Section: New Results

Circuit realisations of filter responses: determination of canonical forms and exhaustive computations of constrained realisations

Participant : Fabien Seyfert.

This work has been done in collaboration with Smain Amari (Royal Military College, Kingston, Canada), Jean Charles Faugère (SALSA EPI, Inria Rocquencourt), Giuseppe Macchiarella (Politecnico di Milano, Milan, Italy), Uwe Rosenberg (Design and Project Engineering, Osterholz-Scharmbeck, Germany) and Matteo Oldoni (Politecnico di Milano, Milan, Italy).

We continued our work on the circuit realizations of filters' responses with mixed type (inductive or capacitive) coupling elements and constrained topologies [1] . For inline circuits, methods based on sequential extractions of electrical elements are best suited due to their computational simplicity. On the other hand, for circuits with no inline topology ,such methods are inefficient while algebraic methods (based on a Groebner basis) can be used, but at high computational cost. In order to tackle large order circuits, our approach is to decompose them into connected inline sections, which can be directly realized by extraction techniques, and into complex sections, where algebraic methods are needed for realization. In order to do this, we started studying the synthesis of filter responses by means of circuits with reactive non-resonating nodes (dangling resonators) [22] . Links of this topic with Potapov's factorization of J-inner functions are currently being investigated.

In this connection, sensitivity analysis of the electrical response of a filter with respect to the electrical parameters of the underlying circuit has been published in collaboration with the University of Cartagena and ESA [20] . We essentially proved that the total electrical sensitivity of a filters' response does not depend on the coupling topology of the underlying circuit: the latter however controls the distribution of this sensitivity within each resonator.