A Modified Vector Fitting Technique to Extract Coupling Matrix from S-parameters

Abstract

. In this paper, a modified vector fitting technique to extract coupling matrix from S-parameters is introduced. This work allows designers to extract the coupling matrix of different or any pre-defined topologies from the simulated or measured S-parameter data. A study on vector fitting (VF) equations that can extract the rational polynomial of bandpass filter responses is carried out. VF is a robust numerical method which is applied widely in rational approximations due to its fast convergence and able to apply for high order polynomials. The rational polynomials are formed by applying the VF process to S-parameter responses without having to remove the phase offset and de-embedding the transmission lines. Focus fitting as the first enhancement can avoid VF overfitting spurious as poles; Poles forcing as the second enhancement is able to ensure the poles of all S-parameters are the same. Finally, the desired coupling matrix configuration is generated directly from the extracted polynomials using unconstrained and finitely bounded non-linear polynomials (NLP) optimization. Without the need for matrix transformation, the matrix elements are still able to show a one-to-one relationship in coupling values of resonators. Two bandpass filters are shown as examples to illustrate the performance of the new variation of VF.