptions that input
and output impedance of the LNA sees 50 Ohms of Source and Load impedances and is matched. In
reality, there exists a trade off between noise Figure and input matching and use of feedback mechanism do
ease this trade-off, but it is largely topology dependent, second that assumption that LNA provides same
gain for the entire bandwidth that is a flat gain over the entire bandwidth, third the noise Figure (NF)
remains same for the entire band, as in real circuit design parameter change with change in the frequency,
signal, bias etc. Therefore, these quantities are considered to be stable or as average value over the entire
bandwidth. Low noise amplifier is treated as a gain block and is placed as a black box in the noise block as
shown in the Figure 3.52 below. The noise is induced in the signal, by the AWGN noisy channel, where the
noise spectrum is controlled by the variance. The input to any stage is from the preceding stage and the
very first stage has noise floor equal to the receiver’s thermal floor. As, explained in the Noise block
description that all the active devices are considered as black box and that the final noise Figure is
calculated by having the ratio of input SNR to the output SNR.
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An Oscillator System for UWB QDAcR
Figure 3.52: Modeling of Low Noise Amplifier Block in MALAB
The model needs black box parameter that is gain in case of LNA as input and the other input is variance of
the AWGN channel to calibrate the system to the desired Noise Figure. The LNA is simulated for various
noise Figures pertaining to One particular value of gain and then gain is sweep over different values. The
correlation is noticed by comparing the fundamental signal with the iterations, that is for every gain, the
autocorrelation levels are noticed when noise Figure is ‘1’ that is the system is totally noiseless and this
signal is termed as “fundamental”, then for different values of noise Figure the correlation levels between
the transient signal and fundamental signal are calculated. The data is first tabulated and then plotted.
12
14
15
16
18
1.5
99.99
99.99
99.99
99.99
99.99
2
99.928
99.95
99.94
99.97
99.99
2.5
99.57
99.66
99.71
99.75
99.80
3
98.8
99.047
99.18
99.09
99.25
3.5
98.35
98.6
98.47
98.45
98.516
4
97.38
97.9
97. 94
98.014
98.171
Gain (dB)
Noise Figure(dB)
Table 3.7: The Noise Figure and Gain dependency on Auto-Correlation
The graph plotted below shows the correlation for different noise Figures and sweep for different gains.
The result is quite interesting as it shows not much deviation or change in the correlation value with respect
to the Noise Figure. The reason is inside the mechanism of distribution of the noise on signal and the autocorrelation architecture of the QDAcR. If mechanism be described, the noise interacts with the LNA input
signal in 3 ways, it either modulated the Amplitude of the signal (AM) or partially results in the phase
modulation of the signal (PM) or AM to PM conversion and rest acts as a thermal floor. As it is shown in
the previous section while modeling the LO that QDAcR does not require high phase noise specifications
in comparison to the narrowband system, so does the Phase modulation does not result in much of the
signal distortion in different active stages. Second, the noise present in the signal as amplitude modulated
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An Oscillator System for UWB QDAcR
auto-correlates with the delayed amplitude modulated signal, since the two correlated signal are subjected
to the same frontend and stochastic perturbations therefore the net effect of such perturbations is reduced
and is distributed over a bigger bandwidth or averaged out over a big frequency range.
Correlation (%)
Correlation vs. Noise Figure of LNA
Gain=18dB
Gain=16dB
Gain=15dB
Gain=14dB
Gain=12dB
96
1.5
2
2.5
3
Noise Figure (dB)
3.5
4
Figure 3.53: Correlation vs. Noise Figure of LNA
The succeeding stage to LNA in proposed QDAcR is a band stop filter, which has already been described
in detail in the earlier section. The separate inclusion of bandstop filter not just helps cleaning the
bandwidth from the interferers, but also eases the complexity of designing a combined LNA and a filter.
The main focus is behind having the largest possible stable gain over the entire bandwidth, which is
required in order to improve the signal levels and improve the overall Noise Figure and linearity of the
QDAcR.
3.5 Conclusion
The main results obtained in this chapter are summarized as follows. The complete system level modeling
in matlab of a QDAcR is presented, which provided with vital specifications pertaining to the
Downconverter design. The first highlight of this analysis was the use of filters that increased the
bandwidth utilization to 76%, also it was shown that time-frequency domain relationship if exploited
properly using pulse shaping, then the use of bandwidth can be more efficient. The main highlight was the
designing of downconverter for the first time it was shown that a Q-VCO with a phase error of 5degrees
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An Oscillator System for UWB QDAcR
and a phase noise of -90dBc/Hz @ 1MHz offset suffices to an autocorrelation of 90% or more for a
QDAcR. The modeling and analysis of different possible pulses highlighted the importance of pulse
shaping and high spectral efficiency, it finally resulted in the choice of Sinc and Gaussian Mono as the two
most efficient pulses for QDAcR. The noise modeling of complete QDAcR provided with the specs in form
of Link budget analysis and LNA design. The analysis of LNA provided with the specs of gain and noise
figure for optimal correlation.
The circuit design of oscillator for QDAcR is presented in the next section.
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An Oscillator System for UWB QDAcR
Section II
Methods and Techniques for Circuit Level Designing
This section comprises of two chapters, which describe the adopted methodology while designing the
circuits for an Oscillator System for impulse radio Quadrature Downconversion Auto-Correlation Receiver.
The underlying problem statement is to design a Quadrature Voltage Controlled Oscillator, which meets the
specifications that were derived in the previous section (system level analysis of QDAcR).
The problem is approached in a systematic fashion; throughout the design, the problems pertaining to the
process technology are being sincerely addressed from the very initial of schematic design levels, so that
not much deviation should be noticed between the results obtained at schematic simulation and post layout
simulations. This is done by proper component modeling and understanding the process related problems
(PVT effects) characterized for generalized components in IBM (130nm node, CMRF8SF) process
technology Design Manual.
Initially starting with the understanding of the Oscillator system in Chapter 4. In chapter 4, we further
proceed with the choice of oscillator topology and identification of key elements in circuit design that
define and translate into performance of an oscillator. This leads to the exploration of merits and demerits
posed by different LC-Tank Oscillators, namely Differential NMOS, PMOS and Complementary
Oscillators. The choice of Oscillator Topology and passive elements is made based on the analysis of
circuit simulation results, while meeting the specifications and targeting low power consumption.
Chapter 5 describes the circuit level implementation of Quadrature Voltage Controlled Oscillator (Q-VCO),
starting with the principles and methods of Quadrature generation followed by a circuit design description
and discussion about the cross coupled-VCO. The two topologies for Q-VCO were designed and analyzed,
these were parallel-coupled Q-VCO and series coupled Q-VCO. The result provided us with a realistic
solution to our problem that is a Q-VCO for QDAcR. Furthermore, we investigated Oscillator-Polyphase
filter topology, which can be another possible solution, because of its advantages like less chip area and
power consumption. Last section related to circuit design in this chapter deals with the design of output
buffers for an oscillator system. The buffer is analyzed for its load driving capabilities, power consumption,
harmonic output and its loading effect on the oscillator. In these two chapters the complete design
procedure is explained, while the results are analyzed with respect to the degree they meet the
specifications.
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An Oscillator System for UWB QDAcR
The Q-VCO circuit is designed in IBM (130nm node, CMRF8SF) process technology. The desired
specification set for Q-VCO, which were derived in system analysis is as follows.
Design Specifications:
Phase Noise (Spectral Purity): A minimum phase noise of -90dBc/Hz at and offset of 1MHz is required in
order to near perfect auto-correlation.
Phase Error: The maximum perceivable Quadrature Phase Error is 4 degrees.
Final Output Signal Power (Buffer Output): A minimum signal level of -5dBm Vpk-pk is required for
driving mixer and providing necessary conversion gain.
Tuning Range: As derived earlier that for ir-UWB QDAcR system the Oscillator should run at fixed
frequency 5.6GHz, with a tolerance of ±117MHz. This simplifies the design by negating the use of a Phase
Lock Loop (PLL). However in order to countermand the Process, temperature and supply voltage (PVT)
effects the Oscillator should have a minimum of ±5% tuning range.
Power Consumption: Though none specifications were provided or derived regarding power consumption
by the Oscillator system, however a sincere effort has been made to keep the power consumption levels to
bare minimum, while meeting the desired specifications.
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An Oscillator System for UWB QDAcR
4 CHAPTER 4
Oscillators: Introduction and Circuit Design Methodology of Negative
Transconductance (-Gm) Voltage Controlled Oscillator
Voltage Controlled Oscillators (VCOs) over the years have served as an integral part in RF transceiver
design. VCO are mainly used for signal processing jobs like Upconversion/Downconversion of modulated
baseband/rf signals, frequency selection or synthesis or the generation of reference periodic signal in time
domain (clock) in modern Digital Circuits. The VCO design has continuously advanced over the years
owing to developments and innovations in semiconductor process technology, packaging and better
understanding of circuit design problems effecting VCO performance. The development has spanned from
the use of vacuum tubes to highly precise low frequency crystal oscillators to present day monolithic
oscillator design.
In this chapter an attentive attempt has been made to present the design methodology for -Gm VCO in a
concise but effective manner covering all the major trade-offs, design rules and VCO performance related
nuances. As we know that performance of a VCO is characterized by the spectral purity of the its signal in
frequency domain or accurate periodicity in time domain, which directly translates into two variables that
define figure of merit of an Oscillator these are 1. Phase Noise and 2. Timing Jitter. The relationship
between and effect of these two variables has been discussed and presented in previous chapters, in this
chapter circuit design description starts with the understanding of the term -Gm (Negative
Transconductance) and further understanding the rules that lead to the design of an efficient LC-Tank. The
effectual design algorithm for optimal LC tank design is presented, in which firstly the rules and results
regarding the choice of an inductor are stated followed by rules and theory regarding the implementation
and choice of MOS varactors. The succeeding section describes designing of MOS LC-Tank Oscillator,
with a very brief description about Single transistor Oscillator and then concentrating on the main goal of
designing and characterizing LC-Tank VCO by understanding and exploiting various topologies and
validating the findings with the help of simulated results. In end all the major findings are summarized and
compared against the specifications.
4.1 Overview of Oscillator Fundamentals
Ideally, an oscillator can be defined as a system that produces stable periodic and sustained signal over an
indefinite time span. However, due to non-idealities, the signal strength is decayed over the period of time,
signal energy is not totally conserved, resulting in a change in period and signal stability. Therefore, in a
refined manner an Oscillator can be described as a system which comprises of a sustainable periodic signal
generation block synchronized with a signal compensation block (Amplifier).
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The output (voltage signal) of an oscillator can be defined by the equation Aout (t ) = Alo cos(ωo t + φ0 (t ))
where ‘ Aout (t ) = Vout (t ) ’ is LO output at time ‘ t ’, where ‘ Alo = V0 ’ is the maximum signal (voltage ‘ V0 ’)
swing amplitude of LO, the angular oscillation frequency is ‘ ωo ’ and a constant phase reference of‘ φ0 (t ) ’.
Based on phase response oscillator can be divided into single phase and multiphase output oscillator; beside
phase noise and signal output power, one of the figure of merit for multiphase oscillator is the accuracy
between the phase responses. The figure 4.1 below shows the model of an oscillator based on the above
discussion. Where X(s) is the input signal, A(s) the Amplification function, H(s) the frequency selective /
shaping function and Y(s) as Oscillator output.
A(s)
Figure 4.1: Oscillator Block Diagram
Obtaining the transfer function
Y ( s)
A( s )
=
X ( s) 1 − A( s ).H ( s )
(4.1)
Now solving the above equation for s = jω0 , for sustained and indefinite oscillation, we obtain the
following conditions
A(ω0 ).H (ω0 ) = 1
(4.2a)
∠A(ω0 ).H (ω0 ) = 2 nπ ; n ∈ Ζ
(4.2b)
Where the set of equations numbered 4.2a and 4.2b forms the Barkhausen’s Criteria. The equation 4.2a
implies that the loop gain should be a minimum of ‘1’ in order to start and sustain the oscillations and the
condition for phase stability is given by equation 4.2b.
Developing the model for electrical oscillator based on the Barkhausen’s criteria, in this case the startup
signal X(s) is replaced by the white noise, which is then amplified by the amplifier block. The noise is then
shaped by the narrowband frequency selective filter H(s); the signal is fed back to the input through
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An Oscillator System for UWB QDAcR
positive feedback loop formed by the amplifier and narrow band filter block. If the loop gain condition is
satisfied the oscillation starts at angular frequency ω0 and the signal amplitude continuously grows until it
saturates and reaches the peak value. The frequency selective (narrowband) filter implemented by H(s)
ensures single harmonic oscillation that is why commonly known as harmonic oscillator and the oscillator
in which the narrowband filter is implemented using passive LC-network is commonly known as LCOscillator.
The other type of oscillator is Relaxation Oscillator, which employs the principle of charging and
discharging of capacitor through a non-linear element. Due to the use of highly non-linear component, the
relaxation oscillators consists of different harmonic components, which translates to the fact that for the
same power consumption relaxation oscillators show poor phase noise performance in comparison to the
LC-tank oscillators. Owing to non-linear mechanism, relaxation oscillators are not totally sinusoidal; they
have typically a saw tooth or a distorted square wave output. A typical example of relaxation oscillator is
Ring Oscillator, which forms a ring using an odd number of inverter stages. the oscillation frequency is
decided by the switching time ‘ τ p ’ and the number of inverter stages used, switching time is determined
from the switching current and RC-network time constant at the gate of the inverters. Ring Oscillators can
be designed to have a high tuning range by controlling the switching current and number of inverter stages,
while consuming comparatively less die area and this gives them a formidable advantage over LCoscillators. A comparison between the two Oscillators is presented in the table below.
LC (Harmonic) Oscillators
Ring (Relaxation) Oscillators
Phase Noise
High ‘Q’ resonator. Good
Poor
Power Consumption
Low Power required for same
Higher Power required for same
phase noise
phase noise.
Narrow, require use of Capacitive
Wide Tuning Range
Tuning Range
Banks / Varactors at the cost of
higher power consumption /poor
phase noise
Multiphase Output Generation
Requires
filter
(Poly-Phase),
Intrinsically Produced
Couple VCOs
Table 4.1: Comparison between LC-Tank and Ring Oscillator
Considering design specifications specially targeting lower power consumption for a minimum phase noise
of -90dBc/Hz @ 1MH offset and non-desirability of wide tuning range. It seems sensible to go for a LCTank Oscillator topology instead of Ring Oscillator. Henceforth, the focal point of this circuit design
section will be to design and describe a LC-Tank Oscillator.
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An Oscillator System for UWB QDAcR
4.2 Quality Factor (Q-Factor), Impedance Transformation,
Single Transistor Oscillators and Differential Oscillators
The output (voltage signal) of an The ‘Q-Factor’ of a system, often relates to the system’s performance and
widely considered as figure of merit, which is used to measure efficiency of the system. Therefore, the
conventional way in which ‘Q-Factor’ can be described is shown in equation 4.3 below.
Q-Factor=
2π .Energy Stored
Energy Dissipated per unit cycle
(4.3)
In case of passive elements and their networks, the ‘Q-Factor’ determines the ideality of the component that
is the effect of passives on the performance and the efficiency of energy conversion in a network. There are
several definitions of ‘Q-Factor’ pertaining to the parameter, which is being measured. Particularly in case
of a passive network the Q-factor can be defined as given by the equation 4.4 below
Q-Factor(series network)=
Im(Z)
Im(Y)
orQ-Factor(parallel network)=
Re(Z)
Re(Y)
(4.4)
The Q-Factor for series and parallel networks are interchangeable and simply corresponds to the system
‘Q-factor’. Sticking to these crude definitions of ‘Q-Factor’, we can delve into the concept of Impedance
Transformation, which states that impedance can be converted to higher or lower value and from complex
to real. The two popular is to convert series networks to higher Q parallel networks or vice-versa. The
impedance transformation is widely used in Oscillators in order to ensure the High Q resonator, which in
turn results in a better harmonic oscillator. Figure 4.2a and 4.2b shows the impedance transformation from
series to parallel network and vice-versa. The series impedance is converted into parallel admittance and
the comparison on real and imaginary parts give the transformed values.
Let Cs, Ls and Rs be the values of passive in series configuration and Cp, Lp and Rp be the corresponding
values in parallel configuration. Then the series impedance for the two networks is given by
Z s = Rs +
1
for RC network and Z s = Rs + jω LS for RL network, converting series impedance into
jωCS
parallel admittance and finding the value of Q-factor according to equation 4.4 we get equation 4.5 the RC
network, which is shown below
Ys =
2 2
jω CS Rs + ω 2 CS RS
and Qc =
2 2 2
1 + ω CS RS
1
ωCS RS
(4.5)
For RL network the value of admittance and Q-factor are given by equation 4.6, as shown below
Ys =
Rs − jω Ls
and
2
RS + ω 2 L2
S
QL =
ω LS
(4.6)
RS
Comparing the obtained admittance values of equations 4.5 and 4.6 with the admittance values of parallel
networks in figure 4.2 and 4.3. It can be deduced that
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An Oscillator System for UWB QDAcR
Q2
Q2
CS and subsequently LP =
L
RP = (1 + Q 2 ) RS , CP =
2
2 S
1+ Q
1+ Q
(4.7)
Figure 4.2: RC Network Transformation
Ls
Lp
Rp
Rs
Figure 4.3: RL Network Transformation
As it is proverbial from the Oscillator’s generalized definition that for sustained and periodic oscillation an
amplification /compensation block is required. In electronic transistor oscillators this block is often
implemented by an active device that is a MOSFET or BJT. Now considering an oscillator with single
transistor as shown in Figure 4.4a below, it can be seen from the discussed figure that oscillation can be
obtained if the positive feedback is imparted to the Base/Gate or Emitter/Source node of the transistor.
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An Oscillator System for UWB QDAcR
Feedback applied to the Base/Gate will fail to provide the positive feedback as for non-inverting input gate
node the drain node will act as an inverting output node and vice-versa, thus this configuration will provide
negative feedback. However by the use of 1:n transformer (where n being a high valued integer) in the
drain/collector and base/gate feedback loop, the oscillation can be achieved. Moreover, at the resonance
frequency, the reactance is zero and net impedance seen by the active device is real, which implies that
voltage and current are in phase, therefore in order to maintain the same phase the feedback loop should be
connected to the emitter/source node. The problem with configuration shown in Figure 4.4a is that the LCtank is loaded directly and it sees
1
1
as resistance, which severely degrades the Q-factor and
−
g ds g m + g mb
the loop gain deteriorates less than one and generation of sustainable oscillation is not possible. This is a
perfect example where impedance transformation can be applied that is the source impedance would be
converted to much higher value and seen in parallel with the LC-tank, which increases the loop gain and
provide sustainable oscillation, as shown in Figure 4.4b. [39]
Figure 4.4: Single Transistor implementation of an oscillator (a) Direct Feedback, (b) With
Impedance Transformer
As seen from the Figure 4.4b the importance of impedance transformation resulting in sustained oscillation.
This impedance transformation can be implemented in two ways, firstly either by the use of passive
network or by use of active stage in feedback. The two well-known topologies namely Hartley Oscillator
and Colppits Oscillator, which are implemented using passive networks and are shown in the Figure 4.5
below. The impedance transformation is achieved by employing Inductive and Capacitive dividers for
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An Oscillator System for UWB QDAcR
Hartley and Colpitts oscillators respectively. The other concept involves use of an active feedback loop,
that uses transistor as an active impedance transforming element, which provides high impedance between
the tank and the emitter of the transistor M1. The transistor M2 further increases the impedance between
the tank and M1 emitter by transforming the emitter impedance of M1using the beta transform (as in the
case of source follower) to a higher value. The approximated values of equivalent parallel resistance and
inductance in case of Hartley Oscillator are given by the expression as follows
1
Req =
g m + g mb
2
L1 + L2
.
And Leq = L1 + L2
L2
1
And in case of Colppits Oscillator Req =
g m + g mb
2
C1 + C2
1
1
.
And Ceq = +
C1 C2
C1
−1
dd
dd
dd
C
L1
1
C
p
Lp
L
C
2
+ve Feedback
Loop
C
+ve Feedback
Loop
L2
bias
M2
M1
+ve Feedback
Loop
bias
bias
(a)
bias
(b)
(c)
Figure 4.5: (a) Hartley Oscillator, (b) Colpitts Oscillator and (c) Single Ended Oscillator using a
Source Follower as a positive Active Feedback.
In this section fundamentals of positive feedback loop and single transistor oscillators were discussed in
brief. The performance of the single device transistors suffers degradation due to its topology constraints.
Firstly, in order to have required transformed impedance ratio required for inductive and capacitive dividers
should be high enough in order to compensate the loading effect and have higher voltage swing, however
the increased use of passives makes the oscillator more susceptible to process variations. Second, in order
to have lower noise contribution from drain and gate of the transistor, the bias current should be decreased
and the device size should be increased. However, one degrades the voltage swing and other increases the
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An Oscillator System for UWB QDAcR
parasitic and thus decreasing the tuning range. Third, the common mode noise effects are more pronounced
in single ended oscillators as the noise due to supply perturbation and substrate noise bound to lower the
phase noise and lastly, single ended oscillators are not much suitable for Zero-IF or Low-IF receiver
architectures or differentially operated transceiver architectures.
4.2.1 Differential Topology Oscillators
The As it could be interpreted from the conclusions drawn at the end of Single Transistor Oscillator
analysis that single transistor topology is marred by constraints that limit its use in modern transceiver
architectures. The Differential topology offers simplistic solution by reducing the duty cycle by half that is
50% duty cycle as in the transceiver chain generally, oscillator block output drives the gate of Mixer gate
thus reduction in duty cycle improves the 1
f
switching noise contribution [49]. Further differential
topology benefits in improving the common mode noise rejection, in circumventing the even harmonics
and easing the dependence upon passive impedance transformation networks. The block diagram of a
cross-coupled differential oscillator is shown in the Figure 4.6 below.
Figure 4.6: (a) PMOS cross-coupled differential oscillator with current sink and (b) NMOS crosscoupled differential oscillator with current source.
Due to its posed advantages the differential topology is chosen as the topology of choice for designing
oscillation system required for ir-UWB QDAcR. Its nuances and analysis is presented in detail in the
subsequent sections.
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An Oscillator System for UWB QDAcR
4.3 -Gm (Negative Transconductance) and LC-Tank Design
Essentials
Negative Transconductance acts as a loss compensating negative resistance in parallel with the loss tank
resistance. As we know that LC-tank acts a oscillation damping narrow band filter, the damping happens
because of the parasitic present in passive components. Therefore, in order to have sustained oscillations a
compensating mechanism is put in place, in case differential topology, it is provided by the
Transconductance of two transistors. Considering a lossy LC-tank where Rs and Rc denotes total resistive
parasitic loss in the inductor and capacitor subsequently, the Figure 4.7 shows the equivalent parallel RLC
network obtained by the impedance transformation of the lossy LC network at the frequency of
oscillation ω0 . Only the resistive transformation is shown as at oscillation frequency the reactance offered
by the tank is zero. In Figure 4.7 below the active compensation stage is implemented by Gm stage,
transformation from series parasitic resistance to the parallel given by Rp at oscillation frequency in last
stage it the negative resistance ‘-Rp’ depicts the compensation provided by active Gm stage.
Figure 4.7: Negative Transconductance transformation.
In case of differential cross couple topology for e.g. the one shown in the Figure 4.5 the negative resistance
seen can be approximated by Ractive =
of
Ractive ≤ R p ,
to
be
on
the
−2
, now in order to compensate for the losses in the tank, the value
gm
safer
side
and
for
the
surety
of
sustainable
oscillation
k '.Ractive ≤ R p where 2 ≤ k ' ≥ 3 . Thus, the emergent propositions from this discussion are that the
Transconductance offered by the transistor should be high and second that a LC-tank should have as high
‘Q’ as possible.
For the determination of the angular frequency, let us consider the LC-tank with parallel parasitic
resistance. impedance of parallel LC-tank is given by the equation 4.8 below
ZTank (ω ) =
L2 RPω 2
LR 2ω (1 − LCω 2 )
+j 2 2 P
L2ω 2 + ( RP − LCRPω 2 ) 2
L ω + ( RP − LCRPω 2 ) 2
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(4.8)
An Oscillator System for UWB QDAcR
As we know that at resonance the imaginary impedance that is the reactance of the tank is zero, therefore at
ω = ωo , the value of angular frequency of oscillation is given by
ωo =
1
(4.9)
LC
Similarly the angular frequency of oscillation for LC-tank with parasitic in series in given by
ωo =
L − Rs2 C
L2 C − LC 2 Rc2
(4.10)
Is can be discerned that equation 4.10 results in equation 4.9, if the parasitic are negligible. Therefore, once
again the statement that LC-tank should consist of passives with least parasitic is in order to have high
phase noise is proved. Therefore, the dominant factor is tank ‘Q-factor’, earlier section a very generalpurpose definition of Q-factor was presented, which is not applicable in its totality on the LC-Tank,
because LC-tank exhibits band-pass filter response as described in [50]. The normalized equation of
transfer function is given as
H ( s) =
s2 +
ωo .s
ωo .s
QTank
(4.11)
2
+ ωo
Where Q-tank is given by the expression QTank =
ωO
, where ∆ω is 3dB frequency bandwidth. Considering
∆ω
the equation 4.8 for parallel LC tank , comparing and solving it for equation 4.11, the Q-factor is given as
QTank = R p
C
, for ω = ωo the real part of tank impedance given by equation 4.8, that is
L
Re Z (ωo ) = R p = Z Pk , where subscript ‘Pk’ stands for peak value of the parameter. However at resonant
frequency the QTank = QPk , therefore, for and only for ω = ωo it is a valid assumption to write the tank Qfactor as QTank = Z Pk
C
L
(4.12)
The reasoning behind formulation of equation 4.2 will be dealt in more detail while characterizing the
Inductor for LC-Tank.
4.3.1 Designing of LC-Tank for Low Power and Low Phase Noise
In this section the basics regarding design of LC-Tank as given in [51] are discussed, the quantitative
analysis provide the clear insight into designing and optimization of the LC-tank for the desired constraint
of Low-power as well as targeting the possible low phase noise.
Applying the principle of energy conservation in the tank as shown in figure 4.6, that is the energy stored in
the capacitor is equal to the energy stored in the inductor. We get equation 4.13 as shown below
1
1
CVo2 = LI o2
2
2
(4.13)
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An Oscillator System for UWB QDAcR
Where ‘Vo’ and ‘Io’ represent the peak value of voltage and current across the LC-tank, that is voltage
across the capacitor and current through the inductor. However, due to parasitic there is power loss or
energy dissipation in LC-tank, which is given by equation 4.14 below
Ploss =
2
R .C.VO2 Rs .VO2 ωo .Rs .C 2 .VO2
1
Rs I o2 = s
=
=
L
2
2ωo2 L2
2
(4.14)
from the previous chapters, we know the fundamental equation of phase noise as described by Leeson’s
formula as given by equation 2.51. Considering the leeson’s noise for the phase noise contributed due to
thermal noise and re-writing equation 2.51, using the relations we figured out in equation 4.12-4.15, as
shown in equation 4.15 below
2
2
RC ω
1
ω
i o = 10.log 2kT (1 + F )i s 2 i o
L {∆ω} = 10.log 2kT (1 + F )i 2
QTank Ploss ∆ω
LI o ∆ω
2
2
1 ωo
1 ωo
= 10.log 2kT (1 + F )i
i
i
OR = 10.log 2kT (1 + F )i
2
R p I o ∆ω
Z Pk I o2 ∆ω
(4.15)
The equations 4.5,6,7,12,14 and 15 serves as fundamental equations, which characterize the LC-tank. In
their treatment of design of LC-tank under the hood of Linear time invariant theory [52,53,54,55] have
emphasized on the ratios of inductance L and series resistance Rs and the ratio of inductance and the total
L
L
R
oscillator capacitance that is C . The crux is that s should be maximized in order to have maximum phase
L
C ratio should be maximized for same desired
noise at minimum power consumption and similarly
effects. These propositions are productive in wholesome, however do suffer from limitations. The
L
L
Rs and minimization of C are summed up in the
limitations as well as effectiveness of maximization of
table 4.2 below.
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Passive
Action
Phase Noise
Power
Limitations
Dependency
Inductor (L)
Maximize
Improves
Quadratic,
Power
Strictly depends upon the
gain
reduces.
designing
and
characterization
of
Inductor. Other issues such
as Tuning range, chip area,
etc.
Series
Linear (for 1st
Characterization and proper
Resistance
order
design, depends upon the
(R)
temperature
process
/Parasitic
For
effects)
Metallization layers.
Quadratic
Device sizes for required
Total
Minimize
Improves
Minimize
Improves
Capacitance
e.g.
and
technology.
properties
of
gain and operation regions.
Design Specific, for e.g.
the device size and loading
of
output
stage
like
buffer/mixer etc.
Amplitude
Minimize - For
Improves phase noise,
lower
when
power
Quadratic
Power Budget, The device
increased.
reliability (too high swing
this
can break the Cox faster).
comes
Power-Phase Noise trade-
consumption
However,
Maximize – for
improvement
high phase noise
at the cost of more
*Balance should
power consumption.
off.
be found, based
upon
the
specifications
Table 4.2: Summation of prepositions as well as limitations
In this section the fundamentals regarding the LC-tank were presented, which serve, as the basic guidelines
while designing LC-tank. However, there are other process or technology and design related factors, which
need to be understood as these factors play an important part in optimization of LC-tank. In next section
characterization and choice of Inductor and tank capacitance is presented, while understanding and
addressing the process related factors.
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An Oscillator System for UWB QDAcR
4.4 LC-Tank Design
The conclusion drawn at the end of all sections lead to the fact that the design of optimized LC-tank is of
prime importance and in this section methodology for optimized LC-tank design is presented. Since the
advancement in process technology it is possible to fabricate the passives in a monolithic fashion, which
has provided designers with degree of freedom by relatively less dependence on the off-chip passives. The
off-chip inductors have high Q-factor in comparison with the monolithic inductors; however, the
performance of off-chip inductor is severely degraded and marred by problems like the pad capacitance,
package pins and interfacing of off-chip inductor with the integrated circuit at RF frequencies.
4.4.1 Inductor Modeling and Characterization
The monolithic inductors are fabricated using metallization layers offered by the technology and in the
form of spiral geometries using microstrips. The monolithic inductors suffer from Ohmic and substrate
related losses, based on the possible modes of signal propagation ohmic losses can be further classified as
skin-effect, slow wave and quasi-TEM modes specially seen on insulating substrates. The skin effect is
visible in heavily doped and low resistive substrates as the graph Figure 3.4 in [50] shows that skin effect is
visible in substrate with resistivity one or two fold less than 1 Ohm/cm. Since IBM CMF8SF-RF has
substrate resistivity between 1-2 Ohm/cm, therefore the skin-effect is not quite evident in this case. If we
look graph carefully with respect to the technology parameters it can be figured out that apart from slow
wave effect, other ohmic losses will not dominate at the desired RF-frequency and substrate resistivity.
Substrate Losses: the low resistivity of Si substrate results in degradation of Q-factor due to multiple loss
mechanism, as explained in detail in [57, 58]. Firstly, considering the Maxwell-Faraday Equation, this
physically translates that any change in the magnetic field creates an electric field. The increase in the
number of turns results in delocalization of the coil magnetic field in spiral, which is no longer confined to
the center of the inductor; which in ideal case should be. The transient magnetic field expands well into the
inner turns, which induces the electric field and ultimately generates eddy current in the inner conductors of
spiral. Now interpreting Ampere Circuital Law with respect to the generated eddy currents, it results in a
magnetic field that is in opposite direction to the spiral magnetic field. This reduction in net magnetic field
results in decrease of the inductance value.
The inductance of any spiral with substrate resistivity of higher than 1 Ohm/cm, can be modeled by its
compact π -model as shown in the Figure 4.8 below. The inductance of any spiral can be calculated by
scaling the single π -model by the number of microstrips in a single spiral that is adding in series of
inductance, resistance and parasitic capacitances of each π -model. The shunt arms of the π -model denote
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An Oscillator System for UWB QDAcR
the inner and outer winding parasitic, therefore denoted by different set of values because of asymmetry in
the inductor layout. Where Co represents the total capacitance that includes mutual coupling capacitance
Cm in parallel with the capacitance obtained from sum of bend capacitance Cb and overlapping underpass
parasitic capacitance, as described in detail in Figure 3-12 [50]
Figure 4.8: (a) Compact lumped-element π -model of an inductor and (b) Single Port Excitation of
equivalent inductor model.
Grounding the second port in figure 4.8a, applying the impedance transformation of π -model in to simple
parallel circuit as shown in the Figure 4.8b. Where the values of Rp and Cp are given by, equation 4.16
below, these represents the approximated total value of the parasitic resistance and capacitance in an
Inductor. The effect of parasitic in an inductor results in inductance loss, the parasitic resistance gives rise
to substrate loss in the form of eddy current and parasitic capacitor begets substrate loss in the form of
displacement current.
RP =
2
R (C + C ) 2
1 + ω 2 (Cox + Csi )Csi Rsi
1
+ si ox 2 P and CP = Cox i
2
2
2 2
ω Cox Rsi
Cox
1 + ω (Cox + Csi ) Rsi
(4.16)
2
The value of ‘Q-factor’ for an inductor can now be defined in a much robust manner.
The net energy stored in an inductor is calculated as Esoted =
2
Vse
2
L
− (CP + Co ) , where first
2
2 2
( Rs + ω L )
denote the magnetic energy stored in an inductor an second part as electrical energy stored in parasitic
capacitor that is why with negative sign.
Now calculating the energy dissipated per oscillation cycle as Ediss =
the calculated Q-factor can be given as shown in equation 4.17 below
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2
R
2π Vse 1
⋅
⋅
+ 2 s 2 2 , therefore
ω 2 RP Rs + ω L
An Oscillator System for UWB QDAcR
RP
ω L Rs2 (Co + CP )
QL =
⋅ 1 −
− ω 2 L(Co + CP ) ⋅
Rs
L
ω L 2
RP +
+ 1 ⋅ Rs
R
s
Or QL =
Or
ωL
Rs
⋅ Self Resonance Factor ⋅ Substrate Loss Factor
(4.17)
(4.18)
1
1
1
=
+
QL QConductor QSubstrate − Loss
The equation 4.18 is important one as in order to find an appropriate and optimized inductor for LC-tank it
is necessary to understand effect of parasitic in order to characterize the inductor properly.
4.4.2 Defining Process Related Parameters*
*The Information is classified and property of IBM – Technologies, therefore the exact details, component
design specifications sheet’s screen-shot, graphs and numbers about process related parameters, simulated
plots are not (re-)produced in this thesis. However, inductor model was chosen only after study of design
manual and model guide and verifying various model parameters and results as given in model guide.
The choice of inductor is a symmetric and differential driven inductor from the IBM CMRF8SF-DM (Dual
Metal) process component model library, the advantages of symmetric, parallel and differential driven
inductor are explained in detail in [50]. The merits can be highlighted as, firstly, the differential driven
symmetric inductor offers approximately twice large Q-factor, because of enhanced mutual coupling
between the windings in contrast to single-ended excited inductor, this is can be seen from graph Figure 317 of [50] and secondly differential symmetric inductors consumes less area in comparison to single-ended
symmetric inductor.
A symmetric inductor with parallel metal lines and differentially driven ‘Symindp’ was chosen from the
model library for LC-tank designing. The preliminary investigation was mainly based upon the simulation
and reading from the IBM-Design manual and model guide. The geometrical lay out of symindp spiral is
octagonal, which poses an added advantage in terms of less acute turning angles, which lessen the current
crowding and bend capacitance. Secondly, symindp is more symmetric than a square or hexagonal spiral,
because eccentricity of an octagonal structure is lower and closer to a circle than a square or hexagonal
structure. Next was about the decision to choose the metallization layers for inductor design, the process
offers different combinations for which the simulated and correlated plots of Q-factor and model predicted
inductance value with respect to variable temperature and frequency are presented in IBM classified design
manual and model guide. The metal layers combination (metal layer 3 and metal layer 2), which shows the
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highest value of Q-factor and best correlation values were chosen for preliminary simulations and model
comparisons.
The next step was in making a choice for groundplane for an inductor. The choice of proper groundplane is
essential towards partial mitigation of substrate losses, this can be explained as shielding of inductor. As it
is described in previous section that currents flow into the substrate through capacitive coupling and
induced currents through the magnetic coupling, therefore the isolation of inductor from substrate becomes
necessary in order to minimize the substrate losses. Therefore, use of rugged / patterned ground plane is
done; it is placed above the substrate in order to stop the currents from entering the substrate. The use of
groundplane increases parasitic capacitance that adversely effect the inductance and Q-factor value (eq.
4.18) by decreasing the self-resonance frequency, however if the operating frequency is well lower from
the self-resonance frequency, the use of groundplane is advisable. The frequency of operation in our case is
5.6GHz, and from the preliminary simulations and design manual data, it is evident that self-resonance
frequency is beyond the operational frequency; therefore in inductor designing the groundplane shielding is
used. Other downside of groundplane is that due to conducting nature of groundplane, more magnetic
currents are induced, but this problem is circumvented by patterning of the ground plane. In patterning the
regular nature of groundplane is broken by cutting slots into it, which are perpendicular to the direction of
magnetic current flow. These slots further reduces the loop length, thus magnetic current circulate in much
smaller loops and thus less opposing lossy magnetic field, also such patterning helps to cancel out lossy
magnetic fields because opposite polarity currents are self induced at the broken edges of ground plane,
which helps in canceling out lossy magnetic field effects.
The technology offers two choices in groundplane selection, for the proposed inductor the patterned metal
M1 groundplane that acts as a faraday shield is selected. There are other layout related rules specified in
design manual regarding specifying the AC-ground and desired way to do ground plane connections during
the simulation and layout. The preliminary choice of inductor was defined in this section, hence-forth the
word/term inductor in thesis will replicate the inductor symindp, with optimal choice of metal layers and
metal-patterned ground plane as provided by the technology.
4.4.3 The optimized inductor design methodology
After preliminary investigation and understanding of inductor and process related variables, the final choice
of inductor was made, it was based on the analysis of data collected from iterative simulations. The
simulations were performed based on the set of design rules as given in [50, 51, 59], these design principles
are mentioned hereunder.
Choice of interline spacing: It should be kept to minimum value, as specified by the technology. This
improves the mutual coupling between the metal lines, thus improving the inductance.
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The strip width should be kept in between 10 and 15 micrometers. The increase in metal line width results
in decrease in Q-factor and making it more susceptible to frequency.
The thickness of isolating oxide layer should be kept as thick as possible, in order to minimize shunt
parasitic and dissipation.
Connection of metal layers in parallel, this reduces the Ohmic losses and increase the Q-factor.
Maintaining a space width of minimum of five linewidths, between the outside turn of spiral and any
surrounding metal features.
Number of turns: The number turns in an inductor depend upon the operational frequency and desired
inductance value and Quality factor. Some propose ‘n’ to be as high as possible [51] because it improves
the inductance to series resistance ration. The inductance value ‘L’ is quadratic and directly proportional to
number of turns that is L ∝ n 2 and Rs ∝ n , therefore the ratio improves by ‘n’. However this comes at the
cost of increased parasitic capacitance in the form of interwinding capacitance, which reduces the selfresonance frequency and will effect the Q-factor, therefore the choice must be an optimized one.
These illustrated points served as basic design rules. The start was made first by following the rule number
1 that is keeping the space width to its minimum, which is 5micometers as available from the technology.
An iterative algorithm was followed with different set of inductance values in order to find the optimized
value. The algorithm followed is as follows.
The line spacing was kept to its minimum value of 5 micrometers as provided by the technology.
Second Step was to find the optimized value of metal line width. Hence, the model determined inductance
values of 500pico Henry, 1nH, 1.2nH, 1.5nH, and 2nH were simulated with an ideal capacitor from
analog.lib, for widths of 8, 10, 12, and 12.5 micrometers. The number of turns was kept similar for each
inductance value by adjusting the outer diameter length for different widths. The value of capacitor in each
simulation was chosen so that LC-tank should resonate nearest to the frequency of oscillation, that is
5.6GHz. The Q-factor of inductor (tank), since the capacitor chosen is ideal one, was calculated as
Q∆ω −3 dB or QBandwidth it was noted that barring from 500pico Inductance with width of 8 and 10 micrometers,
which has marginally higher Q-factor than same inductance at line width of 12micrometers, the Q-factor
for line width equal to 12 microemeters provided the highest value for each inductance value. The value of
Q-factor dipped as line width was increased to 12.5 micrometers. Therefore, after computer simulations and
iterations the line width was fixed to 12 micrometers.
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The next step involved characterization of inductance value, that is finding the effective value of
inductance. The technology model gives extrapolated or interpolated values of inductance based on the
generalized inductor characterization as references to variable values. However, for particular variable
values the technological model values of inductor are not often correct, therefore it was necessary to find
the exact value of the inductance.
Figure 4.9: Test Bench for Inductor Simulation
For this, the inductor with model predicted values of 500pH, 900pH, 1nH, 1.2nH, 1.5nH, 2nH, 2.5nH and
3nH were simulated as shown in the test-bench Figure 4.9. Again the tank was made to resonate at 5.6GHz
with ideal capacitor, with capacitor value given by C =
1
2π f L
, f is oscillation frequency = 5.6GHz. But
there were seen the aberrations in the oscillator frequency from the desired 5.6GHz, the value of resonating
frequency for each model predicted inductance value was tabulated till nearest 4th decimal place and each
inductance value has 5 such runs, of which the standard deviation was approximately zero. The deviation
from the oscillation frequency can be seen from the Figure 4.10 below. If the tank if not oscillating at its
desired frequency of 5.6GHz, when we use ideal capacitor of value calculated in accordance with the
inductance value predicted by model, it results that the model specified inductor values are not correct. This
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clearly validates that effective inductance is different from model predicted inductance value and we need
to characterize inductor properly.
Figure 4.10: Showing the fault in the model predicted inductance value
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Next step involved correction of inductance value for the same capacitance and obtained mean frequency
and simulating the circuit for corrected inductance value and fixing the oscillation frequency to 5.6GHz to
nearest 2 decimal places. Repeating the process for each inductance until the oscillation frequency was
fixed to 5.6GHz. The table 4.3 below shows the effective value of inductance
Number of Turns
Outer Diameter (um)
Inductance Model (nH)
Inductance Effective (nH)
2
130.8
0.5
.45075
2
182.7
0.9
.845226
2
194.8
1.0
.9485
2
218.3
1.2
1.16183
2
252.18
1.5
1.50304
3
221
2.0
2.136086
3
250
2.5
2.85882067
3
278.2
3.0
3.7297
Table 4.3: Calculation of Effective Inductance.
As an extension to this in same step, another iteration was to choose the optimum number of turns, as it
can be seen from the table 4.3 that the following iteration involves the rule to keep the inductor as hollow
as possible by maximizing the Outer Dimension (diameter). This is to ensure that all the magnetic flux
passes through the core and less parasitic capacitance. However, in order to verify the effect of maximum
turn, the same iteration was done and the effective inductance were calculated for maximum number of
turns possible for minimum OD as shown in table 4.4 below.
Number of Turns
Outer Diameter (um)
Inductance Model (nH)
Inductance Effective (nH)
3
156
1.004
0.9593
3
169.7
1.201
1.201475
3
189
1.492
1.4965
4
195.4
2.0
2.1345
3
215.9
2.5
2.875
5
224
3.106
3.99983
Table 4.4: Calculation of Effective Inductance
4. The next step was to finalize between the two set of inductors, in order find the best suitable inductor
with optimize number of turns. Therefore, the Q-factor that is 3-dB Q-factor was calculated for both set of
inductors. The LC-tank was oscillated for nearest possible values to the desired oscillation frequency using
the effective inductances and ideal capacitor. The following Figure 4.11 (a) and (b) shows the Q-factor
comparison between the inductance obtained by maximizing the outer dimension while keeping the number
of turns to minimum that is Q-factor (Hollow) in Figure 4.11(a) and inductor designed with maximizing the
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An Oscillator System for UWB QDAcR
number of turns Q-factor (Max. Turns) in Figure 4.11(b). This comparison leads to the first result that at
desired frequency we should go for inductor with less number of turns, as Q-factor of hollow inductor is
higher than the Q-factor value for the comparable inductance with more number of turns in design.
Q-Factor Comparison
30
25
15
10
5
Q-factor (Hollow)
0
4.51E-10
8.45E-10
9.49E-10
1.16E-09
1.50E-09
2.14E-09
2.86E-09
3.73E-09
Inductance
Figure 4.11:(a) Q-Factor for the set of Hollow Inductors.
Q-factor (Max. Turns)
25
20
Q-factor
Q-factor
20
15
10
5
Q-factor (Max. Turns)
0
9.59E-10
1.20E-09
1.50E-09
2.13E-09
2.88E-09
4.00E-09
Inductance
Figure 4.11: (b) Q-factor for the set of Inductors with Maximum Turns.
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5. After deciding on the number of turns, the main point was to decide upon the value of Inductance. As it
can be figured out from the analysis of Q-factor for the set of hollow inductors (Figure 4.11a) that peak
value of Q-factor at the desired frequency occurs at inductance value of around 1nH. However, this
criterion of having highest Q-factor does not substantiate the proposition that we should go for 1nH
inductor. Firstly, until now we have not calculated the net paraisitc associated with each inductor as well as
we have not looked for highest inductance to parasitic series resistance ratio or highest inductance to
parasitic capacitance or required capacitance ratio as postulated earlier. Therefore going for highest value
of Q-factor at 5.6GHz is amateurish and needs to be verified.
First step is to find the value of all the parasitic associated with the inductor model. In this regard, we
simulate S-parameter analysis of the inductor set from 1Hz to 100GHz frequency, our main interest is to
find the parasitic value. We know that at the self resonance frequency the reactance offered by inductor
model is zero that is the value of Imaginary (Z11)=0, the frequency at which Im(Z11)=0 is called the self
resonance or imaginary bandwidth frequency. In order to have the value of parasitic series resistance, we
plot the value of Real(Z11) and see the value of resistance at DC that is at very low frequency. It is noticed,
which is inline with the theory that series resistance is frequency dependent and it shoots up drastically at
very high frequencies close to self-resonance frequency and remains very much constant at lower
frequencies. We have spooled the value of effective inductance from previous iterations, now we calculate
the net parasitic capacitance and resistance from the present set of simulation, the tabulated data is shown
in table 4.5 below. The series resistance for LC-tank at 5.6 GHz is calculated separately using the previous
test bench as shown in Figure 4.9, where by adding the capacitor and then making the LC-tank to Oscillate
at 5.6GHz.
Effective
Imaginary
Value of Net
Value of Net
Value
Inductance
Bandwidth
Parasitic
Simulated
Series
Series
of Re(Z11)
(nH)
Frequency
Capacitance
Capacitance
Resistance
Resistance
at
(Hz)
(Cp+Co)
required
(Rs) @ DC
(Rs) in Ohms
oscillation
in Ohms
(When
frequency in
Farads
in
LC-tank.
by
(Farads)
of
Value
of
LC-
tank
Peak Value
Ohms.
Oscillating at
5.6GHz)
.45075
.9485
1.16183
1.50304
2.136086
2.85882067
3.7297
6.51E+10
13.2544E-15
1.79E-12
0.1981
0.8238
305.32
3.79E+10
20.8667E-15
9.56E-13
0.29264
1.22343
715.22
3.44E+10
.845226
22.5919E-15
8.51E-13
0.31458
1.36
808.134
2.90E+10
25.8488E-15
6.95E-13
0.35707
1.72
953.21
2.36E+10
30.2399E-15
5.37E-13
0.41841
2.52
1074.533
1.74E+10
39.3199E-15
3.77E-13
0.50082
4.716
1150.22
1.43E+10
43.306E-15
2.80E-13
0.57939
1134.68
1.22E+10
45.893E-15
2.12E-13
0.65589
8.4675
15.385
1052.79
Table 4.5: Simulated and Tabulated values for Parasitic at self-resonance and at Oscillation
Frequency (with ideal capacitor).
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The table 4.5 shows a variety of simulated data, firstly calculation of all the parasitic resistance and
capacitance for Inductor, which are necessary in order to characterize it fully. With the help of this data we
can verify the various postulates for optimized LC-tank , as mentioned in section 4.3. Firstly, plotting the
ratio of inductance to parasitic capacitance and ratio of inductance to series resistance, which seen from
Figure 4.12(a) and (b) below.
90000
80000
Ratio of Leff/Cpara.
70000
60000
50000
40000
30000
20000
10000
Leff/Cpar.
0
4.51E-10
8.45E-10
9.49E-10
1.16E-09
1.50E-09
2.14E-09
2.86E-09
3.73E-09
Inductance
Figure 4.12: (a) Ratio of Effective Inductance to Parasitic Capacitance.
Ratio of Leff/Rseries
6E-12
Ratio of Leff/Rseries
5E-12
4E-12
3E-12
2E-12
1E-12
0
4.51E-10
8.45E-10
9.49E-10
1.16E-09
1.50E-09
2.14E-09
2.86E-09
Inductance
Figure 4.12: (b) Ratio of Effective Inductance to Series Resistance
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An Oscillator System for UWB QDAcR
If we analyze Figure 4.12 (a) and (b) in light of the prepositions developed in section 4.3, that in order to
have higher phase noise less power consumption, the desired ratios should be maximized. As it can be seen
that the desired ratios keep on increasing with increase in the value of inductor, while we noticed
previously that Q-factor drops for higher inductances. These two are not in line with each other. Therefore,
an upper limit over the value of ratio must be specified in-order to have the optimized inductance value. In
[56] defines the upper limit of the inductance value by defining the upper limit on series resistance, which
is termed as effective resistance. However, this theory also falls short because it can be applied only and
only after complete characterization of tank capacitance, which is highly dependent upon the choice of
varactors and other source of parasitic capacitance like active devices, loading stages, current source size
etc. Therefore, there is a need to have a theory that allows to optimize the LC-tank and inductance as a
whole, while targeting phase noise and power consumption also.
In this regard, if we go back to the Figure 4.8 and equation 4.17 and 18 then it can be discerned that for an
optimize inductance or tank, it is necessary to consider the effect of substrate loss and self resonance also.
Therefore maximization of ratio of inductance to series resistance will not suffice as it does not include the
effect of parasitic resistance ‘Rp’; in order to include the simultaneous effect or parasitic resistance as well
as series resistance, we should look to parameter ‘Zpk’ , which is defined as the peak Re(Z11). The peak
value that is the real value of Z11 at the oscillation frequency, clearly and compositely takes into account
the effect of all the Ohmic losses at resonance. Now, plotting the graph for inductance value versus peak
Re(Z11) in Figure 4.13
Zpk Vs. Inductance
1400
Peak Re(Z11) Ohms
1200
1000
800
600
400
200
Zpk Vs. Inductance
0
4.51E-10
8.45E-10
9.49E-10
1.16E-09
1.50E-09
2.14E-09
2.86E-09
Inductance
Figure 4.13: Peak Real (Z11) Vs. Inductance at Oscillation.
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If we analyze Figure 4.13 and Q-factor graph, some similarities are noticed easily. Firstly, the peak value
starts dropping as inductance value increases because capacitive substrate losses start dominating, same can
be confirmed, if we see the value of self-resonance frequency from table 4.5. The imaginary bandwidth
frequency starts dropping, which means that it starts becoming more effective as inductance value goes
high. In terms of physical behavior inside inductor it can be explained as capacitive component of substrate
losses (that is gradient increase in the opposing magnetic field due to coupling of induced current with
substrate) takes over the parasitic resistive component (effect due electric field penetration of the substrate
that is eddy current generation).
Therefore, if we look back and analyze Figure 4.13 with regard to equations 4.12 and 4.15, it can be
discerned that in our case in order to design an optimized LC-tank, which simultaneously meets low phase
noise and low power consumption requirements, then ZPk should be maximized. Furthermore, it can be
noticed that maxima for peak resistive impedance occurs for inductance value of 2.13 nH, therefore it is
wise and desirable to choose an inductor with effective inductance in range of 2.1-2.3 nH. The proposition
to go for peak value, in reality gives the value of optimized Q-factor of a tank as it captures all the lossy
effects and provides and effective solution to meet the limitations, as expressed in table 4.2. This approach
is further validated by running the simulation for a differential pair oscillator with LC-tank comprising of
an ideal capacitor and firstly with an inductor of 2.13 nH and in second run with an inductor of 1nH. It was
found that for the same power consumption the phase noise obtained from optimized inductor was
approximately 5dB better than the one obtained from 1nH inductor. This in short concludes the
characterization and designing of inductor and in order to have optimize LC-tank at 5.6 GHz the symindp
with an effective inductance of 2.134 nH will be used. Figure 4.14 below shows the basic layout of the used
inductor, the peripheral dimensions are 254.08umx254.08um.
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Figure 4.14: The Basic Layout of the symindp inductor of value 2.1nH
4.4.4 Varactor Design Methodology
In LC-tank design, we mainly emphasized on design of the inductor, with an assumption that the
capacitance required is having very high ‘Q-factor’. However, in reality capacitors have finite ‘Q-factor’,
which means that they do affect LC-tank performance and in turn performance of an oscillator. Therefore,
it becomes imperative to define LC-tank capacitance and its characterization. First, we should define the
term capacitance with in the LC-tank, the term ‘C’ in angular frequency formula stands for the total
capacitance which is seen by the tank. This includes capacitance from varactors, parasitics from active as
well as passives and loading capacitance. Therefore, we can define tank capacitance as given by equation
4.19 below
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CTank = CVaractor + CParasitic ( Active + Passive ) + CLoad ( Buffer , Mixeretc.)
(4.19)
therefore, a more refined expression in order to describe angular frequency of an oscillator can be written
as
ωo =
1
Leff CTotal
. If we consider the system to be oscillating at frequency of 5.6GHz, with effective
inductance of 2.1nH, then the value of CTotal should be equal to 385fF. Therefore, while designing the
oscillator we should be careful that the total capacitance seen by the LC-tank should not increase more than
385fF. If we analyze equation 4.19 it can be seen that varactor capacitance offers designers degree of
freedom to counter against Process and temperature variations and to re-calibrate the tank to defined
oscillation frequency in case of any mismatch. Another important property of varactor capacitance is to
provide tuning range to an oscillator, that is an oscillator can often be used to generate oscillations at
different frequencies depending upon the application requirement and this be done by changing the
capacitance across the tank for e.g. by switching the capacitive bank. As stated earlier that in our system
design we do not have any such tuning range requirement, also relaxation of roughly ± 120 MHz eases the
frequency stabilization problem and fends off the use of Phase lock loop or PLL in circuit design. However,
oscillator circuit does need a desired tunability of 10% in order to cope with PVT variations.
The tuning range of a varactor is defined as the ratio between the maximum and minimum capacitance,
when MOSFET is swept over certain voltage range. Mathematically it is given by equation 4.20
α=
CV , Max
CV , Min
2
f 2 C
C
+ CV , Paras.
f Max
Max
Parasitic
=
= Varaiable, Max
+ 2 ⋅
− 1 ⋅
CVaraiable, Min + CV , Paras.
f Min
CV , Min
f Min
(4.20)
Where CVaraiable is the series capacitance of the gate oxide capacitance Cox and depletion region capacitance
Cd and the varactor’s parasitic capacitances are given by overlap and fringing capacitances between the
gate and source-drain regions [60]. The MOSFET application as a variable capacitor or Varactor (Change
in capacitance due to change in voltage across the capacitor) is a well-known method. When the DrainSource and Bulk (depending on the bias voltages and process technology) terminals are tied together then
MOSFET works as a capacitor, whose capacitance can be modulated by controlling the Bulk to Gate
voltage VBG , as shown in Figure 4.15 below. As seen in the Figure 4.15 below, five distinctive regions are
marked namely 1 to 5, therefore in accordance with the design requirements, we can choose mode of
varactor operation.
The varactor modeled is a P-Channel device and it works in moderate inversion or region 2 if bulk to gate
voltage is greater than the threshold voltage or VBG > VTh . In region 2, the capacitance is series sum of gate
oxide capacitance Cox and capacitance Cd due to space charge width ( xdt ) [61], since in this region we see
moderate inversion that is the concentration of holes in channel (minority carriers in PMOS) is not yet
peaked. Which means that the minority charge carrier concentration beneath the channel is same as in the
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bulk, and it improves on increasing VBG , which means that on increasing VBG the dominance of space
charge density starts diminishing and effect of holes channel charge density starts increasing . If VBG is
increased further, it ensures device operation in region 1 that is in strong inversion region, in this region a
complete channel of holes is created beneath the gate and total capacitance seen is dominated by channel
charge density capacitance that is gate oxide capacitance Cox , also space charge width is at its minimum,
which means Cd ≈ 0 . However, lowering of VBG or increase in the gate voltage drives the device towards
region 3, which is a weak inversion region, in this region space charge width reaches its maxima and the
effect of gate-oxide capacitance is at its minima. The space charge density is peaked and in this region we
do not see any big change in capacitance over change in voltage or this region offers least tunable range.
However, due to best varactor sensitivity, which is offered in this region, translates into an Oscillator with
better phase noise performance, but negligible tunability, which undermines the very definition of VCO
and pragmatic feasibility of such oscillator.
A-MOS vractor can be defined when varactor operates in regions 4 and 5. That is further decrease in VBG
OR increasing the positive gate voltage, the electrons majority carriers in case of P-Channel device, start
filling the channel and a depletion layer of electrons is formed beneath the gate and device starts working in
region 4 of depletion. On increasing the gate voltage in region 4, the channel charge density
capacitance Cox becomes prominent. But this time channel now comprises of higher concentration of
majority charge carriers (electrons for PMOS) and the varactor capacitance is controlled totally by positive
gate voltage or VG > VB . If we further increase the gate voltage it drives the device into accumulation,
which means that a complete channel of majority charge carriers appears underneath the gate. However, the
gate-oxide capacitance Cox in case of accumulation is lower than gate-oxide capacitance when device is
working in strong inversion mode. This happens because of change in effective channel length beneath the
gate, which reduces the maximum value capacitance Cox in two cases. The reasoning followed is that when
device is working in inversion mode the gate and drain nodes have same charge polarity that is minority
charge carriers as in the channel therefore the effective length of channel under the gate is higher than it is
in
case
of
accumulation
mode
when
channel
consists
of
majority
carriers
only
OR
CV , Max − Inversion > CV , Max − Accumulation . Furthermore, it can be noticed that because of the change in effective
length under the gate, varactor working in inversion mode or (I-MOS Varactor) has high sensitivity when
compared with Accumulation mode varactor (A-MOS). Here sensitivity relates to gradient of change in
capacitance with respect to voltage. The better sensitivity offered by accumulation mode varactor results in
marginal better phase noise performance than an inversion mode varactor oscillator. The proper
quantitative reasoning is presented in the next section.
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Figure 4.15: Variation of Capacitance for change in Bulk-Gate Voltage
In our above analysis of varactor we did not, much considered the effect of parasitic. If we carefully
analyze Figure 4.15, it can be noticed that the minimum capacitance occurs in region 3 that is weak
inversion mode and as discussed space charge depletion capacitance Cd dominates. In weak inversion the
gate control of channel conductance is controlled by the parasitic gate-channel capacitance in this case is
given by gate-source capacitance Cgs and gate-drain capacitance C gd , where C gs and Cgd are formed by
overlapping of source and drain regions with gate. Mathematically the value is given by expression as
follows C gs = Cgd =
W .l.Cox
, therefore CV , Min = Cgs + C gd + Cd , similarly in strong inversion mode or
2
accumulation mode CV , Max = Cox ( inv./ accu .) + Cgs + Cgd . As stated in [62] that the effect of C gd is minimal when
the device is in deep saturation, since MOSFET works as a capacitor that is VDS = 0 , therefore when
operating in accumulation mode the effect of parasitic capacitance C gd is minimized.
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The next in parasitic analysis is comparison channel resistances for I-MOS and A-MOS varactors. The
comparison between A-MOS, I-MOS and Diode in Figure 10 of [63], clearly shows that A-MOS offers
shows least parasitic resistance, while diode varactor shows the most resistance. The parasitic resistance
offered by I-MOS is given in [64] can be expressed as Rpara =
1 1
l
W
⋅ ⋅ RChannel ,□ ⋅ + RPoly ,□ ⋅ . This gives
12 N
W
l
insight into parasitic resistance, in order to have minimum parasitic firstly the number of gate fingers ‘N’
should be large, second the process available node length should be kept to its minimum value. This
analysis also substantiate the fact that channel length should be kept at minimum to reduce the parasitic
resistance and increase the ‘Q-factor’.
The analysis presented so far depends upon the small-signal behavior of device. However the signal at the
gate of varactor is a large signal sinusoid, which changes from +Vpk to – Vpk for a complete cycle, this
changes the value as well as mode of operation of Varactor. Therefore, it becomes mandatory to investigate
the large-signal behaviour and make sure the mode of operation of varactor. A detailed quantitative
analysis explaining the large signal behaviour is presented in [65], which is summed up and presented as
follows.
1.
The
total
capacitance
seen
by
tank
is
given
by
term
effective
capacitance
1
C (v(t )) or Ceff = Cavg − C2nd Harmonic , where Cavg is dominant and the total capacitance at fundamental for a
2
complete
as Cavg ≈ Ceff
oscillation
cycle
C + CMin CMin − CMax
= Max
+
2
π
and
can
be
approximated
2
sin −1 Veff + Veff ⋅ 1 − Veff
⋅
Vlo Vlo
Vlo
(4.21)
In equation 4.21, Veff = VGate − VTune − VThreshold
2. The Low frequency AM noise is upconverted and translated into Phase noise due to varactor nonlinearity and varactor noise conversion sensitivity can be defined as K AM → FM = −
ωO
2Ceff
⋅
∂Ceff
∂Vlo
, this clearly
shows that phase noise can be better if the sensitivity can be lowered. A little tweaking to above expression
leads us to K AM → FM = −
ωO
2Ceff
⋅
∂Ceff
∂Vlo
=−
∂Ceff ∂VTune
ωO ∂Ceff ∂Veff
ω
⋅
⋅
=− O ⋅
⋅
2Ceff ∂Veff ∂Vlo
2Ceff ∂VTune ∂Vlo
(4.22)
the equation 4.22 clearly indicates the dependency of phase noise over the tuning range sensitivity and also
predicts upon the need of stabilize amplitude over the tuning range. Also highest phase noise can be
obtained when either Veff = Vlo or Veff =0. In both cases it means that biasing the varactor either to value of
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CMin or CMax . Further it can be deduced from equation 4.22 that larger the tuning range less is the phase
noise. As a solution a digitally controlled capacitor switch bank can be employed.
Using the postulates of large signal analysis in order to find the Varactor providing the effective
capacitance as required, which in turn will automatically provide the lowest AM to FM noise conversion
sensitivity. Therefore simulating for Ceff ≅ Cavg , by using the iterative process in which different set of
values for DC biasing variables that includes VGate and VTune were used.
Figure 4.16: Effective Capacitance Vs. Tuning Voltage Sweep
It can be seen from Figure 4.16 above, that using large signal analysis the size of varactor, which shows
constant value of average capacitance over complete tuning range voltage for different values effective
voltage, the graph is derived from parametric sweep of tuning voltage for each seep of effective voltage.
Also, it can be noticed from Figure 4.16 that value of average capacitance is 373fF, which is very close to
the theoretical value derived for 2.134nH inductor to resonate at 5.6GHz.
Next step in our analysis involves to do the small signal analysis of varactor. Before going forward, firstly
we need to decide on the mode of operation, as far we have seen through parasitic analysis and sensitivity
analysis that A-MOS offers best solution in comparison to I-MOS and it can be verified from detailed
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results published in [60, 63, 66]. If we see carefully, it is found that the tuning voltage and gate large signal
voltage play crucial role in defining tuning range and capacitance value for a varactor. In case of PMOS
varactor, in order to make MOSFET work as A-MOS VG > VB and VBG << VTh , the value of gate voltage
depends upon the root means square value of oscillation cycle amplitude that is Vlo , the peak value of Vlo in
ideal case can be 1.2volts. Firstly, the value of threshold is technology define and in order to have higher
Q-factor and low resistance, we should keep the gate length to its minimum value, as we can change lower
the threshold by increasing the gate length. Now considering the case when D-S-B nodes are tied together
and typical threshold value VTh of 450-550mV, which implies that device can work in accumulation mode
if and only tuning voltage is less than 650mV. This means the reduction in tuning range and increase in
sensitivity. Therefore, to ensure accumulation working the novel solutions have been proposed in [50, 60,
63, 64, 66], these mainly includes doping the source and drain of PMOS with n+ impurity or tailor made
varactors as technology do not provide such devices. Also, in comparison analysis through literature it was
noticed that A-MOS does not provide much significant betterment in phase noise value and specifications
for phase noise are bit relaxed therefore, it was logical to go for Inversion mode or I-MOS varactors. Next
step was to look for tuning range, because as described in [50, 67] the tuning range can be increased by use
of differential varactors that is PMOS and NMOS varactors in inversion mode. However on the count of
tuning range also our specification are bit relaxed and the tuning range required is to meet the PVT
variations. After carefully looking at all aspects, finally it was decided to use I-MOS varactors.
In I-MOS varactor the bulk node was connected to highest positive supply that is 1.2Volts, in order to
ensure operation in inversion region. The typical I-MOS capacitor change is shown below in Figure 4.17.
The Figure 4.17 also shows the effect of gate bias voltage, as discussed and proved earlier the graph shows
the anticipated change for gate bias voltage. As it increases the tuning range that is the ratio of maximum to
minimum varactor capacitance decreases.
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Figure 4.17: Varactor Capacitance Vs. Tuning Voltage for different gate bias voltages
The Figure 4.18 and 4.19 below show the tuning range and resistance of the desired MOSFET varactor,
when gate bias voltage is kept at 500mV. In Figure 4.18 the maximum capacitance achieved is around
430fF when tuning voltage is 1.2V and minimum capacitance is 239fF at tuning voltage of 0V. therefore
the maximal tuning range that can be possibly attained by this varactor is given by equation 4.23 below
α=
CV , Max
CV , Min
=
430
= 1.79 or ≈ 18%
239
(4.23)
this is the maximal attainable tuning range, however in an oscillator this capacitance needs to be trimmed
and tweaked in order to maintain as high tuning range as possible. The capacitance from active circuit and
loading circuit will degrade the tuning range as the tunable capacitance provided by varactor needs to be
decreased in order to compensate for other parasitic. In Figure 4.19 the net parasitic resistance is modeled,
it can be witnessed that the resistance increases when the varactor is in moderate inversion or triode region.
In moderate inversion the holes concentration at the gate start increasing, in beginning space charge region
controls the active area (area beneath the gate and P+ region) and in reverse bias condition the hole-electron
pair generated in space charge region combined to keep the thermal equilibrium. However, as change in
bias makes holes migrating towards the gate, the diffusion currents [61] come into play and so does the
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effect of diffusion resistance. As the device migrates towards the inversion region the diffusion resistance
peaks and when the channel is made or device enters in strong inversion the effect of diffusion process
recedes and so does the value of diffusion current and parasitic resistance. Another dominant parasitic
effect is because of well resistance ‘Rwell’ as described in [60] and is determined by the active area.
Therefore from figure 4.19 we can say that rise in the value of dominant series parasitic resistance in
moderate inversion region is a cumulative effect of Diffusion, well and Poly resistances, which then
reduces mainly to the effect of Channel and well resistances in strong inversion mode.
Figure 4.18: Tuning Range offered by the characterized varactor.
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Figure 4.19: The change in parasitic resistance over the tuning range.
In this section analyses and characterization of the desired varactor was presented. The emphasis was to
keep the varactor design simple and as per the requirements, which fortunately are relaxed. Therefore, the
design of differential varactors was not implemented at final design level. The varactor was optimized
using large signal analysis for its property to convert low frequency AM noise generated in tail current or
power supply to FM noise near the fundamental and second harmonic.
The varactor biased at tuning voltage of 619mV, when used in tank with characterized inductor; the tank
oscillates at 5.6GHz frequency. This can be seen from the Figure 4.20 below, it can be noticed that the zero
crossing for the reactance graph occurs nearly at 5.6GHz. The Q-factor of varactor was calculated to be
95.4, which determines over-all tank Q-factor of 14.7. This concludes the study of LC-tanks fundamentals
and design of LC-tank for the proposed oscillator. The LC-tank was designed keeping in mind phase noise
and low power consumption. In next section the design methodology for oscillator is explained in brief.
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Figure 4.20: The LC-tank reactance sweep over frequency.
4.5 Oscillator Design Methodology
In this section the circuit design aspects for an oscillator are discussed and implemented. As mentioned at
the time of Phase Noise modeling at system level, the understanding of phase noise due to oscillator circuit
is dealt in succinct manner in starting. This then followed by a short discussion about the oscillator start-up
condition and highlighting the design points that can improve the results. It is succeeded by step-by-step
design methodology, starting with cross-coupled and complementary oscillator topologies description, the
parameters that affect the oscillation start-up, the choice of active device and rules followed. The last
section compares the results of different oscillators and complements results with the reasoning for choice
of Complementary Differential Cross Coupled Oscillator, which is then verified by treatment of design for
its robustness and resilience towards other process and temperature related variations.
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4.5.1 Phase Noise in an Oscillator System
The phase noise at system level was modeled and discussed in detail in Chapter 2 and 3. However, our
discussion fell short of effect of real device and circuit parameters. In this section, the phase noise analysis
is revisited but pertaining to differential cross-coupled topology only. Our previous analysis of phase noise
was based on Demir’s model which consider phase noise as a stationary random process which is nonlinear and time variant system, and the system can be diluted to a linear time variant system for the
condition of stationary process as presented in [22]. The time invariant model of phase noise based on
circuit analysis has been researched and developed very well, to name a few classic papers, the model is
presented in [28, 54, 68, 69]. As proved in [69] that for a memory-less non-linear system the ratio of carrier
to phase modulated noise sidebands is equal at the input and output of a system. This helps in transforming
and analyzing various noise sources in an oscillator and allow us to use basic circuit analysis laws.
The first step is about defining the noise sources present in cross-coupled oscillator. If we look at Figure
4.5, we see three possible and distinctive source of noise, which are LC-Tank or Resonator, The active gain
part or transitors and lastly biasing / power sources which includes tail current source and other low
frequency bias/power sources for e.g. Vdd.
Resonator Noise: We have characterized the LC-tank in previous sections and know that loss can be
depicted in terms of a parasitic resistance ‘Rp’ as shown in Figure 4.6. The value of output voltage ‘Vo’
over an oscillation cycle, across the parallel RLC tank is given by the well known expression Vo =
2
π
I o RP ,
where ‘Io’ is tail current. The phase noise component of the tank is given by equation 4.15 which can be re-
4kTR ω 2
o
P
i
written as L {∆ω} = 10.log
.
2
Vo 2Q∆ω
Phase noise contribution by active part of an oscillator: The simplistic view of the switching diff-pair can
be a tail current source with a cascoded transistor and the output noise is a current noise pulse as described
in [54, 68]. The switching effect of diff pair at oscillation frequency ωo , mixes and folds all the components
of noise from all the sources around the fundamental and even harmonics. The total contribution by diff-
8kT γ I R 2 ω 2
o P
o
pair is given by L {∆ω} = 10.log
i
, where γ is noise factor for non-linear circuit and
3
π Vo
2Q∆ω
for MOSFET typically γ =
2
. It can be seen from the expression for diff-pair phase noise contribution that
3
phase noise contribution is independent of device sizes [54, 68].
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As we understood from our non-linearity analysis of varactor and from [65, 69, 70] that upconverted AM
noise is transformed into phase noise. The low frequency tail current noise is upconverted to with sidebands
around the fundamental. However, this AM noise is modulated by the varactor, with components at low
frequency and at 2ωo . Therefore, the noise current at frequency 2ωo is commutated in the loop and shows
noise sidebands at fundamental and third harmonic. The total phase noise contribution by tail current
kT γπ 2 ω 2
o
source is given by L {∆ω} = 10.log
i
as in [68, 70].
2 I oVeff 2Q∆ω
Therefore if we sum up phase noise contribution by all the noise sources, the final phase noise equation we
arrive at is given by equation 4.24 below
4kTR 2γ I R γ I R
o P
P
L {∆ω} = 10.log
i1 +
+ o P
2
π Vo
2Veff
Vo
ωo
2Q∆ω
2
(4.24)
Now in order to design low phase noise oscillator we can target optimization of phase noise at each noise
source level. This done by applying set design rules as expressed here under.
4.5.2 The Oscillator Start-up condition
It is extremely necessary to select the proper set of devices in order to make sure that oscillator starts
properly. It becomes imperative to find the oscillation condition, according to the theory of negative
resistance the active part should compensate for the losses in the tank. Losses in the tank are defined by the
term ‘Rp’ therefore active part should provide Transconductance (Gm) which is equal or more than tank
losses
or GTank
≤ GM .
Mathematically
1
= Ractive ≤ RP ,
GM
however
to
safeguard
the
start
the k '.Ractive ≤ RP , where k'= 2-3 , which means the value of active resistance should be as low as possible.
If we look at the Figure 4.21 below, the tank voltage Vo connects to its driving transistor M1 through cross
coupled transistor M2. The capacitor CL denotes the capacitance of the current source. The path sees
transistor M2 as a source follower, therefore the input impedance is given by
Z in =
The
Z tot =
gm2
1
1
+
−
jωCgs2 jωCL ω 2 Cgs2 CL
total
active
impedance
(4.25)
seen
by
tank
is
given
by
equation
gm2
−1
1
1
+
+
−
g m1 jωCgs2 jωCL ω 2 Cgs2 CL
4.26
(4.26)
The condition for start-up is given as RP ≥ k '. 2.Z tot , the factor ‘2’ because of diff-pair topology.
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An Oscillator System for UWB QDAcR
Figure 4.21: Starting Condition for an Oscillator.
Therefore, analyzing the factors, which influence the start-up condition. the effect of parasitic
capacitance C gs , as discussed previously it reduces the tuning range, this calls for device with minimum
channel length in order to reduce the overlapping capacitance.
The maximization of Transconductance, this can be done by increasing the width of the device as higher
value of g m ensures stable start-up. The g m of a transistor depends more on the transistor geometry than
the bias current as it is directly proportional to the width, while in square-root to the bias/ tail current.
Another factor is capacitance of the tail current source, which adversely effect the start-up condition, as it
loads the tank as parasitic capacitance hence decrease the tuning range as well lowers the LC-tank Q-factor.
The current source design is discussed in detail in next section
4.5.3 Methodology for Oscillator Design
In order to meet the criteria of low power consumption and low phase noise, certain design rules needs to
be followed, which are described hereunder:
Firstly, considering the resonator noise source, we have already tried to optimize the resonator associated
phase noise component during LC-tank design. However, there is always some room for certain trade-off,
that is to better the phase noise at the expense of tuning range. As reducing the varactor average value
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results in reduced tuning range and less non-linearity, which directly results in reduced phase noise
contribution from LC-tank and the tail current source.
The focus shifts to the optimization of phase noise component due to diff-pair. On careful screening and
simplification it can be discerned that active device phase noise contribution can be better by increasing the
tail current. However, in low power or power-limited regime this is not the case, therefore a careful
attention needs to be given to the choice of device sizes. There are two contradictory theories one by [68],
which mathematically proves that phase noise is independent of device size. On the other hand in [71, 72]
propose that phase noise in 1
f2
and 1
f3
is dependent upon the device parameters, specifically on the
overdrive voltage ( VGS − VTh ) and transistor cut-off frequency f t , and as the device width is reduced so does
the improvement in the phase noise. The reasoning presented in [71] gives useful insight in preliminary
device selection, however the optimum limit on overdrive voltage derives from the oscillator start-up
condition which is dependent upon higher value of ‘ g m ’. The value of ‘ g m ’ decreases steadily on increase
in overdrive voltage under constant current scheme and in our case, lower power is a big constraint.
The choice of devices for the diff-pair was made first by setting the DC bias-points and maximizing the
over drive voltage for the sufficient value of ‘ g m ’. The DC bias points were checked at -50, 30, and 140
degree Celsius. This was done to ensure that the over-drive value of minimum 80-100mV does exist and
under no condition any transistor should be switched off. The gate length was kept at minimum, because
the parasitic capacitance effects the tuning range and since our design does not employ any switchable
capacitor bank, we have to make sure the practicality of the tuning range. Another reason as discussed is
adverse effect of parasitic in providing stable oscillation start-up. Second constraint was power
consumption, to keep it as low as possible, while achieving derivable, this also put constraint on
maximization of over-drive voltage, as a trade-off between ‘ g m ’ and over-drive voltage needs to be strike.
In case of complementary diff-pair topology the Transconductances of NMOS and PMOS were kept as
close as possible so that cycle can have equal fall and rise time that is symmetry over the horizontal axis.
Next is to make sure that diff-pair always work in saturation mode, any increase in the oscillator output
voltage, will result in increase of gate voltage for the diff-pair MOSFETs and can make transistor to go in
triode region. Such instance will initiate non-linearity in the current and thus affecting the phase noise. The
saturation mode can be assured if the gate-source feedback if decoupled and gate of diff-pair transistors can
be biased separately. But this will definitely de-Q the tank and influence the tuning range as well degrade
the phase noise based upon the value of biasing circuit impedance. However, as described in [49]
decoupled and switched biasing can improve the phase noise performance in 1
f3
region. In our case, this
situation is dealt by selecting the minimum length device for highest threshold, so that even increase in
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over drive can be compensated for. Second The cascoded tail current stabilize the source voltage and
source degeneration reduces the tank voltage swing thus effectively checking the gate bias.
Design of Current source: A cascoded current mirror source is employed in the design. The current mirror
serves as tail current biasing source and does modulates the value of ‘ g m ’ in order to guarantee sufficient
loop gain for sustainable oscillations. However, tail current degrades the phase noise by introducing flicker
noise into the oscillator. As discussed in [54, 68, 70, 73] in detail the mechanism, effect and filtering of low
frequency tail current noise, which is seen at frequencies around the fundamental in carrier power spectrum
and flicker noise commutates in loop with the frequency of 2ωo . Several solutions have been proposed in
literature, with most of them converging on the deployment of LC filter with resonance frequency of 2ωo ,
as source degeneration in an oscillator. In our design we have approached the problem in two ways.
Firstly, design of basic current mirror, The large transistors, in width and gate length larger than the process
node. The main reasoning behind this was that larger transistors offer less 1 contribution, because short
f
channel MOSFET exhibits higher flicker noise in comparison bipolar or large channel MOSFET. The
flicker noise current spectral density is inversely proportional to width and channel length, therefore
increasing W .l products improves the phase noise. Second benefit from large channel current mirror is that
the threshold voltage is reduced, which enables to have higher overdrive voltage and higher ‘ g m ’.
However, the draw back of big devices is capacitive loading of Oscillator, as we saw from our analysis that
it can affect oscillator stability. Another effect is that due to capacitive loading the tuning range is reduced
and also due to capacitive loading the amplitude modulation or amplitude instability sets in due to
difference in high frequency oscillator time constants and low frequency bias circuitry time constants.
Secondly, as stated in [50, 74] a smaller transistor as cascode was implemented. Firstly, it reduces the effect
of capacitive loading and secondly that it provides high output impedance for the current source, which is a
desirable effect. It further, improves the performance of the Oscillator in two ways. If we look from the
oscillator node the tail current cascode transistor works as source degeneration impedance for the common
node of diff-pair. The smaller cascode transistor works in triode mode, which replicates a resistive
degeneration at the common node for the Diff-pair and increasing the CMRR; however trade off should be
attained so as the triode-resistive effect should not load or change the parallel resistance of tank. Therefore,
a small sized and optimized cascode current source not only reduces flicker noise and capacitive coupling
(as smaller capacitor in series with big current source) but also suppress the common mode variations. As
an extension to this, the further improvement in the phase noise can be achieved if resistors are put at the
source of diff-pair. However, a trade-off based in simulations is required, because this will decrease the
output voltage swing across the tank. As presented in detail in [71] the PMOS offers less noise contribution
than NMOS for both thermal noise and flicker noise regions, when transconductance of both PMOS and
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NMOS are kept same. Therefore, the emphasis was on the design of PMOS Oscillator + PMOS current
source, in order to reduce the flicker noise component in phase noise.
4.6 Oscillator Design and Comparison
We have discussed the basic design methodology for an oscillator so far. Now we compare the performance
of three basic oscillators, namely NMOS, PMOS and Complementary (Push-Pull) Oscillator; which were
designed on the basis of methodology discussed.
Firstly, a discussion about complementary oscillator topology. As it is seen from Figure 4.20c, that a pushpull topology consists of two PMOS and NMOS cross-coupled diff-pair, which inherently bears the
functionality of a typical CMOS Inverter and called as push-pull topology. If we look at the start-up
condition then for a push-pull topology, then negative resistance is given by Ractive
for
−2
and as
g mp + g mn
k '. Ractive ≤ RP if we compare the starting condition under ideal case that is parasitic to be
we know that
zero,
=
a
simple
PMOS
/
NMOS
and
Push-pull
than
the
tank
transconductance
GM Push−Pull ≈ 2.GM PMOS / NOMOS , considering that g mp = g mn . This results easily into increase of the output
voltage amplitude and in case of Push-Pull the output Vo ( Push − Pull )
=
4
π
I o RP = 2.Vo ( PMOS / NMOS ) . These
deliberations are under ideal case scenario and considering that LC-tank remains the same. This means that
for same current consumption large transconductance as well as large voltage swing is achieved by PushPull topology. This directly results in better phase noise performance (by equation 4.15) and more stable
oscillation condition for Push-Pull in comparison to simple cross couple diff-pair topology.
However, if we consider the effect of parasitic added by extra diff-pair stage then it is clearly visible that
the swing is not exactly two times. It will suffer a loss of 3dB due to the parasitic
Cgs added by extra diff-
pair and also degrade the tuning range. Secondly, the addition of extra active devices will add the noise to
the oscillator. Therefore, in order to reap the benefits from push-pull stage a few trade-off should be made.
Firstly, the size of added diff-pair and
g m obtained, should be optimized; because parasitic increase with
increase in width and this can be done by iterative computer simulations and measuring the tuning range
change ratio. Secondly, making g mp
≈ g mn , this provides better symmetry that same rise and fall time for
the oscillator cycle across the horizontal axis. In [74] the detailed large signal analysis of push-pull
topology is provided, however the theoretical claim of 6dB improvement is not noticed in simulations. A
modified equation of phase noise for a push-pull topology is as given below and in [50]
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4kTR γ n + γ p ω 2
P
o
L {∆ω} = 10.log
i1 +
2
2 2Q∆ω
Vo
(4.27)
The Figure 4.22 shows the block diagram of implemented circuit for (a) PMOS, (b) NMOS and (c) Pushpull. The circuits were implemented based on the discussed design methodology and trade-ff for lower
power consumption. In order to find the correct choice for oscillator topology it was critical to test these
three configurations for there figure of merit and meeting the specifications. The three oscillators were
primarily compared using same LC-tank for amplitude swing, phase noise and tuning range provided for
the same power consumption, the oscillation frequency deviation was kept to a minimum of 50MHz using
the tuning voltage. The power specs chosen were to consume between 1-1.5mW at 1.2V supply.
Degeneration Resistance: The use resistance ‘Oprrpres’ from the process library. This resistor was chosen
based on the study of design manual. The resistor with lowest parasitic capacitance and lowest mismatch is
provided by L1 BEOL, however the use of this resistance comes with a rider. Firstly, after layout the
parasitic of L1BEOL is not extracted by software tools and second rule is that there should not be any
device or wiring placed under or above the L1BEOL resistors, also many foundries does not include either
L1BEOL or KxBEOL in their library. These rules prompted for the use of other resistor.
The next option after careful simulation was ‘OPRRPRES’ it is a P type, lightly doped OP (Mask Level)
poly silicon resistor. The OPRRPRES provides the highest sheet resistance with lowest parasitic
capacitances and best absolute resistance sensitivity. On the hind side, this resistor suffers from higher
mismatch and tolerances. However, for tolerance and mismatches the effect can be taken care at the time of
simulation. The simulation with ±25% were done, and also since the value of source degeneration
resistance is 100 Ohms. Therefore the effect of higher mismatches and tolerance does not make much effect
on the result. It was calculated that a resistance of 100 ohms, will have a change of 23.46 Ohms over a
temperature gradient of 200 degree Celsius. Therefore over complete process and temperature variance the
resistor can have values between 57 and 120 Ohms. The results at 50 Ohms and 120 Ohms are taken and
tabulated. The polysilicon resistor has voltage limit 5V, which is under control as highest voltage swing
attainable is 2.4V; and Current Limit in our case varies from a minimum of 5mA to 90mA. This is not an
issue in our case as the current in oscillator is between 800micro Amp to 2mA, consumption in buffer is
also less than 6 mA range in buffers.
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Figure 4.22: (a) Diagram of a PMOS Differential Oscillator, (b) NMOS Differential Oscillator
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Figure 4.22:(c) The Block Diagram of Push-Pull Differential Oscillator Schematic
4.6.1 Comparison of Different Oscillator Designs
In our comparison we start with the comparison of the tuning range for same varactor, which was designed
in previously in this chapter followed by phase noise and swing comparison for power consumption of
1mW. Figure 4.23, 4.24 and 4.25 shows subsequently the tuning range that is frequency variation over the
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tuning voltage, phase noise and amplitude comparison between (a) NMOS, (b) PMOS and (c) Push-Pull
oscillator
1. For NMOS diff pair Oscillator the tuning range is least, which is 245MHz or 4.3%. The main reason is
because of the size of NMOS devices, which was needed to make high in order to have firstly, the much
required over drive and high
gm
ratio in order to make device work in saturation region. The device length
g ds
was increased to 480nM in order to lower the threshold to maximize the overdrive and then maximize
for g m , while the device length of PMOS/Push-Pull diff-pair was kept at minimum. The influence of
parasitic in NMOS can be seen in the phase noise graph, which for 1mW of power was found to be 104.2dBc/Hz. These leaves us with a definite result that NMOS only Oscillator is not going to be used in
Q-VCO. Firstly, the tuning range is poor and secondly the phase noise is not so good in comparison to
PMOS and Push-Pull for same amount of power consumption.
2. Since we are left with now PMOS only and Push-Pull topology, and analyzing Figures 4.23 and 4.24 (b)
and (c), we notice that the tuning range offered by PMOS only topology is around 800MHz or 14.28% in
comparison to 721MHz or 12.78% offered by Complementary oscillator. The Phase noise comparison
follows the analysis that was presented in section before, with an improvement of around 1dB of phase
noise in push-pull topology not 6dB as derived in [74]
Figure 4.23: (a) Tuning Range NMOS Diff-Pair Oscillator
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Figure 4.23: (b) Tuning Range PMOS Diff-Pair Oscillator
Figure 4.23: (c) Tuning Range Complementary Diff-Pair Oscillator
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Figure 4.24: (a) Phase noise of NMOS Diff-Pair Oscillator @ 1MHz offset
Figure 4.24: (b) Phase noise of PMOS Diff-Pair Oscillator @ 1MHz offset
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Figure 4.24: (c) Phase noise of Push-Pull Diff-Pair Oscillator @ 1MHz offset
The Figure 4.24(c) also shows the variation of phase noise with respect to change in value of source
degeneration resistor, as we can analyze that phase noise get better by 2.3dBc@1MHz offset when a source
degeneration resistor of 100 Ohms is used when compared to phase noise when a resistor of 500m Ohms
was placed.
If we try to arrive at certain result using the tuning range and phase noise results, it is founded that not
much conclusive enough to choose between PMOS only and Push-Pull topology as one offers 1.5% higher
tuning range and other offers phase noise improvement of 1.2dBc/Hz. Next is to look onto the swing
offered by PMOS only and Push-Pull topology. The swing is differential peak to peak oscillator output
voltage. Which can be maximum of 2.4V as our Vdd is 1.2V. The swing as stated is plotted in Figure 4.25
below.
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Figure 4.25: (a) Peak to Peak Differential Voltage output of NMOS Oscillator
Figure 4.25: (b) Peak to Peak Differential Voltage output of PMOS Oscillator
On comparing Figure 4.25 (a) and (b), it is noticed that NMOS offers terribly low swing of 559.61 mV in
comparison to PMOS swing of 1.365Volts. If we look at the Figure 4.25 (c) the push-pull topology offers
the highest swing of 1.955Volts, which follows the theory and as anticipated. Therefore, voltage swing,
which is needed to be as high as possible in order to compensate for the loss in buffer and or poly-phase
filter, is chosen. This translates that push-pull topology to hold merit over PMOS only topology for low
power consumption.
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Figure 4.23: (c) Peak to Peak Differential Voltage output of push-pull Oscillator
The Results of complete analysis are summed up in the table 4.6 below
Oscillator
Tuning
Oscillation
Phase Noise @
Tuning Range
Differential
Voltage (V)
Frequency
offset of 1MHz
(%)
Voltage Swing
(GHz)
(dBc/Hz)
peak to peak
(V)
NMOS only
.43
5.59981
-104.2
4.3
0.55961
PMOS only
.65
5.60207
-111
14.28
1.365
Push-Pull
.68
5.6063
-112.2
12.78
1.955
Table 4.6: Oscillators Comparison
Since we have made choice of going for push-pull oscillator, therefore for its robustness and functionality it
should be tested. From the very start of circuit design through the reading of design manual, the process
related variations like (stress effect, matching proximity and body resistance etc.) were used to strict
conditions so that final circuit can qualify for its robustness. However, a few changes and small parameter
tweaking were required in end.
In Figure 4.26 (a) and (b) the results of all the process corners (7 in total), 5 performance based which are
TT (typical or normal run), FF (fast-fast, used for delay and particularly for oscillators), SS (slow-slow, for
delay and for oscillator performance of jitter that is phase noise), SF and FS (Slow-Fast and Fast-Slow, for
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skewness between NMOS and PMOS devices) and FF-Functional and SS-Functional (to verify circuit
performance under extreme conditions). *For more on process corners, refer to IBM-CMRF8SF Model
Design Kit.
Figure 4.26: (a) Tuning Range comparison of push-pull oscillator for all the process corners.
If we analyze the Figure 4.26 (a), it is noticeable that circuit does qualify for extreme SS-F and FF-F
corners. An average tuning range of 13.6% is observed over all the process with worst of close to 13% for
FS corner. Therefore the circuit needs some tweaking and the varactor average capacitance needs to be
reduced to around 350 fF in order to raise the oscillation frequency. This is done also because the layout
and packaging related parasitic are mainly capacitive and resistive in nature, which will automatically bring
down the oscillation frequency. Therefore to be sure that post layout oscillator works in the vicinity of
5.6GHz frequency, it becomes imperative that we raise the oscillation frequency. Now the question is by
how much, because the net effect of parasitic can only evaluated after post layout simulation and parasitic
extraction. However by some reading from manual and mainly learning from the experience of ICdesigners, an offset of 100-200MHz was considered, also QDAcR architecture provides a tolerance of
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±125MHz , which safely qualifies our oscillator. The Figure 4.26 (b) shows the value of differential peak
to peak amplitude for all the process corners.
Figure 4.24: (b) Amplitude comparison of push-pull oscillator for all the process corners.
The amplitude 4.26 (b) shows that highest amplitude is noticed for SF corner and lowest for FFF corner, in
phase the worst phase noise -110.55dBc/Hz was recorded for SS-F corner, while the best phase noise was
found out to be -114.88dBc/Hz for FS corner. However, during circuit design care was taken that
transconductance of both PMOS and NMOS should be same however it is noticed that PMOS transistors
have higher influence, reason could be their comparatively large size and /or the use of PMOS current
source.
The final corner analysis with changed varactor for SS-F and FF-F corners is given below in Figure 4.27 (a)
and (b).
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Figure 4.27: (a) Tuning range comparison of push-pull oscillator for all SS-F & FF-F process
corners.
The Figure 4.27 (a) shows the tuning range with reduced varactor capacitance. The tuning range is
somewhat reduced to average value of 12.33%, however our circuit can safely work in extreme conditions
and some effect of possible parasitic has been compensated during schematic design only. Figure 4.27 (b)
shows the differential peak to peak output voltage swing and it can be inferred that the voltage swing in
adverse effect has changed by ±4% . The phase noise values of two corners SS-F and FF-F at 5.75GHz
oscillation frequency were noticed to be -113.8dBc/Hz and -113.38dBc/Hz respectively. Therefore, we can
now comment for sure that our design does meet low power (1mW), considerable better phase noise than
required and high swing.
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Figure 4.25: (b) Amplitude comparison of push-pull oscillator for all SS-F & FF-F process corners
Hence, this concludes our design of LC-tank oscillator, the in depth process analysis was necessary as this
oscillator will serve as the main component while design of Quadrature output VCO (Q-VCO), whether we
use the cross-coupling method or poly-phase RC-filter for the generation of quadrature signals, this
oscillator will serve has the back-bone of Q-VCO.
4.7 Layout Design Considerations
Points to ponder about layout: The layout in itself has required complete set of design rules to be followed,
which are mostly process technology specified. But, it is advisable to consider the effect of parasitic while
designing the schematics. The parasitic, which can de-Q (lessen the Q-factor) or affect change in the value
of any vital component should be paid attention. With regard to LC-tank performance the main elements
are parasitic capacitance from interconnects, bond-pads and active devices and parasitic resistances and
inductances from interconnects, bond-wires, rf-lines etc.
The value of bond-wire inductance in some cases is very much comparable to the required value, therefore
it becomes essential to mitigate such performance degrading effects, the effect of bond-wires depend solely
upon the type of packaging used for the chip, for e.g. flip-chip does not require bond-wires but suffer from
high capacitive loading. In order to connect chip to outer-pads bond wires are not required then the value of
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chip inductor is not influenced till extent and taken care by proper ground shielding and isolation. In this
case the advantages of high Q-factor of inductor and high-phase noise can still be reaped. The length of
interconnects between the oscillator and other RF on chip components, because as discussed previously
interconnects serves as transmission lines and do suffer from ohmic losses in different mode of operations.
The inductive parasitic component of the parasitic can be harmful, this can be taken care of by having high
width or increased maximizing interconnects, which not only decrease the parasitic inductance but parasitic
resistance also. However, this comes with cost of increased parasitic capacitance. The resistivity and
capacitance of different metal layer as interconnect are defined and characterized in the design manual.
However as of now, the oscillation frequency is offset by 150MHz. to take care of parasitic capacitance and
inductances. The layout of current-source should be as symmetrical and square or in ring geometry, with
high numbers of fingers as prescribed and simulated in [68].
4.8 Conclusions
In this chapter a complete overview of LC-tank design was discussed, our discussion and analysis resulted
in design of a LC-tank, which based on analysis should provide optimum results. Further in the chapter a
design methodology regarding oscillator design was discussed and verified through simulations. Three
differential oscillators, namely NMOS, PMOS and Complementary (Push-Pull) oscillators were simulated
and analyzed. The Push-Pull topology turns out to provide best results which meet our required
specifications and mainly constraint of low power consumption. The complementary oscillator was tested
over all the process corners and the result seconds our choice of topology. Therefore, Push-Pull oscillator is
a solution to proceed further on to the design of Quadrature VCO. An Oscillator being the fundamental
component for Q-VCO design, the solution turns out to be a complementary oscillator. In next chapter we
discuss and design Q-VCO, which meets our specifications.
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5 CHAPTER 5
Quadrature Voltage Controlled Oscillators (Q-VCO): Introduction and Circuit
Design Implementation
We have seen in our discussion of receiver architectures in chapter 3, that for LOW-IF, Zero-IF or
Homodyne receiver architectures the importance of a proper quadrature signal becomes even more crucial.
As we see that for high data rate or high bandwidth applications the LOW-IF topology is becoming popular
and gaining more n more interest of designers. In this chapter we explore and compare the ways to generate
the quadrature signals from an oscillator, this study is primarily based on the literature research. The next
section follows with the description the principle of quadrature generation, followed by principle of
injection locking. We then further investigate primarily two Q-VCO topologies, these are Parallel Q-VCO
or P-QVCO and Bottom Series Q-VCO or BS-QVCO. The conclusions are drawn after careful analyses
over wide range of influencing parameters.
Next, we try to investigate the suitability of quadrature signal generation using a Polyphase filter and delve
into the merits and demerits and which way suits most our specifications, whilst consuming the low power.
The succeeding topic discusses the usability, design and implementation of the output buffers. The buffers
are loaded with variable output, to test the robustness and worthiness of our complete design. The final
conclusions are drawn on the basis of quantitative analysis of the results obtained. In this chapter the
process corner run or lay-out issues have been discussed invariably, where ever required. This chapter in
total presents a complete picture of proposed quadrature oscillator required for impulse radio QDAcR.
5.1 Methods of Quadrature Signal Generation and Q-VCO
Principle
In theory and practice we define signals (consisting of real and imaginary parts) to be quadrature in nature
if over a period they differ by an angle of ±45
o
or ±
π
4
in their phases. For example if we consider a
oscillator output sinusoid, then its equation in the form of quadrature components can be written as given
by equation 5.1 below.
I (t ).sin(ωot ) + Q(t ).cos(ωot )
(5.1)
where I(t) is generally termed as in-phase component and Q(t) as quadrature component. And these
components are given by equation 5.2 as
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I (t ) = Vo (t ).cos(φ (t )) and Q(t ) = Vo (t ).sin(φ (t ))
(5.2)
For Q-VCOs the quadrature signals are generally generated in three different ways and these are described
as following
1. Q-VCO using a frequency divider: The basic principle of designing of Q-VCO, using an oscillator and a
frequency divider is to take a high performance oscillator, which oscillates at twice the required frequency
of oscillation and then the frequency is downconverted using a digital divide by two flip-flop or an analog
divider as described in [75]. This solution serves two purposes firstly it saves the chip area as the
operational frequency goes p the ladder the size and value of inductance required goes down the ladder.
Secondly, digital divider generates a more precise quadrature signals, by using digital inverters, which
inherently produces Quadrature signals. However, at very high frequencies the ‘Q-factor’ of LC-tank
degrades severely, with decrease in inductance value and shifting of operational frequency towards the selfresonance frequency. Until and unless the phase noise and power requirements are relaxed, the digital
frequency divide by two solution in not advised. Due to power budget constraints and relaxed
specifications for phase error, this solution was not opted.
2. The Use of Poly-Phase filter: Poly-phase filter consists of a RC-CR network, which provides signal a
phase shift of ±45 . This solution consumes less power in comparison to previous one. However, this
o
solution is also marred with process related PVT variations, degradation in phase noise and relatively high
phase error. Also, the loading of poly-phase filter to an oscillator directly, can cause the change in the LCtank properties and therefore it requires buffers or high de-caps. In our case, a poly-phase can be a solution
due to relaxed specification on phase noise and phase error, and we shall discuss it in detail later in a
separate section.
3. The third option consists of cross-coupling of two LC-tank oscillators, as firstly proposed in [76]. This
solution surpasses above two in power consumption and offers a variety of other advantages. However, this
comes with extra chip area, which should not be much of a constraint if the specification demands so. The
option of cross coupled Q-VCO provides high phase noise and more precise quadrature signals than a polyphase filter and at lower power. Next, the output swing that is provided by LC-tank cross coupled Q-VCO
is a much desired output quantity as generally in a RF-chain the next stage is depicted by a mixer, for
which LO output serves as an input. Therefore, due to posed advantages the option to have two VCO crosscoupled together seems to be a lucrative one for low power design, while matching all the specifications.
5.2 Q-VCO Principle
In this section we discuss the principle of quadrature signal generation through the cross coupling of two
VCOs. This principle was first published in [76], which involves two LC-tank oscillators coupled together
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through MOSFETs in parallel to the oscillator transistors, where one coupling is direct one and other is
cross coupled. The Figure 5.1 adapted from [76] shows the complete principle of Q-VCO. The two core
oscillators are with transistors pairs M1,M2 and M`1,M`2 and the direct coupling transistors are M`c3 &
M`c4, while the cross coupling transistors are Mc3 & Mc4.
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Figure 5.1: Two Quadrature Coupled Oscillators.
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The principle involves that the oscillation in two oscillators can only happen when and only when they are
synchronize and are in quadrature to each other that is oscillations are anti-phase.
A more generic but in-depth quantitative analysis for couple Q-VCO is presented in [77], this serves as a
classic as it deals with the issue of stability and oscillation start-up conditions, irrespective of oscillator’s
circuital parameters like sizes of device, dc voltages and currents etc. The postulates from [77] were
investigated thoroughly through simulations and quantitative analysis and it was found that there arrives no
need to reproduce the mathematical analysis in the thesis. However, the main postulates, are analyzed and
further simplified and are presented in brief here, as they serve the very basis for the design of Q-VCO.
1. Stability: The stability is foremost criteria, which is addressed by the Barkhausen’s criteria. This stands
for start-up condition as well as phase stability. The solution given is given by equations 24-26 in [77],
where the stable modes of oscillation and amplitude stability are expressed. The equation are given as
equation 5.3 here
ωosc ,2
ωo
4I R
m cos φ
; A1 = O P (1 − m sin φ )
2Q 1 + m sin φ
π
4I R
ω
m cos φ
= ωo + o ⋅
; A2 = O P (1 + m sin φ )
2Q 1 + m sin φ
π
ωosc ,1 = ωo −
⋅
(5.3)
The subscript ‘1’ and ‘2’ stands for two stable modes, however first mode is conditionally stable and
second
and m =
mode
I Coupling
I Osc
is
unconditionally
stable
and φ =Phase Shift between Direct and Cross coupling currents . Now, if we consider the
two LC-tank oscillators with exact devices and all passives parameter and coupling transistors with
transconductance of ‘ g mc ’ then the loop gain equation according to Barkhausen is given by equation 5.4
jωosc L
2
1 ≤ − g mc
1
2
− g m − ωosc LC
1 + jωosc L
RP
2
(5.4)
Solving this equation for composite oscillation frequency of both the oscillators, we can deduce that it also
shows two modes of oscillation, one with oscillation frequency which is ahead of normal oscillation
frequency that is without coupling. In second state the oscillation frequency lags behind the normal
oscillation frequency. The values are given by equation 5.5
ωosc ≈ ωo ±
g mc
2C
(5.5)
If we analyze we see that the coupling transconductance and coupling factor are dependent through the tank
‘Q-factor’, higher the quality factor most strong will be coupling. Therefore for quadrature oscillation
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stability and amplitude stability a high ‘Q’ and high value of ‘m’ or high value of transconductance of
coupling transistors is necessary
2. Phase Error due to mismatches: In [77] it is postulated that phase error‘ ∆ϕ ’ is a function of phase shift
‘ φ ’ and the quadrature accuracy is most dependent on the mismatches and PVT variations when φ = 00 and
least dependent when φ = 900 . In [78] this postulate is extend to the circuit parameter, and it results that in
order to have a better phase noise and less amplitude and mismatch errors than a common current source
should be used for oscillator core as well as coupling transistors.
3. Phase Noise: the phase noise of Q-VCO is given by equation 52 in [77], which is as follows and reproduced as equation 5.6
2
R
ω
L {∆ω} = 10.log kT (1 + F )i 2 P 2 i o ; where Q eff-Tank = Q
Qeff −TankVO ∆ω
1
m cos φ
1+
1 + m sin φ
If we see the value of phase noise for couple Q-VCO we find that for 0 ≤ φ ≤
π
2
2
(5.6)
the value of phase noise
improves with a maximum of 2dBc/Hz in comparison to un-coupled or stand-alone oscillators.
This sums up as fundamental but robust analysis of main factors, which can seriously degrade the
performance of a cross coupled Q-VCO.
5.3 Principle of Injection locking
So far we analyzed all the major influencing factors for quadrature accuracy and stability. However, we
have not discussed about the limit of frequency fluctuation. We have noticed that cross coupled Q-VCO
operates at a common frequency, which is deviated or at a difference from the oscillation frequency of a
stand-alone oscillator. This deviation or the frequency range over which two oscillators can lock with each
other is called lock range ‘ ∆ω ’ and the principle in itself as injection locking. Mathematically it is given
by equation 14 and 15 in [77], which are expressed here as equation 5.7
I Inj
Io
≥
4
∆ω
π
ωo
2
+ ∆ω
2Q
2
; where ∆ω =
ωo
2Q
⋅
1
4I o
π I Inj
2
−1
=
ωo I Inj
⋅
2Q I Osc
⋅
1
2
(5.7)
I Inj
−1
I Osc
If we analyze this equation of importance then we see that in order to safe guard that our oscillator lock to
provide quadrature oscillator then we should trade off with phase noise, by decreasing the Q-factor or
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increasing the Injection current of coupling transistors, which in turn results in higher g mc and higher
oscillator bias current. Therefore, we should go for high transconductance for coupling transistors or high
value of coupling factor ‘m’ for robust locking range and ensuring quadrature oscillations.
5.4 Implementation of Q-VCO using injection locking
If we consider any differential pair cross-coupled stand-alone oscillator, then we can easily find that the
injection into this oscillator can happen in 3ways, firstly by parallel injection, which is most common and
proposed in [76] and commonly known as P-QVCO or parallel coupled Q-VCO. The second topology is as
described in [79, 80] where injection is done in series with the oscillator core transistor, this can be done at
drain or source node therefore commonly known as Top series Q-VCO or TS-QVCO and bottom series or
BS-QVCO. Third and lastly by modulating the gate of cross-coupled oscillators by injecting signal [81].
The far reaching claims of better performance has been made by [79, 80, 81] over the P-QVCO. Therefore
it was decided to investigate P-QVCO and BS-QVCO topologies in their entity and use the best option. The
last topology was left out of analysis, because preliminary analysis showed not much conclusive difference
between the results with respect to BS-QVCO
5.4.1 Methodology for Quadrature Oscillator Design
The basic design principles for oscillator design remain the same as discussed in the previous chapter in
detail. Also, the push-pull topology designed oscillator is used to design the Q-VCO. The points of
consideration we have mentioned in our stability and injection locking analysis. Now we first start with
analysis of BS-QVCO followed by analysis of P-QVCO and then arriving at the conclusion. A few design
considerations
1. Increasing the oscillator bias current to 1mA, in order to ensure proper locking.
2. DC-Biasing re-evaluation, in order to make sure sufficient overdrive and to ensure sufficient gain to keep
diff-pair transistors in saturation
3. Using same or common current source as mentioned in [78, 79, 80] to reduce amplitude related errors
and better quadrature performance.
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a) Bottom Series Q-VCO : The theory and implementation of series injection has been reported with
added emphasis and quoting very good results in [79, 80]. The model for BS-QVCO with its basic analysis
has already been presented in these papers. The highlighted points are that series QVCO provides better
phase noise, higher output swing and better phase error than P-QVCO, under the conditions of same power
consumption and same coupling factor.
We started with taking already optimized push-pull VCO which suits our requirements. Then two
transistors were added in series with the PMOS-diff pair as shown in Figure 5.2. The single VCO is shown
as two vco are exactly similar and the coupling nodes are connected in direct and cross-coupled fashion as
desired. Two points are worth mentioning here 1) Use of Degeneration resistor, in order to keep the
simulations and design conditions as similar as possible, we did not omit out the degeneration resistors.
One would argue that when series transistor in itself acts as a degenerated source, but it was seen in
preliminary analysis that phase noise was 2dBc/Hz. better with degeneration resistors. Therefore resistors
were kept part of the circuitry. 2) The DC analysis of the circuit, as we have already designed the push-pull
topology in accordance with the prescribed design methodology therefore all the changes were made in the
coupling transistor in order to change the coupling factors for analysis.
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Figure 5.2: BS-QVCO (Half Circuit)
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As mentioned in [80] the coupling factor in series injection is defined by the ratio of transconductances of
coupling transistor and Oscillating transistor that is ratio transconductances of transistors Mc1 and M1. The
results for various values of coupling factor are tabulated below.
Coupling
Factor
Voltage
Phase Noise
Tuning
@
5.6GHz (V)
Phase Error
Tuning
Differential
Amplitude
@
(degrees)
Range (%)
Voltage Peak
Error
to Peak (V)
(Relative)
1MHz
offset
(dBc/Hz.)
1.2V=Vtune
.3302
1.022
-115.5
0.1
13.06
1.8173
.055
.354
.99
-114.892
0.2
12.75
1.972
.051
.4362
.91239
-113.982
0.25
11.55
2.131
.05
.4826
.8344
-113.92
0.25
10.95
2.21
.047
.5162
.7535
-113.93
0.1
10.51
2.247
.043
.5416
.67109
-113.98
0.08
10.16
2.265
.035
.5975
.01
-114.33
0.013
9.25
2.27
.031
Table 5.1: BS-QVCO Simulation Analysis
In the simulation analysis of BS-QVCO two important observations were made.
1. The coupling factor in BS-QVCO is very much range bound. This means that for constant current and
low supply voltage regime, the way to change coupling factor is to change the device size. Therefore, for
low coupling factors in our case m=0.3, the coupling transistor MC1 sends the oscillator transistor to cutoff region that is the gate drive voltage of M1 becomes less than the threshold voltage. Second, the upper
limit of coupling factor is dictated by current clipping. Because on increasing the coupling factor or
transconductances ratio we observe that, the current drawn into the oscillator become higher, the reason is
the increase in the current source output impedance, due to coupling transistor, which works as a high
resistive impedance in triode region. However, after certain value in our case m=0.54, the amplitude swing
starts to saturate.
2. If we observe the table 5.1 carefully then it can be noticed that better phase noise performance is also
range bound. The reason of high phase noise associated with degeneration/triode state of coupling transistor
has been commented and appreciated in [80]. However, the effect of series coupling topology in lowering
of flicker noise contribution is optimal till only certain extent, as matter of fact Mc1 working in deep triode
region starts adding its own thermal noise current to the oscillator and the desired advantage to be reaped
from less flicker noise up conversion is lost in total. In addition, the parasitic capacitive effect due to large
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size of coupling transistor starts effecting the tuning range and furthermore, due to increase in parasitic
capacitance the phenomenon of amplitude modulation that is ‘squegging’ is visible.
In conclusion, it can be said that BS-QVCO is best suited for much more power budget relaxed oscillator. It
definitely offers higher swing as anticipated and explained in [80] but on the other hand deteriorates tuning
range and phase noise. In low power oscillator design the advantages offered by BS-QVCO can not be fully
explored or some drastic design changes needs to be made for e.g. use of switchable capacitive bank as
varactor in order to preserve the tuning range.
b) Parallel Coupled Q-VCO or P-QVCO: In P-QVCO the desired coupling is performed by putting
coupling transistors in parallel with the oscillator diff-pair. The principle, mathematics has been described
in detail in [76, 77]. The half circuit of P-QVCO is shown in figure 5.3 below. The coupling transistors
Mc1 and Mc2 necessitate the proper injection locking with the core oscillator. As discussed and derived
previously the quadrature accuracy and locking can be achieved through high coupling factor values. The
results of simulation are tabulated in table 5.2, where the coupling factor is changed by changing the width
of the coupling transistor, while keeping the devices in saturation mode of operation.
Figure 5.3: The Mirror half circuit of P-QVCO
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Coupling
Tuning
Factor
Voltage
Phase Noise
@
5.6GHz (V)
Phase Error
Tuning
Differential
Amplitude
@
(degrees)
Range (%)
Voltage Peak
Error
to Peak (V)
(Relative)
1MHz
offset
(dBc/Hz.)
1.2V=Vtune
.3293
1.001
-115.5
0.21
12.4
1.8139
.063
.3512
.98871
-115.48
0.2
12.33
1.807
.0635
.435
.9623
-115.4
0.16
11.7
1.78
0.54
.4828
.94276
-115.28
0.13
11.56
1.77
.051
.5170
.9263
-115.25
0.1
11.49
1.764
.045
.5425
.91814
-115.21
0.03
11.41
1.76
.044
.613
.9103
-115.169
0.015
11.23
1.74
.040
Table 5.2: P-QVCO Simulation Analysis
The coupling factor ‘m’, this is given by m =
I coupling
I osc
=
WMc1
, serves as the most influencing parameter in
WM 1
defining the Quadrature accuracy and as far now, it was varied by changing the device width. For
simulation purposes this works fine. However, in real circuit, one the device has been fabricated, no more
changes in geometry are plausible. Therefore, three solutions are possible, first that choose a fixed
geometry that corresponds to a particular coupling factor. However, this solution suffers from PVT
variations and mismatch, therefore in order to guarantee Quadrature oscillations, the designer needs to
characterize the design for its robustness and secondly need to keep the a large coupling factor. The
necessity to keep large coupling factor comes at an added cost of lowering the phase noise and swing.
The other method is to control the gate bias of the coupling transistors and thus controlling the current
through the device and hence controlling the coupling factor. In such design, an extra reference circuitry is
required in order to calibrate against the PVT and mismatch variations. Therefore, this solution does not
guarantee much desired dynamic coupling factor, until and unless the reference circuitry characterized for
its accuracy.
The third viable option is to put switchable bank of coupling transistors in parallel to the oscillator diff-pair.
This solution is best suited, since we can control the coupling factor dynamically. In order to ensure
Quadrature generation the initial factor can be set to high value like .5 or .6 and then reduced to .3 or .2 in
order to take full advantage of better phase noise and large swing.
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An Oscillator System for UWB QDAcR
The use of option three seems to be lucrative because of its posed advantages, however in low and constant
current regime, the option one is most suitable. The reasoning being that the transconductance of the diffpair plays an important role in the start-up condition and it is dependent on the oscillator bias current. Since
we are using a common current source for coupling transistors as well as oscillator biasing, therefore the
bias current is being shared by oscillator core, and coupling transistors in accordance with the coupling
factor value. So, any sudden switching of coupling transistors will lead to change in the transconductance
of the diff-pair.
If we analyze tables 5.1 and 5.2 simultaneously, we can draw some realistic comparisons between the
performance of BS-QVCO and P-QVCO. Firstly, if we compare the phase noise change in two Q-VCOs
with respect to the same coupling factor and for same power consumption. As shown in the Figure 5.4 (a)
the phase noise of P-QVCO is less susceptible to coupling factor in comparison to BS-QVCO. P-QVCO
performance is better than BS-QVCO for low power consumption and smaller device size. A difference of
1dBc/Hz @1MHz offset is measured for coupling factor of 0.6.
Figure 5.4: (a) Phase Noise comparison between P-QVCO and BS-QVCO
The next graphs 5.4 (b) and (c) depicts the comparison between P-QVCO and BS-QVCO for tuning range
and the phase error. If we analyze these graphs then again it is quite visible that P-QVCO give better phase
noise and comparative phase error. Therefore, apart from swing, on all accounts the P-QVCO performances
better than BS-QVCO. These results and analysis which shows that P-QVCO is best choice for low power
and constant current regime. Therefore, we zero upon P-QVCO as our choice for Quadrature oscillator for
QDAcR. In next section we test the robustness of our P-QVCO over all the process corners and Monte
Carlo analysis .
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An Oscillator System for UWB QDAcR
Tuning Range Comparison
14
Tunig Range (%)
12
10
8
6
4
2
Tuning Range P-QVCO
Tuning Range BS-QVCO
0
0.3302
0.354
0.4362
0.4826
0.5162
0.5416
0.5975
Coupling Factor
Figure 5.4: (b) Tuning range comparison between P-QVCO and BS-QVCO
Phase Error Comparison
0.3
0.25
Phase Error (deg)
Phase Error P-QVCO
Phase Error BS-QVCO
0.2
0.15
0.1
0.05
0
0.3302
0.354
0.4362
0.4826
0.5162
0.5416
0.5975
Coupling Factor
Figure 5.4:(c) Phase Error comparison between P-QVCO and BS-QVCO
After making the choice between the BS-QVCO and P-QVCO, the robustness of P-QVCO design is tested
against the PVT variations. The process corner analysis of P-QVCO is presented in Figures 5.5, 5.6 and
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An Oscillator System for UWB QDAcR
5.7. The Figure 5.5 shows the tuning range across all the process corners. It can be seen that design and
devices do qualify for specs regarding the tuning range requirement, the worst tuning range provided is
11.231% at coupling factor value of 0.6. The phase noise variation across all the process corners is shown
in the Figure 5.6, from which it can be discerned that even for a higher coupling factor of 0.6 the circuit
provides good enough phase noise of -115dBc/Hz @1MHz offset, which is better than the required specs
and provide the extra cushion at low power consumption. Furthermore, from Figure 5.7 we can discern that
output signal of P-QVCO in worst case provides a single ended Vpk-pk swing of 800mV, which allows
extra headroom in power consumption for succeeding buffer stage.
Figure 5.5: Process Corner Analysis of P-QVCO for tuning range
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An Oscillator System for UWB QDAcR
Figure 5.6: Process Corner Analysis of P-QVCO for phase noise.
Figure 5.7: Process Corner Analysis of P-QVCO for Quadrature Swing
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An Oscillator System for UWB QDAcR
The process corner analysis confirms the robust design nature of Q-VCO. This P-QVCO stands on all the
counts of performance and suffices to be a good solution to our problem statement. Therefore, with a total
power consumption of 2.4mW, phase noise of -115dBc/Hz @1MHz. offset and average differential swing
of 1.7Vpk-pk, this P-QVCO is our choice as a Quadrature oscillator for QDAcR. Therefore, it can be
concluded that P-QVCO proves to be best possible option when compared with BS-QVCO. However,
Poly-Phase filter does provide another viable option, which is being exploited in next section.
5.5 Q-VCO implementation using Complementary VCO, PolyPhase filter and output buffers
This Q-VCO is designed using the basic and optimized push-pull VCO from the Chapter 4. The Poly-Phase
filter is loaded to the VCO using the ouput-buffers, which are designed to drive variable and can be
implemented as output stage in case of P-QVCO. The implementation in block diagram is show as in
Figure 5.8
Figure 5.8: Implementation of Q-VCO with Poly-Phase Filter
5.5.1 Poly-Phase Filter Design and Implementation
In this section the design and implementation of Poly-phase filter is depicted. As described in previous
sections that a poly-phase filter consist of RC-CR networks. The generic poly-phase filter is shown in the
Figure 5.9 below, the two outputs are in quadrature that the phase difference between the two outputs is 90
degrees. The mathematics is described in detail is [39], which results that the outputs are in quadrature for
all the values of frequency, however they are equal in magnitude that is in amplitude only when the angular
frequency, ω =
1
.
RC
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An Oscillator System for UWB QDAcR
Figure 5.9: RC-CR Network (Poly-Phase) [39]
Due to very nature of passives, the poly-phase performance is dependent upon the PVT variations,
therefore an intelligent design methodology has to be adopted for choosing the appropriate passives and
passive specs based on the simulation and information gathered from technology design manual and taking
into account layout and PVT variation considerations. The design strategy is explained hereunder.
1.
Calculation for number of stages required: The desired poly-phase filter should be able to provide
quadrature outputs while meeting the specs. Firstly, the bandwidth of the filter response should
match or more than the tuning range of the oscillator. Therefore, the best way is to put two poles at
lowest and highest frequency of the tuning range. Therefore, the minimum required stage turns out
to be a 2 stage poly-phase filter.
2.
The choice of proper passive from the process library: The spreads in RC filter should be as
minimum as possible for less amplitude error and phase error. Based on the investigation of design
manual and comparing all the resistors for best mis-match sensitivity, least parasitic, absolute
resistance value and tolerance. It resulted in the choice of L1-BEOL, however this resistance does
poses layout hardship, but by having one extra mask and proper layout this problem can be taken
care of. Therefore, finalizing on L1-BEOL resistor.
3.
The choice of capacitor was limited to MIM cap as offered by process technology (DM), while
High K MIM cap are available for OL/LM options. Therefore, deciding on the MIM cap, next step
was to choose the number of layers. In DM process metal layers 2, 3 and 4 can be used as thin
metal later and 1 and 2 as thick metal layers. Choosing layer 3-2 for the MIM caps, by simulating
and reading the correlation plots in design manual for the least parasitic and feature size. The next
step involved was to choose between the single or dual MIM cap, analyzing the data from manual
results that for small value of capacitance single MIM cap gives better error% and less parasitic
for comparable mismatch. Therefore, finalizing on single MIM cap with 3-2 metal layers.
4.
Next Step, was to choose the proper values of passives that is the values for resistor L1-BEOL and
MIM cap. In case of resistance the resistor cut-off frequency plays the limiting constraint as
parasitic capacitance increases, which results in increased phase error. Also, large resistors induce
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An Oscillator System for UWB QDAcR
more thermal noise, but since phase noise and phase error requirements are bit relaxed and
importantly larger resistor helps in low power design, therefore we go for largest resistor. This
makes to minimize the value of MIM cap, which in turn also effective as it reduces the capacitive
loading and amplitude squegging. Choosing the minimum capacitance size that is 97fF for
5micron x 5micron MIM cap feature size, gives us resistance value of approximately 293 Ohms.
5.
Since we have chosen passives with lowest possible error, parasitic and mismatch offered my
technology, therefore spreads are curtailed down therefore choosing poles with total tolerance of
10% .
The design process described above serves as the basis poly-phase filter design. The Figure 5.10 below
shows the complete circuit design of VCO, buffers and Poly-phase filter. The design of output buffer is
presented in the next section
Figure 5.10: Circuit Design for Poly-Phase Filter Q-VCO.
5.5.2 The design of Output Buffer
In order to mitigate the effect of direct loading of Poly-Phase filter either a de-coupling capacitor of a
minimum value of 30pF , however it will De-Q the resonator, as well compromise the amplitude swing of
the oscillator and employing such a big de-cap depends upon the layout size also. Therefore, a careful
option is to employ output buffers, the output buffer presented here also serves for P-QVCO as the Sparameter analysis provides with almost similar matching impedances, because of common VCO in both
the cases. In case of P-QVCO buffer drives the bond-pad (modeled on the basis of design manual) or mixer
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An Oscillator System for UWB QDAcR
gate, therefore tested to drive predominantly capacitive load from 50fF to 600fF for a maximum power
consumption of 3mW.
Choice of buffer topology: Voltage buffer or common drain serves as a basic topology for VCO buffers,
however the swing is sacrificed in this case and also big biasing ‘T’ inductor and capacitor is required in
order to make voltage buffer functioning for low power regime. Also, the output loading at source node of
common drain buffer can severely degrade oscillator’s performance, because the effect of Beta
transformation the capacitive load or impedance effects the input impedance of the buffer and this needs
careful matching and designing. However, Common source topology, if properly biased serves as a basic
output buffer withholding the oscillator swing amplitude. Nevertheless, in order to have proper design and
desired gain at low power consumption a proper design of common source is required like use of
neutralization capacitors and inductor for biasing as well as proper pole management. The differential
parallel inductor is used in buffers.
Also, common source buffer further reduces the common-mode noise, therefore choosing Common Source
as out-put buffer topology. Starting with the biasing current source/Mirror design, the approach as used in
oscillator current source design is being employed here. For the same reasons of lesser noise contribution
and suppression of common-mode oscillations at fundamental and second harmonic as explained in detail
in previous chapter. The net contribution of common-mode noise and common-mode oscillation is tackled
using cascode source with a very small transistor, the common mode oscillation is highly undesirable in
order to ensure stability.
The instability or unwanted oscillation can also be caused by C gd of buffer transistors, that needs to be
mitigated by use of inductive biasing and mainly using the neutralization capacitance. This neutralization
capacitance reduces the effect of C gd and improves the gain of amplifier by reducing the feedback effect
through parasitic gate-drain capacitance. The neutralization capacitors are implemented as shown in Figure
5.10 as the cross-connected capacitors. The small signal analysis provides the mathematical insight into
neutralization capacitance value, which is given as Cnz ≅ (1 + α ) Cgd , where α is a ratio of gate resistance
of buffer transistor and total negative resistance of the oscillator at oscillation frequency. it can be further
approximated as Cnz ≈ C gd , however a bit higher value is good, however over compensation can lead to
positive feedback and in turn oscillation and instability. Since, the value of C gd is device size and bias
dependent, therefore S-Parameter analysis of the buffer, looking at the input impedance is desirable in order
to find value of neutralization cap. The value for the chosen buffer comes out to be approximately 80fF.
Therefore, neutralization capacitance in nearing range is used. The Figure 5.11 shows the sweep of phase
noise for various values of neutralization cap, which additionally supplements the value derived from S-
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An Oscillator System for UWB QDAcR
Parameter analysis. The best phase noise of -109.6dBc/Hz@1MhZ is observed for neutralization cap of
80fF.
Figure 5.11: Phase Noise Vs. Neutralization Cap
The other validation of proper design of output buffer is proved by Figure 5.12 below, it shows the
differential amplitude swing and it can be seen that for 80fF and power consumption of 3mW the buffers
provides output gain of approximately 4dB, where as the loss of 6dB is noticed within poly-phase filter.
Figure 5.12: Output Swing Comparison for Oscillator, Buffer and Poly-Phase outputs.
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An Oscillator System for UWB QDAcR
The comparison for performance of P-QVCO and Poly-phase Filter is presented in the table 5.3 below as
Oscillator
Tuning
Voltage (V)
Oscillation
Phase Noise @
Frequency (GHz)
offset of
1MHz
(dBc/Hz)
P-QVCO
.800
5.6530
Poly-Phase
.680
5.60689
Differential
Voltage
Swing peak
to peak
(V)
Power
(mW)
-115.1
1.7815
2.4
-109.7
1.16
4.8
Table 5.3: Comparison between P-QVCO and Poly-Phase Implementation
It can be seen that P-QVCO surpasses the performance of poly-phase implementation on all specs and
mainly the low-power consumption. Therefore, it is a right decision to choose P-QVCO as a Q-VCO
required for QDAcR.
5.6 Conclusion
In this chapter, we extensively investigate various Q-VCO topology, a comparison between P-QVCO and
BS-QVCO serves as highlight, as it is realized that different topology offers different merits. BS-QVCO
definitely matches ad surpass the performance of P-QVCO but this is only possible in higher power
consumption regime. For low power consumption P-QVCO is a definite and best possible choice among
the options investigated. A complete robust design of P-QVCO with degenerate resistors being provided
and its comparison with a poly-phase implementation further stamps the selection of the P-QVCO. The
output buffers with neutralization cap and variable load driving capacity were also presented. This in total
suffices as a complete circuit design for an Ultra-wideband Oscillator system, designed to perform at low
power consumption, while exhibiting noticeable figure of merit. A Q-VCO system with a figure of merit of
186.36dB is presented, which satisfies all the laid down specifications.
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An Oscillator System for UWB QDAcR
6 CHAPTER 6
Conclusions and Future Work
6.1 Conclusions
This thesis work encompasses a complete design of QDAcR Downconverter and Quadrature Oscillator
System for QDAcR in particular. The extensive quantitative analysis and modeling at system level helped
in deriving the vital specifications, while the proper and robust circuit design resulted in a pragmatic and
fully operational Q-VCO system.
Starting by highlighting the results obtained and important conclusions drawn from system level modeling,
which hold importance to this work as well as in regard to scientific community.
1.
A complete quantitative modeling of QDAcR is being presented in chapter 2. This results is
arriving at equation of prominence (Equation 2.43), which not only captures the total effect of
stochastic perturbations such as noise, jitter and device behaviour for QDAcR in particular, but
provides a simplified and ready to use model for other low (Zero) – IF receivers.
2.
Re-visiting the relationship between timing jitter and phase noise, while characterizing jitter as a
Gaussianly distributed stationary stochastic variable.
3.
Modeling of a real oscillator in matlab, this modeling served as the basis in order to find the
desired specifications for a QDAcR downconverter.
4.
Unraveling for the first time based on comprehensive quantitative modeling and system analysis
the phase noise requirement in QDAcR in particular and fully extendible to template and energy
correlating wideband receivers.
5.
Modeling, implementing and testing of different pulse for their spectral efficiency
6.
An all-inclusive modeling of QDAcR while addressing the issue of interference, a proposed
architecture with filters, which increases the process able bandwidth to 76% of the total available
bandwidth. The composite view of time and frequency domain treatment of bandwidth.
Thus summing up the important conclusions drawn from the system level modeling, this helped in laying
the basis for the circuit design. The circuit design involved the design of Q-VCO, that meets all the desired
specifications. The work in circuit design can be highlighted as follows:
1.
Development and Implementation of algorithm in order to find best suitable or to say optimized
value of inductor ‘L’ and capacitance ‘C’ whist targeting low power consumption and better phase
noise.
2.
Exploiting possible differential topologies for LC-Oscillator and comparing them in depth for the
best possible option in accordance with the specs.
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An Oscillator System for UWB QDAcR
3.
Designing of a robust Push-Pull Oscillator, which satisfies all the specs and operable in deep sub
milli-watt power regime. This oscillator exhibits a figure of merit of 187.5dB and serves as a basis
for designing of Q-VCO
4.
Vital comparison between the BS-QVCO and P-QVCO, this helped in deducing the facts
regarding operating conditions and performance. The results rectifying the claims that BS-QVCO
always performs better than P-QVCO
5.
Comparison between Poly-Phase based Q-VCO and the P-QVCO, this analysis further stamped
the authority of P-QVCO. Poly-Phase filter does not offer the theoretically expected advantages ,
though working at higher frequency poly-phase oscillator can emerge as a contender for Q-VCO
design
6.
Design of a robust P-QVCO, which meets all the requirements under all the process corners.
7.
A comparison of the present work with other notable work as presented below further stamps the
usefulness, scientific viability and credibility of the this thesis work
Technology
[M.Tiebout]
[Willson, Yao] [Ng, Luong]
[Samori, Frey] This Work*
IEEE. JSSC
IEEE. ISSCC
IEEE JSSC
IEEE. JSSC
(simulated)
0.25um CMOS 0.18um CMOS 0.18um CMOS 0.25um CMOS 0.13um
CMOS
Supply Voltage 2.5V
Frequency
1.8GHz
Phase Noise
-143dBc/Hz.
@3MHz offset
1.8V
5.1GHz
-132.6dBc/Hz
@3MHz offset
1V
17GHz
-110dBc/Hz.
@1MHz offset
2.5
4.88GHz
-125dBc/Hz.
@1MHz offset
1.2V
5.64GHz
-115dBc/Hz.
@1MHz offset
Tuning Range
Power
FOM
Phase Error
17%
27.7mW
192dB
N/A
16.5%
5mW
187.6dB
1.4 Degrees
13%
22mW
185dB
2.6 Degrees
11.4%
2.4mW
186.36dB
0.2Degrees
17%
20mW
185.5dB
3 Degrees
As stated earlier that this work comprehensively exploits and mainly builds upon the existing models and
design principles in circuit design and system design simultaneously. This resulted in the form of results,
which are new, publishable and credible.
6.2 Future Work
It is necessary as well as beneficial for the scientific community if the research done raises the question
marks and opens the door for further research and / or investigation. So, does is offered by this work.
1.
At system level present models can be advanced in order to exploit the use of pulse based,
energy/template correlation based systems at higher frequency, preferable in open band that is 2229 GHz. This requires new facets to be added to present wideband receiver architecture, with
emphasis on low-IF architectures.
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An Oscillator System for UWB QDAcR
2.
The system development can open door for fast digital processing near the antenna, further
exploiting the role of pulse shaping and spread spectrum techniques
3.
At circuit level, a more in depth study into Q-VCO is desirable, this should not only include the
quantitative aspect but provide with a comprehensive design strategy and topology for Q-VCO
4.
Possibly comparison present P-QVCO with Q-VCO realized by digital divider and VCO.
5.
Exploiting the devices and topology as why
gm
ratio serves as a bottleneck, specially for
g ds
regenerative oscillators in sub nano nodes.
6.
A complete functional QDAcR IC.
These were a few recommendations for the future work. This work accomplished all its desirables, nw time
to build up further.
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An Oscillator System for UWB QDAcR
References
1.
S. Bagga, S.A.P. Haddad, W.A. Serdijn and J. R. Long: Ultra-Wideband Radio: Unconventional
Circuit Solutions for Unconventional Communication, invited chapter, in Arthur H.M. van
Roermund - Herman Casier - Michiel Steyaert (Editors) Analog Circuit Design, Kluwer Academic
Publishers, 2006, ISBN:14020-5185-9.
2.
Heydari, P.; A study of low-power ultra wideband radio transceiver architectures, Wireless
Communications and Networking Conference, 2005 IEEE, Volume: 2, On page(s): 758 – 763.
Date: 13-17, March 2005.
3.
M. Z. Win and R. A. Scholtz, “On the Robustness of Ultra-Wide Bandwidth Signals in Dense
Multipath Environments,” IEEE Comm. Letters, vol. 2, no. 2, pp. 51-53, Feb. 1998.
4.
M. Z. Win and R. A. Scholtz,” Ultra-Wide Bandwidth Time-Hopping Spread-Spectrum Impulse
Radio for Wireless Multiple-Access Communications,” IEEE Trans. Communications, vol. 48, pp.
679-69, April 2000.
5.
F. Ramirez-Mireles, “Performance of Ultrawideband SSMA Using Time Hopping and M-ary
PPM,” IEEE J. Select. Areas Communications, vol. 19, no. 6, 1186-1196, June 2001.
6.
Aytur, T.; Han-Chang Kang; Mahadevappa, R.; Altintas, M.; Brink, S.; Diep, T.; Cheng-Chung
Hsu; Feng Shi; Fei-Ran Yang; Chao-Cheng Lee; Ran-Hong Yan; Razavi, B.; A Fully Integrated
UWB PHY in 0.13/spl mu/m CMOS , Solid-State Circuits Conference, 2006. ISSCC 2006. Digest
of Technical Papers. IEEE International, Page(s): 418 – 427, Publication Year: 2006.
7.
R.T. Hoctor and H.W. Tomlinson, “Delay-Hopped Transmitted Reference RF Communications,”
Proceedings of the IEEE Conference on Ultra Wideband Systems and Technologies, pp. 265-270,
May 2002.
8.
Simon Lee, S. Bagga and W.A. Serdijn, “A Quadrature Downconversion Autocorrelation Receiver
Architecture for UWB,” Joint UWBST and IWUWBS, May 2004.
9.
Faranak Nekoogar, Ultra-Wideband Communications: Fundamentals and Applications, Prentice
Hall, August 31, 2005; ISBN: 0-13-146326-8.
-187-
An Oscillator System for UWB QDAcR
10. Gerrits, J.F.M.; Farserotu, J.R.; Long, J.R.; UWB considerations for "my personal global adaptive
network" (MAGNET) systems; Solid-State Circuits Conference, 2004. ESSCIRC 2004.
Proceeding of the 30th European, Page(s): 45 – 56, Publication Year: 2004.
11. http://fjallfoss.fcc.gov/edocs_public/attachmatch/DOC-220001A4.pdf.
12. John R. Long; ULTRAWIDEBAND TRANSCEIVERS; Analog Circuit Design; Springer
Netherlands; ISBN: 978-1-4020-3885-3.
13. Behzad Razavi, Turgut Aytur, Christopher Lam, Fei-Ran Yang, Kuang-Yu (Jason) Li, Ran-Hong
(Ran) Yan, Han-Chang Kang, Cheng-Chung Hsu and Chao-Cheng Lee; A UWB CMOS
Transceiver ; IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 40, NO. 12, DECEMBER
2005.
14. Jri Lee; Da-Wei Chiu;
Nat. Taiwan Univ., Taipei, Taiwan ; A 7-band 3-8 GHz frequency
synthesizer with 1 ns band-switching time in 0.18 µm CMOS technology; Solid-State Circuits
Conference, 2005. Digest of Technical Papers. ISSCC. 2005 IEEE International; page 204 - 593
Vol. 1; February 2005.
15. Sandner, C.; Derksen, S.; Draxelmayr, D.; Ek, S.; Filimon, V.; Leach, G.; Marsili, S. Matveev,
D.; Mertens, K.; Paule, H.; Punzenberger, M.; Reindl, C.; Salerno, R.; Tiebout, M.; Wiesbauer, A.;
Winter, I.; Zhang, Z.; Infineon Technol., Graz ; MBOA/WiMedia UWB transceiver design in
0.13/spl mu/m CMOS; Radio Frequency Integrated Circuits (RFIC) Symposium, 2006 IEEE; page
4 , 11-13 June 2006.
16. Ismail, A.; Abidi, A.; A 3.1 to 8.2 GHz direct conversion receiver for MB-OFDM UWB
communications; IEEE International Solid-State Circuits Conference, 2005. Digest of Technical
Papers. ISSCC. 2005; page 208, Vol. 1. February 2005.
17. S. Bagga, L. Zhang, W.A. Serdijn, J.R. Long and E. Busking: A Quantized Analog Delay for an
ir-UWB Quadrature Downconversion Receiver, proc. 2005 IEEE International Conference on
Ultra-Wideband, Zürich, Switzerland, September 5 – 8, 2005.
18. Duan Zhao and Wouter A. Serdijn: A Time-Interleaved Sampling Delay Circuit for IR UWB
Receivers, proc. IEEE International Symposium on Circuits and Systems, Taipei, Taiwan, May 24
- 27, 2009.
-188-
An Oscillator System for UWB QDAcR
19. S. Bagga, S.A.P. Haddad, W.A. Serdijn, J.R. Long and E. Busking: A Delay Filter for an ir-UWB
Front-End, proc. 2005 IEEE International Conference on Ultra-Wideband, Zürich, Switzerland,
September 5 – 8, 2005.
20. S. Bagga, G. Leus and W.A. Serdijn: Mapping UWB Signal Processing onto Silicon, proc. SPSDARTS’2007, Antwerp, Belgium, March 21-22, 2007.
21. S. Bagga, S.A.P. Haddad, K. van Hartingsveldt, S. Lee, W.A. Serdijn and J.R. Long: An
Interference Rejection Filter for an Ultra-Wideband Quadrature Downconversion Autocorrelation
Receiver, proc. ISCAS’2005, Kobe, Japan, May 23—26, 2005.
22. Ali Hajimiri and Thomas H. Lee; The Design Of Low Noise Oscillators; Kluwer Academic
Publishers; ISBN: 0-7923-8455-5
23. S. Bagga ;Ultra-wideband Transceiver Circuits and Systems, PhD. Thesis; ISBN: 978-909024837-0, Published: 2009.
24. Demir, A.; Mehrotra, A.; Roychowdhury, J.; Phase noise in oscillators: a unifying theory and
numerical methods for characterization; IEEE Transactions on Circuits and Systems I:
Fundamental Theory and Applications; page(s): 655 – 674, Volume: 47 Issue:5, May 2000.
25. Melvin Lax; Classical Noise. V. Noise in Self-Sustained Oscillators; Phys. Rev. 160, 290 (1967) –
Published August 10, 1967.
26. Ham, D. Hajimiri, A.; Virtual damping and Einstein relation in oscillators; IEEE Journal of SolidState Circuits, page(s): 407 – 418, Volume : 38 , Issue:3; Mar 2003.
27. John R. Long et. al.; RFIC-Class Notes, Oscillator Design; March 2009.
28. D. B. Leeson; A simple model of feedback oscillator noise spectrum; Proc. IEEE; vol. 54, no. 2,
pp. 329-330, Feb. 1966.
29. Chang, Z.Y. Sansen, W.; Noise optimization of CMOS wideband amplifiers with capacitive
sources; IEEE International Symposium on Circuits and Systems, 1989.; page(s): 685 - 688 vol.1,
May 1989.
-189-
An Oscillator System for UWB QDAcR
30. Thomas H. Lee; The Design of CMOS Radio-Frequency Integrated Circuits, Second Edition;
ISBN-13: 978-0521835398.
α
31. T. Antal, M. Droz, G. Gyorgyi and Z. Racz; Roughness distributions for 1 f signals; Physics
Review E 065, 046140; April 2002.
32. Kent H. Lundberg; Noise Sources in Bulk CMOS; Published 2002.
33. S. Watanabe; Multi-Lorentzian Model and 1/f noise spectra; Journal of the Korean Physical
Society, pages 646 – 650, Volume 46, March 2005.
34. Demir, A.; Phase noise and timing jitter in oscillators with colored-noise sources; IEEE
Transactions on Circuits and Systems I: Fundamental Theory and Applications; page(s): 1782 –
1791, Volume: 49 Issue:12, December 2002.
35. Herzel, F.; An analytical model for the power spectral density of a voltage-controlled oscillator
and its analogy to the laser linewidth theory; IEEE Transactions on Circuits and Systems I:
Fundamental Theory and Applications; page(s): 904 – 908, Volume: 45 Issue: 9, Sep. 1998.
36. Zanchi, A.; Bonfanti, A.; Levantino, S.; Samori, C.; General SSCR vs. cycle-to-cycle jitter
relationship with application to the phase noise in PLL; Proceedings of 2001 Southwest
Symposium on Mixed Signal Design, page(s): 32-37, February 2001.
37. Rick Poore; Phase Noise and Jitter; Agilent EEs of EDA © Agilent Technologies.
38. T. C. Weigandt, B. Kim, P. R. Gray; Analysis of Timing Jittter in CMOS ring oscillator; Proc. OF
IEEE symposium on Circuits and Systems; pages 27 – 30, Published 1994.
39. Behzad Raavi; RF Microelectronics; Prentice Hall, Published 1997; ISBN: 978-0138875718.
40. Marco Pausini; Autocorrelation Receivers for Ultra Wideband Wireless Communications; ISBN:
978-90-9022505-0; Published 2007.
41. A. Batra, J. Balakrishnan, R. Aiello, J. Foerster, and A. Dabak; Design of a multiband OFDM
system for realistic UWB channel Environments; IEEE Trans. Microw. Theory Tech., vol. 52, no.
9, pages 2123–2138, Sep. 2004.
-190-
An Oscillator System for UWB QDAcR
42. Amin Q. Safarian, Ahmad Yazdi, Payam Heydar, Design and Analysis of an Ultrawide-Band
Distributed CMOS Mixer; IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION
(VLSI) SYSTEMS, VOL. 13, NO. 5, MAY 2005.
43. Satyanarayana Reddy Karri Annamalai Arasu, M. King Wah Wong Yuanjin Zheng Fujiang Lin;
Low-Power UWB LNA and Mixer using 0.18-µm CMOS Technology; ESSCIRC 2006.
Proceedings of the 32nd European Solid-State Circuits Conference, 2006; page(s): 259 – 262,
Sept. 2006.
44. S. Bagga, S. A. P. Haddad, W. A. Serdijn and J. R. Long: An FCC compliant pulse generator for
IR-UWB communications, proc. IEEE ISCAS, May 21 – 24, Island of Kos, Greece, pp. 81 – 84.
45. Ishida, H. Araki, K; A design of tunable UWB filters ; International Workshop on Ultra
Wideband Systems, Joint with Conference on Ultrawideband Systems and Technologies. Joint
UWBST & IWUWBS 2004; pages 424 – 428, May 2004.
46. Anka Rao Putla, S. S. Karthikeyan and Rakhesh Singh Kshetrimayum; Design of UWB Bandpass
Filter using Ground Plane Aperture; International Journal of Recent Trends in Engineering ,Vol 1,
No. 3, May 2009.
47. Y. Peng and W. X. Zhang; MICROSTRIP BAND-REJECT FILTER BASED ON INTERDIGITAL CAPACITANCE LOADED LOOP RESONATORS; Progress In Electromagnetics
Research Letters, Vol. 8, page(s) 93–103, 2009.
48. Kamran Entesari; Development of High Performance 6-18 GHz Tunable/Switchable RF-MEMS
Filters and Their System Implications; PhD Dissertation, University of Michigan; Published:
2006.
49. Klumperink, Eric A.M. and Gierkink, Sander L.J. and Wel van der, Arnoud P. and Nauta, Bram;
Reducing MOSFET 1/f Noise and Power Consumption by "Switched Biasing"; IEEE Journal of
Solid-State Circuits, Vol: 35, page(s) 994-1001. July 2000.
50. John R. Long et. al. ; Radio Frequency Integrated Circuit Design, ET4254, Class Notes. 2010
-191-
An Oscillator System for UWB QDAcR
51. M. Tiebout; Low Power VCO Design in CMOS, Springer series in Advanced Microelectronics;
ISBN: 13-978-3-540-24324-3.
52. C. M. Hung and K. O. Kenneth, “An 1.24-GHz monolithic CMOS VCO with phase noise of -137
dBc/Hz at a 3-MHz offset,” IEEE Microwave Guided Wave Lett., vol. 9, pp. 111-113, March
1999.
53. Pfaff, D.; Huang, Q.; A quarter-micron CMOS, 1 GHz VCO/prescaler-set for very low power
applications, Proceedings of the IEEE Custom Integrated Circuits; page(s): 649 - 652 , May 1999.
54. Rael, J.J. Abidi, A.A; Physical processes of phase noise in differential LC oscillators, Proceedings
of the IEEE Custom Integrated Circuits Conference, CICC. 2000; page(s): 569, May 2000.
55. Tiebout, Marc; A Fully Integrated 1.3GHz VCO for GSM in 0.25µm Standard CMOS with a
Phasenoise of -- 142dBc/Hz at 3MHz Offset, 30th European Microwave Conference, October
2000.
56. J. Craninckx, M. Steyaert; Wireless CMOS Frequency Synthesizer Design, Kluwer, London 2000.
57. J. Craninckx, M.S.J. Steyaert; A 1.8-GHz low-phase-noise CMOS VCO using optimized hollow
spiral inductors; IEEE J. of Solid-State Circuits, vol. 32, page(s) 736- 744, May 1997.
58. W. B. Kuhn; Approximate Analytical Modeling of Current Crowding Effects in Multi-Turn Spiral
Inductors; IEEE Radio Frequency Integrated Circuits Symposium Digest, page(s) 271–274, Proc.
of 2000.
59. John M. W. Rogers, Calvin Plett; Radio Frequency Integrated Circuit Design, Artech House
Publishers, ISBN-13: 978-1607839798.
60. Maget, J. Tiebout, M. Kraus, R. ; Influence of novel MOS varactors on the performance of a fully
integrated UMTS VCO in standard 0.25-µm CMOS technology; IEEE Journal of Solid-State
Circuits, Volume : 37 , Issue:7, page(s): 953, July 2002.
61. Donald A. Neamen; Semiconductor Physics and Devices; McGraw Hill Higher Education, ISBN13: 978-0071231121.
-192-
An Oscillator System for UWB QDAcR
62. Paul R. Gray, Paul J. Hurst, Stephen H. Lewis, Robert G. Meyer; Analysis and Design of Analog
Integrated Circuits (4th Edition), Wiley, ISBN-13: 978-0471321682.
63. P. Andreani, S. Mattisson; On the use of MOS varactors in RF VCO’s; IEEE Journal of Solid
State Circuits, vol. 35, no. 6, June 2000.
64. Bunch, R.L. Raman, S.; Large-signal analysis of MOS varactors in CMOS -Gm LC VCOs; IEEE
Journal of Solid-State Circuits, Volume: 38, Issue: 8, page(s): 1325; August 2003.
65. Hegazi, E. Abidi, A.A.; Varactor characteristics, oscillator tuning curves, and AM-FM conversion;
IEEE Journal of Solid-State Circuits, Volume: 38, Issue:6, page(s):1033, June 2003.
66. Ainspan, H. Plouchart, J.-O.; A comparison of MOS varactors in fully-integrated CMOS LC
VCO's at 5 and 7 GHz; Proceedings of the 26th European Solid-State Circuits Conference, 2000.
ESSCIRC '00., page(s): 447, September 2000.
67. Fong, N.H.W. Plouchart, J.-O. Zamdmer, N. Duixian Liu Wagner, L.F. Plett, C. Tarr, N.G.; A 1-V
3.8 - 5.7-GHz wide-band VCO with differentially tuned accumulation MOS varactors for
common-mode noise rejection in CMOS SOI technology; IEEE Transactions on Microwave
Theory and Techniques, Volume: 51, Issue:8, August 2003.
68. Emad Eldin Hegazi, Jacob Rael, Asad Abidi; The Designer's Guide to High-Purity Oscillators,
Springer, 1st Edition; ISBN-13: 978-1441954060.
69. Samori, C. Lacaita, A.L. Villa, F. Zappa, F ; Spectrum folding and phase noise in LC tuned
oscillators; IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing,
Volume:45, Issue:7, page(s):781, July 1998.
70. Darabi, H. Abidi, A.A.; Noise in RF-CMOS mixers: a simple physical model; IEEE Journal of
Solid-State Circuits, Volume:35, Issue:1, January 2000.
71. Jerng, A. Sodini, C.G.; The impact of device type and sizing on phase noise mechanisms; IEEE
Journal of Solid-State Circuits Volume: 40, Issue:2, page(s):360, February 2005.
72. De Muer, B. Borremans, M. Steyaert, M. Li Puma, G. ; IEEE Journal of Solid-State Circuits,
Volume: 35 ,Issue:7, page(s):1037, July 2000.
-193-
An Oscillator System for UWB QDAcR
73. Hegazi, E. Sjoland, H. Abidi, A.A.; A filtering technique to lower LC oscillator phase noise; IEEE
Journal of Solid-State Circuits, Volume: 36, Issue:12, page(s):1921, December 2001.
74. Andreani, P. Fard, A.; More on the
Phase Noise Performance of CMOS Differential-Pair LC-
Tank Oscillators; IEEE Journal of Solid-State Circuits, Volume: 41, Issue:12, page(s):2703,
December 2006.
75. Maligeorgos, J.P. Long, J.R.; A low-voltage 5.1-5.8-GHz image-reject receiver with wide
dynamic range; IEEE Journal of Solid-State Circuits, Volume: 35, Issue:12, page(s):1917,
December 2000.
76. Rofougaran, A. Rael, J. Rofougaran, M. Abidi, A.; A 900 MHz CMOS LC-oscillator with
quadrature outputs; IEEE International Solid-State Circuits Conference, 1996. Digest of Technical
Papers; page(s): 392, February 1996.
77. Mirzaei, A.. Heidari, M.E. Bagheri, R.. Chehrazi, S.. Abidi, A.A; The Quadrature LC Oscillator:
A Complete Portrait Based on Injection Locking; IEEE Journal of Solid-State Circuits,
Volume: 42, Issue: 9, page(s):1916, September 2007.
78. Mazzanti, A. Svelto, F. Andreani, P.; On the amplitude and phase errors of quadrature LC-tank
CMOS oscillators; IEEE Journal of Solid-State Circuits, Volume: 41, Issue: 6, page(s):1305, June
2007.
79. Andreani, P. Bonfanti, A. Romano, L. Samori, C. ; Analysis and design of a 1.8-GHz CMOS LC
quadrature VCO; IEEE Journal of Solid-State Circuits, Volume: 37, Issue: 12, page(s):1737,
December 2002.
80. Andreani, P. Xiaoyan Wang; On the phase-noise and phase-error performances of multiphase LC
CMOS VCOs; IEEE Journal of Solid-State Circuits, Volume: 39, Issue: 11, page(s):1883,
November 2004.
81. Kuang-Wei Cheng Allstot, D.J.; A gate-modulated CMOS LC quadrature VCO; IEEE Radio
Frequency Integrated Circuits Symposium, 2009; page(s): 267 – 270, June 2009..
-194-