Analysis and synthesis of randomized modulation schemes for power converters

After establishing that the proper objects of study for randomized modulation of converters are the power spectra of signals, we classify such modulation schemes and present associated spectral formulas, several of which are new. We also discuss numerical (Monte Carlo) verification issues for power spectral formulas. A general spectral formula for stationary randomized modulation schemes is presented, and specialized to several modulation schemes of practical interest for DC/DC converters. Analytical results are then given for block-stationary randomized modulation schemes that are suitable for inverter operation. In the process, we present results for several modulation schemes that have been reported in the literature without analytical explanations. Experimental verifications of some of our analytical results are presented. We formulate narrow-band and wide-band synthesis problems in randomized modulation, and solve them numerically. Our results suggest that randomized modulation is very effective in satisfying narrow-band power constraints, but has limited effectiveness in meeting wide-band constraints.