Compact Wideband 3 × 3 Nolen Matrix With Couplers Integrated With Phase Shifters

This letter presents a compact wideband
$3 \times 3$
Nolen matrix composed of couplers with arbitrary output phase differences. A cross-junction is introduced into the traditional branch line coupler to realize the desired output power ratio and phase difference. Meanwhile, this also increases the degree of freedom by introducing multiple variables. A genetic algorithm is utilized to obtain the optimum solution for each branch. Two couplers with coupling values of 0.707 (3 dB) and 0.82 (1.77 dB) and with output phase differences of 60° and 30° are designed, fabricated, and measured, respectively. Finally, a wideband
$3 \times 3$
Nolen matrix with compact size is realized, which achieves equal amplitude output and equal phase difference output (0°, 120°, and −120°) within the 34.3% fractional bandwidth (FBW) while ensuring lower amplitude imbalance and phase imbalance. Simulation and measurement results show good agreement over the operating frequency band.