An Analytical Time–Domain Expression for the Net Ripple Produced by Parallel Interleaved Converters

Abstract

We apply modular arithmetic and Fourier series to analyze the superposition of $N$ interleaved triangular waveforms with identical amplitudes and duty ratios. Here, interleaving refers to the condition when a collection of periodic waveforms with identical periods is uniformly phase shifted across one period. The main result is a time–domain expression that provides an exact representation of the summed and interleaved triangular waveforms, where the peak amplitude and parameters of the time-periodic component are all specified in closed form. Analysis is general and can be used to study various applications in multiconverter systems. This model is unique not only in that it reveals a simple and intuitive expression for the net ripple, but its derivation via modular arithmetic and Fourier series is distinct from prior approaches. The analytical framework is experimentally validated with a system of three parallel converters under time-varying operating conditions.