Extraction of the Q factor of dielectric resonators from S-parameters using the cauchy method

A modified Cauchy method to generate an accurate rational model of lossy systems from the S-parameters is presented. Based on the property that the losses displace all the zeros and poles of the transfer function horizontally to the left in the complex plane and the complex frequency transformation technique, the accurate evaluation of the unloaded quality factors of microwave resonators can be realized using the Cauchy method. Whether the input/output couplings are weak or strong, nearly the same unloaded quality factors can be obtained by the proposed technique. This algorithm provides an alternative method to measure the unloaded quality factor without the limits of weak coupling strength.