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

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. This rational approximation has to deal with model order selection, which is difficult in circuits with transmission lines. 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. Working with a projection instead of a rational approximation greatly simplifies the stability analysis. When the projection is mapped from the complex plane to the unit disc, the projection boils down to calculating a Fourier series. If a significant part of the impedance is projected on the unstable part, a low-order rational approximation is fitted on this unstable part to find the location of the unstable poles.
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https://hal.inria.fr/hal-01381731
Contributor : Martine Olivi <>
Submitted on : Friday, October 14, 2016 - 3:54:51 PM
Last modification on : Thursday, June 4, 2020 - 11:46:02 AM

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Adam Cooman, Fabien Seyfert, Martine Olivi, Sylvain Chevillard, Laurent Baratchart. Model-Free Closed-Loop Stability Analysis: A Linear Functional Approach. IEEE Transactions on Microwave Theory and Techniques, Institute of Electrical and Electronics Engineers, 2017, ⟨10.1109/TMTT.2017.2749222⟩. ⟨hal-01381731⟩

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