Direct Optimal Synthesis of a Microwave Bandpass Filter With General Loading Effect

This paper presents a direct approach to the synthesis of a general Chebyshev bandpass filter that matches to a frequency variant complex load. The approach is based on the power wave renormalization theory and two practical assumptions, which are: 1) the prescribed transmission zeros are stationary and 2) the reflection zeros are located along the imaginary axis. Three necessary conditions that stipulate the characteristic polynomials associated to the filter are derived through renormalization of the load reference impedances. It has been shown that these three conditions can only be satisfied by an ideal filter circuit model separated by a piece of interconnecting stub from the complex load. The length of the stub will be optimally designed in the sense that the designed filter will best match to the complex load over a given frequency range. The proposed method offers a deterministic, yet flexible way for optimally designing a diplexer or a multiplexer with a realistic loading effect. The effectiveness of the method is demonstrated by two design examples.