A theoretical analysis of some errors in aerial measurements

A theoretical analysis of certain aerial problems is carried out with the help of the idea of a spectrum of plane waves introduced by Booker and Clemmow. The reciprocity theorem, which relates the behaviour of an aerial used for reception to the properties of the same aerial as a transmitter, is used to derive an expression for the power received by one aerial as a result of transmission from a second aerial at any distance from the first. It is shown that under the conditions used in aerial measurements the size of the receiving aerial can influence the errors in measured radiation patterns and power gains. In particular, the side-lobe levels obtained when too small a separation between the aerials is used can either be larger or smaller than the levels for the true radiation pattern. This result differs from that predicted by diffraction theory, which suggests that side-lobe levels measured at too small a distance are always worse than those in the true radiation pattern. Similarly, when the size of the receiving aerial is taken into account, errors in gain measurements are shown to be larger than those predicted by diffraction theory.