Analysis of the randomized wrapped-around pulse position modulation scheme

Abstract

This report describes the analysis of the Randomized Wrapped-Around Pulse Position Modulation (RWAPPM) scheme for switched-mode dc-dc converters. The RWAPPM scheme randomizes the starting position of the pulse in each switching cycle by a randomized delay to mitigate the undesirable discrete harmonics of the standard PWM scheme. It features a simple algorithm and other desirable attributes including a constant switching period, virtually eliminated discrete harmonics, low peak spectral power, and low noise. The RWAPPM scheme was first proposed without any means to adjust its randomness. In this report, we derive an expression for the output spectrum of the RWAPPM scheme with an adjustable randomness level parameter. By means of the derived expression, we analyze the effects of varying the randomness level parameter onto the output spectrum of the RWAPPM scheme. We show that at non-full randomness levels, the output spectrum exhibits undesirable discrete harmonics and high peak spectral power, whereas at a full randomness level, the output spectrum practically comprises a continuous noise-spectrum only and has the lowest peak spectral power. On the basis of this observation, we recommend that the RWAPPM scheme is used at a full randomness level. We also base this recommendation on the fact that generating the random delay with a full randomness level is easier to be realized in hardware than that of non-full randomness levels. We verify the derived expression by computer simulations. A large portion of the work described in this report will be submitted as a conference paper co-authored by the author of this report.