Section: New Results

Stability of amplifiers

Participants : Laurent Baratchart, Sylvain Chevillard, Martine Olivi, Fabien Seyfert, Sebastien Fueyo.

This work is performed under contract with CNES-Toulouse and the University of Bilbao as well as in collaboration with Adam Cooman (VUB, Brussels, Belgium). The goal is to help design amplifiers, in particular to detect instability at an early stage of the design. Activity in this area is gaining importance with the coming of a doctoral and a postdoctoral student along with planned software developments.

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 analyzing 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 the practical approach we develop in collaboration with Adam Cooman, 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, it 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. See [25] for details. Adapting such tools to check the stability of a trajectory, linearizing around the latter, is tantamount to develop a similar theory for time-varying periodic systems. This is the subject of S. Fueyo's PhD work.