Analysis of Unstable Operation in a Basic Delta Modulator for PWM Control

This paper studies dynamics of a delta modulator for PWM control. In order to analyze the circuit dynamics we derive a onedimensional 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. key words: pulse-width modulation, delta modulators, synchronization, circle map, bifurcation