Transmitter-to-Antenna Power Transfer Under Unmatched Conditions

One phase of the electromagnetic compatibility program is the determianation of the electromagnetic energy actually radiated into space by an antenna. Methods have long been established, or proposed, for measuring the power output of a transmitter, the antenna impedance, and the antenna-radiation pattern. However, very little definitive work has been published regarding the methods for computing the transmitter energy coupled to the antenna and radiated at harmonic and spurious frequencies. It is the purpose of this paper to reduce to a simple form the equations for determining the power absorbed by an antenna connected through a coaxial transmission line to a transmitter. Most discussions of transmission-line-power transfer assume the matched conditions so universally desired at the operating frequency. When harmonic and spurious frequencies are considered, both the transmitter and the antenna are likely to be poorly matched to the transmission line and to each other. This paper points out what measurements need to be made and gives the functional relations necessary to compute the power radiated under unmatched conditions. Since the actual power coupled to the antenna in a given instance may be critically dependent upon the exact length of transmission line, some means must be available to take this into account. The expressions derived give the maximum and minimum power that will be absorbed, and also give the probability that any specified intermediate power will be exceeded if a random choice of transmissionline length is used.