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In this work, we focus on the three most relevant pseudo-digital ring oscillator circuits for VCO A/D conversion. First, we show that they can be accurately modeled by an equivalent 2-terminal diode-like element. Next, we study the main analog performance figures: the effective oscillation frequency (which affects the quantization noise of a VCO ADC), the input referred noise and the power efficiency both for voltage and current control. We do this both through theoretical modeling as well as through simulations, which are in good agreement with each other. Our study highlights several important independencies: e.g. most performance metrics are independent on the number of VCO stages and the external load capacitance on the VCO nodes. In contrast to these independencies, we identify several important dependencies. In particular, we show that the biasing of the ring has an enormous impact on power efficiency of the ring. This dependency is different for the case of a voltage- or current mode configuration of the ring.

The Analog Behavior of Pseudo Digital Ring Oscillators Used in VCO ADCs