Noise Optimization of a Resistively-Driven Ring Oscillator for VCO-Based ADCs

Recently a study of the analog behavior of ring oscillators was presented from the perspective of VCO ADC design [1]. In this study it was shown that the electrical behavior between the two tuning terminals of such a ring oscillator can be modeled by a diode element. The VCO (phase-)noise can be modeled as an equivalent input-referred noise voltage source in series with this diode. Unfortunately, it was found that this input-referred noise was dependent on the driving impedance. In the prior study only ideal voltage and ideal current control were elaborated. In this work, we generalize the VCO noise model for an arbitrary driving impedance. This enables the noise optimization of a VCO with an arbitrary driving circuit which was not possible with the prior theory. In this work we present such a noise optimization for the linearizing resistive VCO drive circuit of [2], [3]. We show that for this circuit the biasing of the ring is rather uncritical, which is in strong contrast with the result for a pure voltage mode drive circuit, where the biasing of the ring has a major impact on the noise performance.

I. Introduction

Aanalog-to-digital (A/D) conversion based on time-encoding has emerged as a popular strategy to overcome the limitations associated with CMOS technology scaling for the design of high-performance analog ICs. One of the most successful contemporary time-encoding A/D conversion techniques is based on voltage-controlled oscillators (VCOs) [4], [5]. Their popularity can be attributed to their simplicity, their digital-friendly design and their intrinsic integrating property.