On the front to back ratio of a parabolic dish antenna

Adopting the earlier work of Kouyoumjian's Ohio State group, as recently reviewed and extended by Rusch, an explicit expression for the radiation field in the back zone of a typical parabolic dish antenna is obtained. Evaluation of this expression directly in the back for both the ideal 100 percent aperture efficiency feed and for an arbitrary, feed gives (in conjunction with the known front field for the 100 percent case) the front to back (
f/b
) ratio for the arbitrary feed case of
(f/b) = G + T + K - G
horn
. Here
G
is the gain of the dish with the arbitrary feed,
G
horn
is the on axis gain of the feed,
T
is the feed's average pattern edge taper relative to on axis,
K = 20 \log_{10}{\sqrt{1 + 16(F/D)^{2}}/4(F/D)}
(all being in decibels), and
F/D
is the ratio of the focal length to the dish diameter. Comparison of this result with measured values for dishes ranging from 6 to 15 ft in diameter operating over a 920 MHz to 14 GHz range gives an agreement within several decibels in most cases.