Apparent Breakdown of the Reciprocity Law for Transmission Lines

Abstract

RADIO-FREQUENCY transmission lines are normally matched for maximum power-transfer by making the load impedance as transformed by the line equal to the complex conjugate of the generator impedance. One consequence of the reciprocity theorem is that the same matching condition applies when the transmission takes place in the opposite direction, that is, the functions but not the impedances of the load and generator are interchanged. In an application to multi-element directive arrays, an apparent failure of this principle has been found. Further examination has elucidated the reason for the paradox, but as it is felt that the behaviour of such arrays for incoming radiation is not generally understood, the facts seem worth recording. Similar considerations may arise in other radio-frequency problems (for example, nuclear physics accelerators) where branching feeders are used.