Miniaturized Arbitrary Phase-Difference Couplers for Arbitrary Coupling Coefficients

Abstract

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 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$^{\circ}$</tex></formula> phase difference with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${- }$</tex> </formula> 3-dB coupling coefficient and the other demonstrates a 60 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$^{\circ}$</tex></formula> phase difference with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${- }\hbox{4.77-dB}$</tex> </formula> coupling coefficient. In addition, over 20% fractional bandwidth, which is defined as 5 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$^{\circ}$</tex> </formula> phase error and 0.5-dB magnitude imbalance, is obtained in both of the two prototypes.