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

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. 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. 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.