A Least Square Mode Matching Technique for Waveguide iscontinuities

The fields III various sections of a waveguide network are approximated
by their truncated modal expansions. The magnitude squared of each expression of the boundary conditions is integrated over the respective interfaces. The sum of these integrals is a quadratic function (called error function) of only the unknown modal amplitudes. The minimization of this function reduces to the solution of a linear equation which is directly obtainable from the boundary conditions. The unique minimum of the error function represents the best mode matching procedure in the least square sense. This technique is readily applicable to most waveguide discontinuity problems. However, it is applied here to the off- set junction of two parallel plate waveguides and two rectangular waveguides with mode and current probe excitations. A weighting factor which multiplies the error due to the magnetic field is investigated and conservation of real power is utilized as a criterion for its selection.