Model-Free Closed-Loop Stability Analysis: A Linear Functional Approach

TL;DR

This paper introduces a projection-based, model-free method for closed-loop stability analysis that efficiently separates stable and unstable impedance components to identify potential circuit instabilities.

Contribution

It proposes a novel linear functional approach that avoids rational modeling, enabling both small-signal and large-signal stability assessments with minimal computational cost.

Findings

Effective separation of stable and unstable impedance parts.

Ability to identify unstable poles without internal circuit access.

Applicable to both small-signal and large-signal stability analysis.

Abstract

Performing a stability analysis during the design of any electronic circuit is critical to guarantee its correct operation. A closed-loop stability analysis can be performed by analysing the impedance presented by the circuit at a well-chosen node without internal access to the simulator. If any of the poles of this impedance lie in the complex right half-plane, the circuit is unstable. The classic way to detect unstable poles is to fit a rational model on the impedance. In this paper, a projection-based method is proposed which splits the impedance into a stable and an unstable part by projecting on an orthogonal basis of stable and unstable functions. When the unstable part lies significantly above the interpolation error of the method, the circuit is considered unstable. Working with a projection provides one, at small cost, with a first appraisal of the unstable part of the system. Both small-signal and large-signal stability analysis can be performed with this projection-based method. In the small-signal case, a low-order rational approximation can be fitted on the unstable part to find the location of the unstable poles.