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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 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.
delta sigma modulation; data conversion; voltage controlled oscillators; pulse frequency modulation; time encoding