A direct synthesis approach for microwave filters with a complex load and its application to direct diplexer design

This paper presents a direct synthesis approach for general Chebyshev filters terminated with a complex load. The new approach is based on the fact that the polynomial functions for synthesizing the filters are composed for any matched loads. By normalizing the polynomial functions with assumed complex matched load impedance by a real reference load impedance using power waves normalization, a set of new polynomial functions for the same filter, but with real load impedance, can be formulated, from which the coupling matrix for the physical filter design can be obtained using a standard direct filter synthesis approach. This new direct synthesis approach can find many applications. A practical application is the direct diplexer design with a realistic junction model being taken into account. With the diplexer design is concerned, a fast-converged iterative scheme is proposed. The effectiveness and the validation of the proposed scheme are demonstrated by two design examples.