This paper studies dynamics of a delta modulator for PWM control. In order to analyze the circuit dynamics we derive a one-dimensional return map of switching time. The map is equivalent to a circle map in wide parameter region and its nonperiodic behavior corresponds to undesired asynchronous operation of the circuit. We then present a simple stabilization method of the system operations by means of periodic compulsory switching. The mechanism of the stabilization is considered from viewpoints of bifurcation. Using a simple test circuit, typical operations are confirmed experimentally.

This letter presents a simple A/D converter based on the circle map. The converter encodes a dc input into a binary output sequence and has the trapping window that extracts an available part of the output sequence. Using the available part, the decoder provides an estimation by a fraction with variable denominator: it can realize higher resolution. Theoretical evidences for the estimation characteristics are given.