An Argument for the Relationship Between Spectral Spreading and Probability Spreading for EMI-Reduction in DC–DC Converter

Many studies have sufficiently indicated that random pulsewidth modulation (RPWM) can reduce the harmonics that cause electromagnetic interference (EMI). The probability distribution that governs the switching pattern can be thought of as a controlled variable for EMI reduction. This work investigates the relationship between probability distributions of RPWM and the reduction of conducted EMI. It is hypothesized that, given a fixed pool of RPWM parameters, increasing the spreading out of the probability distributions leads to a monotonic increase in the spectral spreading. Optimization methods can then be employed to reduce conducted EMI in dc–dc converters. Entropy is proposed to quantify spreading in the probability domain as well as in the spectral domain. It is found from the power spectral density formula as well as the Monte Carlo simulations that by increasing the entropy of probability from minimum to maximum, the spectral spreading also increases monotonically.