An Iterative and Analytical Approach to Optimal Synthesis of a Multiplexer With a Star-Junction

This paper presents an iterative and analytical approach to optimal synthesis of a multiplexer with a star-junction. Two types of commonly used lumped-element junction models, namely, nonresonant node (NRN) type and resonant type, are considered and treated in a uniform way. A new circuit equivalence called phased-inverter to frequency-invariant reactance inverter transformation is introduced. It allows direct adoption of the optimal synthesis theory of a bandpass filter for synthesizing channel filters connected to a star-junction by converting the synthesized phase shift to the susceptance compensation at the junction. Since each channel filter is dealt with individually and alternately, when synthesizing a multiplexer with a high number of channels, good accuracy can still be maintained. Therefore, the approach can be used to synthesize a wide range of multiplexers. Illustrative examples of synthesizing a diplexer with a common resonant type of junction and a triplexer with an NRN type of junction are given to demonstrate the effectiveness of the proposed approach. A prototype of a coaxial resonator diplexer according to the synthesized circuit model is fabricated to validate the synthesized result. Excellent agreement is obtained.