%0 Journal Article
%T Generalized Synthesis of Rat Race Ring Coupler and its Application to Circuit Miniaturization
%A Jen-Tsai Kuo
%A Cheng-Hsiu Tsai
%J PIER
%@ 1070-4698
%D 2010
%I 
%R 10.2528/PIER10071705
%X 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 0.97¦Ë-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.
%U http://www.jpier.org/pier/pier.php?paper=10071705