Compact eighth-order microstrip filtering coupler

An eighth-order 180-degree filtering coupler is implemented with a 4×4 array of quarter-wave resonators. All resonators have a 90-degree bend and are configured to fit into a compact area. The geometric spaces among the resonators are determined by the coupling coefficients given in traditional filter synthesis formulas. At 2.4 GHz, an experimental circuit with a fractional bandwidth of 10% is fabricated and measured. Measured magnitude and phase responses of the four-port S-parameters show good agreement with simulation data.