VCO-based phase-domain ΣΔ modulators employ the combination of a voltage-controlled-oscillator (VCO) and an up/down counter to replace the analog loop filter used in conventional ΣΔ modulators. Thanks to this highly digital architecture, they can be quite compact, and are expected to shrink even further with CMOS scaling. This paper describes the analysis and design of such converters. Trade-offs between design parameters and the impact of non-idealities, such as finite counter length and VCO non-linearity, are assessed through both theoretical analysis and behavioral simulations. The proposed design methodology is applied to the design of a phase-to-digital converter in a 40-nm CMOS process, which is used to digitize the output of a thermal-diffusivity temperature sensor, achieving ± 0.2° (3σ) phase inaccuracy from -40 to 125 °C and a sensor-limited resolution of 57 m° (RMS) within a 500-Hz bandwidth. Measurements on the prototype agree quite well with theoretical predictions, thus demonstrating the validity of the proposed design methodology.

An array of temperature sensors based on the thermal diffusivity (TD) of bulk silicon has been realized in a standard 40-nm CMOS process. In each TD sensor, a highly digital voltage-controlled oscillator-based Σ Δ ADC digitizes the temperature-dependent phase shift of an electrothermal filter (ETF). A phase calibration scheme is used to cancel the ADC's phase offset. Two types of ETF were realized, one optimized for accuracy and one optimized for resolution. Sensors based on the accuracy-optimized ETF achieved a resolution of 0.36 °C (rms) at 1 kSa/s, and inaccuracies of ±1.4 °C (3 Σ , uncalibrated) and ±0.75 °C (3 Σ, room-temperature calibrated) from -40 °C to 125 °C. Sensors based on the resolution-optimized ETFs achieved an improved resolution of 0.21 °C (rms), and inaccuracies of ±2.3 °C (3 Σ, uncalibrated) and ±1.05 °C (3 Σ, room-temperature calibrated). The sensors draw 2.8 mA from supply voltages as low as 0.9 V, and occupy only 1650 μ m² , making them some of the smallest smart temperature sensors reported to date, and well suited for thermal monitoring applications in systems-on-chip.