Extraction of Unloaded Q and Coupling Matrix From Measurements on Filters With Large Losses

TLDR: In this paper, a simple solution is described for obtaining an accurate evaluation of the coupling matrix and the unloaded Q from the measured scattering parameters of a microwave lossy filter (assuming all the resonators with the same unloaded Q).

Abstract: In this letter, a simple solution is described for obtaining an accurate evaluation of the coupling matrix and the unloaded Q from the measured scattering parameters of a microwave lossy filter (assuming all the resonators with the same unloaded Q). The Cauchy method is applied in a predistorted frequency domain, where the measured (lossy) parameters refer to a lossless device. In this way, it becomes possible to synthesize a prototype low-pass network using well established techniques, once the topology of the filters has been assigned. With respect to the previous methods available in the literature, the one here proposed allows very accurate results even with filters exhibiting large insertion losses; moreover the computing time is extremely short allowing the use of the method in real time computer-aided tuning procedures for microwave filters. An example of application of the proposed method is reported in the letter for illustrative and validating purposes.