FRESNEL GAIN OF APERTURE ANTENNA

When a transmitting aperture Ao and a receiving aperture Bo are coupled in the Fraunhofer region, the ratio of received to transmitted power is given by the Friis formula. It is known that the Fraunhofer gains Gao and Gbo of Ao and Bo are constant and are determined independently. In this report, the product of the gains GaGb in the Fresnel region is determined as an integral over both apertures, assuming the gains Ga and Gb for Ao and Bo. It is pointed out that GaGb cannot generally be separated into the individual factors, but a formula similar to that of Friis still holds in the Fresnel region. The author proposes to define the gain-product reduction factor, gamma sub a x gamma sub b, as the ratio of GaGb to GaoGbo. The individual gain Ga or Gb may be determined only when Ao and Bo are identical and the illuminations of both apertures are the same. Then, the gain-reduction factor, gamma, is defined as the ratio of Ga to Gao. Assuming uniform amplitude and phase of illumination over Ao and Bo, gamma sub a x gamma sub b and gamma are determined for circular and rectangular apertures. For circular apertures, the same factors are determined for a set of illuminations which approximate commonly used tapers, and the effect of defocusing the prima y feed in lenses and dishes is also discussed. Author