A Pulse Frequency Modulation Interpretation of VCOs Enabling VCO-ADC Architectures With Extended Noise Shaping

TLDR: This paper proposes to study voltage controlled oscillators (VCOs) based on the equivalence with pulse frequency modulators (PFMs) and describes circuit techniques to achieve a good approximation of the required pulse waveforms, which can easily be implemented by practical circuits.

Abstract: In this paper, we propose to study voltage controlled oscillators (VCOs) based on the equivalence with pulse frequency modulators (PFMs). This approach is applied to the analysis of VCO-based analog-to-digital converters (VCO-ADCs) and deviates significantly from the conventional interpretation, where VCO-ADCs have been described as the first-order $\Delta \Sigma $ modulators. A first advantage of our approach is that it unveils systematic error components not described by the equivalence with a conventional $\Delta \Sigma $ modulator. A second advantage is that, by a proper selection of the pulses generated by the PFM, we can theoretically construct an open loop VCO-ADC with an arbitrary noise shaping order. Unfortunately, with the exception of the first-order noise shaping case, the required pulse waveforms cannot easily be implemented on the circuit level. However, we describe circuit techniques to achieve a good approximation of the required pulse waveforms, which can easily be implemented by practical circuits. Finally, our approach enables a straightforward description of multistage $\Delta \Sigma $ modulator architectures, which is an alternative and practically feasible way to realize a VCO-ADC with extended noise shaping.