Analytic Synthesis of Frequency-Dependent Coupling Filter

Abstract

In this paper, a new filter synthesis technology with frequency-dependent coupling (FDC) has been presented by analytical synthesis method instead of exploiting optimization method. Firstly, according to the assigned frequency-independent coupling filter topology, the initial frequency-independent coupling matrix can be synthesized to realize the desired indicators. Then, the expected FDC filter topology should be chosen and the corresponding FDC matrix form can be determined. Finally, and importantly, the obtained FDC matrix for FDC filter topology can be suitably transformed by means of scaling and rotations of coupling and capacitance matrices for realizing the frequency-independent coupling matrix that the form should be consistent with the initial one. To maintain the identical indicators, the frequency-independent coupling matrix which is transformed from the FDC matrix should be equal to the initial synthesized frequency-independent coupling matrix. Hence, the elements in coupling and capacitance matrices can be solved and FDC matrix can be eventually obtained. Above all, the FDC filter synthesis approach has been illustrated with a fifth-order filter example, and the good agreements between the different filter responses have validated the validation of the proposed synthesis method.