A Direct Matrix Synthesis for In-Line Filters with Transmission Zeros Generated by Frequency-Variant Couplings

A direct matrix approach is presented for the first time to synthesize high selectivity in-line topology filters where multiple transmission zeros are generated and independently controlled by a set of frequency-variant couplings. As the resultant network only involves resonators cascaded one by one without any auxiliary elements (such as cross-coupled or extracted-pole structures), this paper provides the best synthesis solution in configuration simplicity for narrowband filters. Considering both the couplings and capacitances of a traditional low-pass prototype, a generalized transformation on the admittance matrix is introduced as the basis of the synthesis, which allows more than one cross-coupling to be annihilated in a single step, while generating a frequency-variant coupling simultaneously. It is then shown that the in-line topology as well as some other unique topologies can be determined by applying a specific sequence of the transformations. For the validation, a group of examples with synthesis as well as experimental results are demonstrated.