A Compact Filtering 180 $^{\circ}$ Hybrid

A novel compact filtering 180
$^{\circ}$
hybrid utilizing coupled resonators is presented. The equivalent-circuit structure is just like a bandpass filter, thus the frequency response is filter-like. The sum and difference port operations respectively correspond to the symmetric and antisymmetric states; therefore, isolation between sum and difference ports is accomplished by geometrical symmetry. The synthesis method of the filtering 180
$^{\circ}$
hybrid is illustrated. The proposed structure is decomposed into one power divider and one balun, which are designed separately. A second-order filtering 180
$^{\circ}$
hybrid prototype centered at 2.4 GHz with 0.2-dB Chebyshev equal-ripple response and 10% fractional bandwidth is demonstrated. The passband insertion loss is about
$({\hbox{3.0}} + {\hbox{0.7}})$
dB, and the isolation between the sum and difference port is greater than 20 dB. Magnitude imbalance is less than 1 dB and phase imbalance is within 2
$^{\circ}$
. Good agreement between simulation and experimental results is achieved.