A Method of Analysis of Symmetrical Four-Port Networks

An analysis of four-arm symmetrical networks such as a branched directional double stub coupler or the hybrid ring (rat race) is presented. The input wave is broken into an even and an odd mode and the vector amplitude out the various arms is computed from the sums or differences of the reflection or transmission coefficients for the two modes. A zero decibel directional coupler is described and its possible use as a duplexer is proposed. The design of multiple stub directional couplers for any degree of coupling is discussed. A method of computing the bandwidth of all these couplers is outlined, and the bandwidth curves, the power out the various arms with respect to frequency of the zero decibel coupler, are computed. A tabulation is made for six different 3 db couplers (even-power split) and their standing wave ratio, evenness of power split and isolation of the fourth arm as a function of frequency assuming perfect performance at the band center.