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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 &#x0394;&#x03A3; modulators. A first advantage of our approach is that it unveils systematic error components not described by the equivalence with a conventional &#x0394;&#x03A3; 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 firstorder 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 &#x0394;&#x03A3; modulator architectures, which is an alternative and practically feasible way to realize a VCO-ADC with extended noise shaping.

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