Measurement of an invariant in directional couplers

How to measure a constant parameter first deduced by K. Araki and Y. Naito (1992) for lossless four-port directional coupler circuits with a reflection symmetry is studied. The constant parameter K can be used to determine the isolation port, the coupling port, and the amount of coupling. The coupling is classified into three types corresponding to the cases K1. The value of the constant is easily calculated from S-parameters commonly obtained by a vector network analyzer in the microwave frequency band. The parameter can be used for predicting the transmission characteristics of a directional coupler without building matching circuits. It is noted that K is a real quantity, although the S-parameters are complex. Because the expression defining K is not explicitly real, the imaginary part of K of this expression shows the derivation from losslessness and the symmetry of the circuit.<>