Polynomial structure of 3 x 3 reciprocal inner matrices

Abstract : The objective of our work is the derivation of efficient algorithms for the synthesis of microwave multiplexers. In our opinion, an efficient frequency design process calls for the understanding of the structure of n x n inner (or lossless) reciprocal rational functions for n > 2. Whereas the case n = 2 is completely understood and a keystone of filter synthesis very little seems to be known about the polynomial structure of such matrices when they involve more than 2 ports. We therefore start with the analysis of the 3 x 3 case typically of practical use in the manufacturing of diplexers. Based on recent results obtained on minimal degree reciprocal Darlington synthesis, we derive a polynomial model for 3 x 3 reciprocal inner rational matrices with given McMillan degree.
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David Avanessoff, Martine Olivi, Fabien Seyfert. Polynomial structure of 3 x 3 reciprocal inner matrices. MTNS- 19th International Symposium on Mathematical Theory of Networks and Systems - 2010, Jul 2010, Budapest, Hungary. ⟨hal-00788393⟩

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