Design Method for Butter–Cheby Bandpass Filters With Even Number of Resonators

A design method for the bandpass filters with even number of resonators is presented for compacter size and wider bandwidth. The design method is based on the conventional filters with two resonators defined as a scattering parameter at a given frequency and a characteristic impedance of a 0^° lumped-element equivalent circuit. The filter designed in this paper can be terminated in equal impedances and may have ripple responses at the same time for the wider bandwidths. Since the filter suggested in this paper has advantages that both Butterworth and Chebyshev filters possess, it is called a Butter-Cheby filter to distinguish from conventional filters. For better performance of the Butter-Cheby filter, a way to make transmission zeros is also discussed. To verify the design method, a Butter-Cheby filter with four resonators having 0.01-dB ripple is fabricated with distributed and lumped elements and measured at a design center frequency of 1 GHz. The measured results are in good agreement with the prediction, achieving less than 0.4-dB insertion loss, more than 20-dB return loss, and a transmission zero of 2 GHz.