Synthesis of In-Line Filters With Arbitrarily Placed Attenuation Poles by Using Non-Resonating Nodes

A general and direct synthesis technique of pseudoelliptic inline filters with arbitrarily placed attenuation poles (APs) (transmission zeros) at real frequencies is presented. The APs are brought about and independently controlled by dedicated resonators, which are coupled to nonresonating nodes. Simple rules to properly determine the phases of the reflection coefficients at the input and output are given. To reduce the effect of roundoff errors, especially for higher order filters, the extraction of the elements of the network is performed from the input and output simultaneously. Multiplicity and scaling properties of the solutions are discussed. Synthesis examples are presented to demonstrate the soundness of the procedure. Theoretical results are compared with measurement to demonstrate the validity of the presented theory.