Direct optimal synthesis of microwave bandpass filters with a general loading effect

This paper presents a direct synthesis method for a general Chebyshev band pass filter that is matched to a general frequency dependent complex load. The method is based on the power wave renormalization theory and the characteristic polynomial representation of a filter network. By renormalizing the termination load impedance, three necessary conditions that stipulate the polynomials associated to a filter matched to a complex load and those related to a unity load are derived. It can be shown that these three conditions can lead to an ideal filter circuit model cascaded by a piece of transmission line between the complex load and the ideal filter. It has been shown that the length of the transmission line is optimal in the sense that the designed filter will best match to a given frequency variant load effect. 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 a design example of a waveguide diplexer.