Generalized synthesis of the rat race ring coupler is developed with its four arms being allowed to have different characteristic impedances. The transmission line theory incorporated with the even-odd analysis is used to formulate the conditions for solving the circuit parameters. The solution shows that a rat race ring with a normalized area of 41.82% or 0.97λ-circumference can be achieved. Based on the solutions, simulated bandwidths of the new ring hybrids are reported. Two experimental circuits are measured for validation check. One uses stepped-impedance sections to realize the four arms for further size reduction. This circuit occupies only 13.12% of that of a conventional hybrid ring at 1 GHz. It is believed that this implementation has the best size reduction for a microstrip ring hybrid in open literature. Measured scattering parameters show good agreement with the simulated results.
"Generalized Synthesis of Rat Race Ring Coupler and Its Application to Circuit Miniaturization," Progress In Electromagnetics Research,
Vol. 108, 51-64, 2010. doi:10.2528/PIER10071705
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