Analysis of the general nonsymmetrical directional coupler with arbitrary terminations

The scattering parameters of the general nonsymmetrical uniformly coupled-line 4-port device with arbitrary terminations are derived in terms of the scattering parameters with characteristic nonmode converting terminations. It is shown that the performance of directional couplers consisting of nonsymmetrical lines with unequal normal-mode phase velocities can be optimized in terms of the terminating impedances. A method to determine the optimum terminations with an example of a 6 dB nonsymmetrical edge-coupled microstrip coupler is presented.