On the Singly Terminated and Complementary Networks

This contribution establishes the relationship between the complementary condition and the singly terminated (ST) networks. The general theory is first presented in the form of bandpass/bandstop complementary diplexers. Furthermore, the well-known limitation of a complementary diplexer, i.e., using maximally flat prototypes, is overcome. From the first principle, it is rigorously proven that predefined complementary features can be obtained by connecting two channel filters in an ST prototype of the same filter function but exchanging the transfer and reflection part. This paper leads to a general design procedure for bandpass and bandstop complementary diplexers using arbitrary functions. A complementary diplexer design example with full electromagnetic simulated results and measured results verified the accuracy of the proposed theory. Finally, the theory is further extended to N-ports networks. A new “partially-complementary” condition is proposed. The new theory leads to an extremely simple and “direct approach” to estimate the performance of contiguous multiplexers without any optimization.