Reflector Antenna Analysis jbh Sept. 24, 2004

Reexamining old Condon point feed analysis....

What is correct method of calculating gain? Assumptions: primary (feed) antenna is far enough from reflector so that there is no reaction, i.e. the primary field is unchanged by the presence of the reflector.

The reflector is in the far field of the feed antenna and incident electric field can be calculated exactly from the properties of the feed.

The final pattern of the antenna can be obtained by adding the far fields produced by each section of the reflector, where 'section' denotes an arbitrary surface element, chosen for ease of calculation.

But is this really true? If we conceptually divide the reflector into small 'panels', will each panel radiate as if it were alone in space? Won't there be considerable interaction between the panels? If the panels are thin strips, won't it matter that the incident electric field may be perpendiular to some of the strips?

Yet if we are confident that we know the induced current density at every point on the reflector, then surely we can divide the reflector into arbitrarily small elements for purpose of integration, since we can add the radiation do to arbitrarily small current elements. This seems to be the key.

See Silver, page 150 (146-150). It is instructive to carrry out Silver's analysis on a reflector antenna consisting of a flat plate of area A. Put a feed is far above the plate at a distance rho. Let it provide uniform illumination over the plate with no spill-over. Thus the gain of the feed is G=4pi rho^2/A. Let the polarization be everywhere in the same direction. In Silver's integral I , the complex exponential is unity and the cross-cross product is unity. Thus the value of the integral is I= (4 pi A)^1/2. Gain, from Equation 77b is just |F1|^2, since F2=0. Here F1 = jI/lambda (since the feed doesn't radiate except onto the reflector). So the gain is (I/lambda)^2 = 4 pi A/ lambda^2, as expected.

Note that A_effective = lambda^2 G/(4 pi) = | I |^2 /(4pi).

Note that -21 dB wrt to uniform illumination is far worse that the value calculated by Condon.

More than 5 dB is do to phase error, as can be verified by removing the "Vec" term from the integrand. The "Geom" term is the cross produce of n, the reflector surface unit normal vector , with the cross product of the (assumed constant) unit polarization vector and the unit vector from the point source to the point on the reflector.

The major cause of loss in this analysis seems to be the feed pattern itself.