Computer aided design for dual-band filters with complex source and load impedances

This article presents a computer aided technique to synthesize the filtering function for dual-band microwave filters with complex source and load impedances. Based on the exchange-Remez algorithm and the power wave renormalization theory, the characteristic function is first obtained with assigned ripple level at the first passband. Two additional transmission zeros are then optimally allocated to control the ripple level at the second passband. By directly modifying the coupling matrix elements in the first and last stages, a simplified method is also presented when the loading impedance is frequency-independent. Three synthesized examples with both controlled in-band and out-of-band responses are presented. Finally, LC multi-coupled circuits are also provided to validate the effectiveness of the proposed method.