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In the paper of Chen and Yeo (2007), the authors demonstrate a four-port coupler for crossover application. In their eigenmode model analysis, the entire circuit is decomposed into tapers and two rings with four external arms. In formulation, the eigenadmittance of the inner substructure is taken account as the load of that of the outer one. A cascade of P short sections is then used to approximate...
Miniaturization of a microstrip rat race coupler is implemented by three approaches. First, a new rat race hybrid design is devised for circuit miniaturization based on the periodic stepped-impedance ring structure. The circuit has a normalized area of 21.5%. In the second approach, miniaturization is carried out by incorporating a broadside-coupled structure and stepped-impedance sections into the...
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