Section: New Results

Detection of the instability of amplifiers

Participants : Laurent Baratchart, Sylvain Chevillard, Martine Olivi, Jean-Baptiste Pomet, Fabien Seyfert.

A new collaboration with the CNES and the University of Bilbao began this year. The goal is to help the development of amplifiers, in particular to detect unstability at an early stage of the design.

Currently, Electrical Engineers from the University of Bilbao, under contract with CNES (the French Space Agency), use heuristics to diagnose instability before the circuit is physically implemented. We intend to set up a rigorously founded algorithm instead, based on properties of transfer function of such amplifiers which belong to particular classes of analytic functions.

We completed the first stage of this collaboration, in that we now have a formal definition of stability within these classes: a stable function is one which, when connected in parallel with a large resistor, yields a $H^{\infty }$.transfer function (in this context tranfer functions might have infinitely many poles). We also obtained a characterization of transferfunctions that may actually be realized in terms of elementary eletric components (i.e., resistors, self, capacities, LEDs, and transmission lines): they are the rational functions in the variable and the exponentials thereof.