Generalised random switching circuits: A time‐domain technique

Abstract

A probabilistic solution of the time-domain performance of an arbitrary switching circuit driven by a generalised random switching sequence is presented. A generalised random switching sequence is the superset of all clock-based random pulse-width modulation schemes and has the best possible spectral spreading. The switching circuits considered are linear and time invariant, have a constant DC input and contain at least one ideal switch. The mean of the probability density updates exactly like a discrete time solution to state-space averaging, with probability replacing the duty cycle. The covariance matrix of the probability density updates using a difference equation. The value of this work is in the prediction of the statistics of transients for randomly switched power converters. A boost converter is presented as an example.