Using Nyquist or Nyquist-Like Plot to Predict Three Typical Instabilities in DC-DC Converters

TL;DR

This paper introduces a Nyquist-like plot that accurately predicts three common instabilities in DC-DC converters, serving as a practical design tool to prevent issues like bifurcations and oscillations.

Contribution

A novel Nyquist-like plot is proposed to predict multiple types of instabilities in DC-DC converters within a single, accurate visualization.

Findings

Successfully predicts saddle-node bifurcation, period-doubling bifurcation, and Neimark bifurcation.

Validated with nine examples on buck and boost converters.

Equivalent to the Nyquist plot, aiding in stability analysis and design.

Abstract

By transforming an exact stability condition, a new Nyquist-like plot is proposed to predict occurrences of three typical instabilities in DC-DC converters. The three instabilities are saddle-node bifurcation (coexistence of multiple solutions), period-doubling bifurcation (subharmonic oscillation), and Neimark bifurcation (quasi-periodic oscillation). In a single plot, it accurately predicts whether an instability occurs and what type the instability is. The plot is equivalent to the Nyquist plot, and it is a useful design tool to avoid these instabilities. Nine examples are used to illustrate the accuracy of this new plot to predict instabilities in the buck or boost converter with fixed or variable switching frequency.