Miniaturized Arbitrary Phase-Difference Couplers for Arbitrary Coupling Coefficients

In this paper, a planar miniaturized arbitrary phase-difference coupler with arbitrary coupling coefficients is proposed. The proposed coupler consists of three coupled-line sections which achieves a compact circuit layout in microstrip implementation. The circuit parameters of this novel coupler can be easily determined by the derived closed-form equations and the corresponding performance analysis in terms of the bandwidth and miniaturization requirement is provided. Two prototypes with this proposed structure, operating at 2 GHz, have been designed and implemented using microstrip technology. One has a 45
$^{\circ}$
phase difference with
${- }$
3-dB coupling coefficient and the other demonstrates a 60
$^{\circ}$
phase difference with
${- }\hbox{4.77-dB}$
coupling coefficient. In addition, over 20% fractional bandwidth, which is defined as 5
$^{\circ}$
phase error and 0.5-dB magnitude imbalance, is obtained in both of the two prototypes.