Reduced-Length Rat-Race Couplers

In this paper, analysis of a rat-race coupler having three equal arms of arbitrary electrical length is presented. All of these couplers have lower characteristic impedances than the conventional 1.5-lambda coupler and some of them have smaller electrical lengths. Bandwidths in terms of isolation, matching, amplitude, and phase imbalances are also discussed. A reduced-size rat-race coupler of length 19lambda/18 at the operating frequency of 0.9 GHz has been fabricated in the microstrip line. Experimental results agree well with the theoretical predictions.