Boundary Conditions of Subharmonic Oscillations in Fixed-Switching-Frequency DC-DC Converters

TL;DR

This paper derives comprehensive boundary conditions for subharmonic oscillations in fixed-switching-frequency DC-DC converters, unifying previous results and introducing new Nyquist-like plots for better prediction and prevention.

Contribution

It extends existing boundary conditions for subharmonic oscillations to general converters, providing closed-form expressions and new design tools.

Findings

Equivalent series resistance influences boundary conditions similarly for voltage and current mode control.

New Nyquist-like plots effectively predict or prevent subharmonic oscillations.

The relation between crossover frequency and subharmonic oscillation is clarified.

Abstract

Design-oriented boundary conditions for subharmonic oscillations are of great interest recently. Based on a subharmonic oscillation boundary condition reported in a PhD thesis more than a decade ago, extended new boundary conditions are derived in closed forms for general switching DC-DC converters. Sampled-data and harmonic balance analyses are applied and generate equivalent results. It is shown that equivalent series resistance causes the boundary conditions for voltage/current mode control to have similar forms. Some recently reported boundary conditions become special cases in view of the general boundary conditions derived. New Nyquist-like design-oriented plots are proposed to predict or prevent the occurrence of the subharmonic oscillation. The relation between the crossover frequency and the subharmonic oscillation is also analyzed.