Filtering rat-race coupler with transmission zeros using compact miniaturized hairpin resonators

A new compact filtering rat-race coupler is implemented by a 2×2 cross coupled configuration based on compact miniaturized hairpin resonators. Passband responses with transmission zeros are synthesized by an (n+4)×(n+4) coupling matrix. The zeros are created in the output ports by adding source-load coupling and their analytical expressions are derived. An experimental circuit is fabricated and measured. The circuit area is only 23.2% of that of a conventional rat-race coupler. Measured magnitude and phase responses of the four-port S-parameters show good agreement with simulation data.