A Model of Continuous-Time Sigma Delta Modulation Based on Pulse Frequency Encoding

The parallelism between a first-order sigma-delta modulator and a VCO-based ADC allows to calculate the DFT of the sigma delta sequence using Pulse Frequency Modulation theory. This paper exploits this parallelism to propose a more general model that links continuous time sigma delta modulators of an arbitrary order with Pulse Frequency Modulators. This novel point of view also predicts the spectral contents of a sigma delta encoded sequence beyond the white quantization noise model. The quantization noise can be split in two components, a deterministic one representing the carrier harmonic sidebands of a Pulse Frequency Encoded signal and a noise shaped pseudorandom signal representing the sampling operation. We seize these findings to propose a conjecture on the stability of a sigma delta modulator.