A formulation of the Cauchy method suitable for the synthesis of lossless circuit models of microwave filters from lossy measurements

In this letter, a novel formulation of the Cauchy method is presented, to be employed in the extraction of circuit models from measured(lossy) response of microwave filters. In particular, it is shown how to generate,from lossy measurements, the characteristic polynomials which allow synthesis of a lossless low-pass prototype (and the evaluation of the coupling matrix). To this purpose, suitable constraints are introduced in order to have the transmission zeros generated with the Cauchy method strictly compatible with the low pass synthesis requirements (pure imaginary or complex pair with opposite real part). The application of the proposed method has been verified employing measurements from a test filter for GSM base stations. This method can find application in computer-aided tuning procedures.