Circuital modeling and physical understanding of dissipation effects for coupled resonator filters transformed into transversal array configuration

This paper presents a new physical understanding of dissipation effects of microwave coupled resonator filters. Using a matrix transformation enables one to express the filter network not only with a well-known cascaded resonator circuit, but also with a transversal resonator array circuit. It is important to note here that the unloaded Q factors of the resonators in the two networks are defined by the same equation form in the circuit models, but they are computed for totally different resonators in terms of eigemodes. Therefore, as an example, the dissipation effect of a typical microstrip bandpass filter is investigated in detail, using new general closed-form equations derived by the circuit analysis in addition to the eigenmode analysis. The physical insights given in this paper can be indispensable for recent advanced filter designs based on a synthesis theory of transversal resonator array filters.