Generalised direct matrix synthesis approach for lossless filters

A generalised direct matrix synthesis is proposed for microwave lossless filters with arbitrary phase shift at centre frequency and complex terminal impedances. The functions of traditional lossless filters, ideal phase shifters, and ideal impedance matching networks are thus substantially combined into one entity to provide an attractive technique for the realisation of compact narrowband microwave front-ends. The synthesis starts with a group of general S-parameters that consider both amplitude and phase responses as well as complex terminations for an Nth-order filter. A transversal array network incorporating resonators as well as non-resonating nodes is then introduced to accommodate the given S-parameters. In result, a canonical (N + 2) × (N + 2) coupling matrix with newly defined source–source and load–load couplings is generated. Some examples, including a fully canonical prototype and a mixed topology diplexer, are demonstrated to show the flexibility of the methodology. Moreover, an eighth-order coaxial cavity filter, with a −120° additional phase shift for S-parameters, is designed and fabricated. The measured results are well consistent with the synthesis ones, which validates the availability of this study in physical implementations.

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