Bifurcation study of sigma-delta modulators - an experimental approach

Abstract

Sigma-delta modulation is a popular technique for high resolution analog to digital and digital to analog conversion. Conventional A-D and D-A converters are based on the linear multi-bit pulse code modulation (PCM) format. They require high-precision analog circuitry and vulnerable to noise and interference. So industry is moving towards oversampled nonlinear converters, one of which is the sigma-delta modulator. In spite of being cheaper, less power-consuming and operable in the voltage range of battery operated consumer devices, they are susceptible to limit-cycle oscillations, which may produce idle tones absent in the original signal. Operation of sigma-delta modulators in chaotic region has been proposed as a solution. In this paper we are investigating chaotic phenomena (bifurcation aspects) in a first order sigma-delta modulator (a modified version) which uses a simple gain element to control operational region shift from normal to chaotic region of operation.