Impedance Transformation Using Lossless Networks

Abstract

Two impedances are said to be compatible if one of them can be realized as the input impedance to a two terminal-pair lossless network terminated in the other impedance. A concise set of necessary and sufficient conditions under which two impedances can be compatible is found. Sometimes it is necessary to augment one of the two impedances by inserting a common factor into both its numerator and denominator in order to make it compatible with the second impedance. The conditions under which such a factor exists and methods for finding it are determined.

On Broadband Matching of Multiport Electrical Networks with Applications.

“…2) On the real-frequency axis, IP2(jw)l satisfies the following: Schoeffler [47] and then by Wohlers [54] and Ho and Balabanian [33].…”

“…Schoeffler [47] and Wohlers [54] studied the problem of compatibility between two passive impedances, the coupling network of which is assumed to be reciprocal. Ho and Balabanian [33] extended their results to the case where the impedances may be either passive or active and the coupling networks may be reciprocal or nonreciprocal.…”

Antenna bandwidth engineering through time-varying resistance

“…The impedances at the considered frequencies must be compatible, and this is not a general feature of input impedances of complex small resonant circuits 26 . Matching networks for two frequencies are known only for simple basic loads such as single reactive element connected to a single resistor [27][28][29][30] . Solutions for matching more than two frequencies become impractical (rather complex and lossy) even if the impedances are compatible at all desired frequencies.…”