Optimal Matching: A New Approach to the Matching Problem for Real Linear Time-Invariant One-Port Networks

A strictly energy-absorbing real linear time-invariant one-port network characterized by an impedance function
Z(p)
is optimally matched by a real linear time-invariant one-port network characterized by an impedance function
Z(-p)
.
Z(-p)
is not realizable in general, but it is the key to the entire study of matching since it dictates fundamental limitations on matching network behavior and a sequence of approximating matching network structures. The problem is formulated in the time domain, but practical realizations are obtained at the final step by means of passive approximation in the frequency domain. Most of the steps to solution of a specific problem may be carried out virtually by inspection.