Fabien Seyfert: A convex optimization approach to the broadband impedance matching problem in finite dimension,

Abstract: The synthesis of filters and antennas present in microwave reception or emission chains are usually done by assuming a fix resistive reference (usually 50 Ohm) at their connecting ports. The antenna's mismatch is then either ignored or compensated by an additional matching network, resulting either in a degradation of the energy efficiency or in an increased footprint of the overall hardware. The aim this talk is to develop a synthesis technique for matching filters, allowing to handle the matching and filtering requirements in a single filter and rendering superfluous the use of an extra matching network. We will begin the talk by a review of the classical approach due to D. C. Youla, R. M. Fano, as well as the more mathematical framework developed by J.W. Helton for his theory of broad-band matching in infinite dimension. We will then present a convex optimization approach, based on the use of the notion of Pick matrix in order to characterize convex admissible sets of passive electrical responses related to the matching problem. We will show, how the latter yields upper and lower bounds, as well as near optimal responses, for the original broad-band matching problem in finite dimension. The resulting non-linear semi-definite optimization problem (NL-SDP) will be discussed as well as practical cases considered.