A Parameter-Extraction Method for Microwave Transversal Resonator Array Bandpass Filters With Direct Source/Load Coupling

A new simple and straightforward parameter-extraction method for a general transversal resonator array filter, which consists of parallel connected resonators in a circuit model, is proposed. Using this method enables one to effectively extract a direct source/load (S/L) coupling, as well as the external quality factor and the resonant frequency of each resonator path only from input reflection phase characteristics of the singly terminated even- and odd-mode networks, without using any complicated optimization techniques and coupling matrix calculations. One of the advantages noted here is that a frequency-dependent S/L coupling in practical physical filter models can be handled with this method. Furthermore, dissipation effects due to unloaded quality factors of the resonator paths is investigated based on a new closed-form formula derived in this paper. The effectiveness of the proposed extraction technique and equations is verified by the comparison with the optimization method results through applications to three planar filter examples. The proposed extraction technique is indispensable for recent advanced filter designs using a transversal array filter synthesis theory for quasi-elliptic function filters having multiple transmission zeros.