Modern communication systems have a strong need for low-cost and high-stability frequency references. Although low-cost crystal oscillators can easily be realized and are available to the market in large quantities, crystal oscillators with frequency stability in the ppb(10^{-9}) range over a wide temperature range are only available at high costs. In 2018, SemiBlocks B.V. proposed an improved technique so-called Multi-Mode Crystal Oscillator MMXO. The MMXO determines the output frequency through a triple mode oscillator and corrects this by an algorithm running on the internal microprocessor. The advantage of the MMXO is that it uses regular AT-Cut crystals and the whole circuitry can be implemented in silicon, and the frequency selective network is implemented by digital technology. This results in a low-cost and high-stability crystal oscillator solution.

However, the measurement result of the first generation MMXO showed that the large temperature dependent phase shift of the analog crystal chain significantly influences frequency stability of the MMXO. This inaccuracy is out of the compensation ability of the multi-mode system since it is highly dependent on the analog network rather than the crystal. For the improvement of the next generation MMXO product, this thesis aims at designing a CMOS crystal filter, which should reflect the characteristic of crystal accurately. Any change of resonance frequency of the tested crystal should accurately match that of the frequency characteristic of the crystal filter. The objective is to control frequency error below 10ppb for the three resonance tones of the tested crystal over -40 to 100 $^{\circ}$C.

The design of the crystal filter follows a structured methodology and combines analysis and simulations in Cadence together with SLICAP (Symbolic Linear
Circuit Analysis Program), which helps researchers quickly find the early design solution and show-stopper before circuit design. The crystal filter is a two-stage amplifier. The first stage is a transadmittance stage, which reflects the frequency characteristic of the crystal by a current output. The second stage is a transimpedance stage, which makes the output of the TA stage observable to the ADC of the MMXO system. The pre-layout simulations show the the frequency error of the base tone and the third overtone is close to $10$ ppb, while the fifth overtone has a large frequency error around $252$ ppb. The crystal filter allows full range input of the tested ADC and is stable under all typical corners, with
$12.83 \mu W$ power consumed by crystal, $95.6 mW/pixel$ total current usage, and the chip area $1.75\times 10^{-8} mm^2/pixel$. The output-referred noise PSD of the base tone and the third overtone is $3.4\times 10^{-13}V^2/Hz$ and $7.3\times 10^{-15}V^2/Hz$. which meets the noise requirements with enough design margin, while the fifth overtone fails with noise specs due to the quantization noise and aliased noise caused by ADC.