Synthesis of Microwave Circuits Using a Series Solution of the Gel´fand-Levitan-Marchenko Problem

In this paper, we present a new technique for the design of arbitrary frequency responses in the microwave range, provided that they are causal, passive and stable. A comprehensive theory development is presented starting from the coupled mode theory formalism in order to obtain an exact series solution for the inverse scattering problem. A clear physical meaning for the terms in the series is stated. Two applications in microstrip technology are included as examples of the versatility of our technique. In the first place, a broadband antenna gain equalizer is designed for Ultra-Wide-Band (UWB) applications. Secondly, the design of a matched filter for broadband communications is presented along with a comparison between theory, simulations and measurement.