Direct Synthesis of Microwave Coupled Resonator Filters Matched with A Frequency-Dependent Complex Load

This paper presents a direct synthesis approach for general Chebyshev filters terminated by a frequency-dependent complex load at one port. The new approach is based on the fact that the polynomial functions for filter synthesis are composed for any matched loads. Using power wave normalization, the polynomial functions with a complex matched load are normalized to new polynomials with real reference loads, from which the coupling matrix can be directly synthesized. The primary application is found for the direct diplexer design. The effectiveness of the new scheme is demonstrated through a diplexer design example.