Analysis and Design of VCO-Based Phase-Domain ΣΔ Modulators

VCO-based phase-domain Sigma Delta modulators employ the combination of a voltage-controlled-oscillator (VCO) and an up/down counter to replace the analog loop filter used in conventional Sigma Delta 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 degrees. (3 sigma) phase inaccuracy from -40 to 125 degrees C and a sensor-limited resolution of 57 m degrees (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.