Broad-band Matching of Two Partially Constrained Networks

A class of matching problems is considered in which a network beginning with a shunt-reactive element is to be matched to a network beginning with a series-reactive element, so that power can be transferred through the junction point without reflection. It is shown that theoretically a perfect match can be achieved over a finite bandwidth, and that to accomplish this match the magnitudes of the impedances must be brought to an optimum value and must be maintained constant over the pass band. Solutions are obtained for the maximum bandwidths and for the optimum impedances by using a new integral-restriction technique that performs a simultaneous solution of the phase and magnitude conditions necessary for match. Methods of approximating the optimum impedances with a finite number of elements are discussed. A table of branch-point integrals is included as an Appendix.