Practical_Antenna_Handbook_0071639586

478 P a r t V I : A n t e n n a s f o r O t h e r F r e q u e n c i e s
Power gain is slightly different from directivity gain because it includes dissipative
losses in the antenna. Not included in the power gain are losses caused by cross-Â
polarization or impedance mismatch between the waveguide (or transmission line) and
the antenna. There are two commonly used means for determining power gain:
G
P
Pa
= 4π
P
NET
(20.29)
and
G
P
PAI =
(20.30)
P
I
where P a = maximum radiated power per unit solid angle
P NET = net power accepted by antenna (less mismatch losses)
P AI = average intensity at a distant point
P I = intensity at same point from isotropic radiator fed same RF power level
as antenna
(Equations assume equal power delivered to antenna and comparison isotropic source.)
Provided that ohmic losses are kept negligible, the relationship between directivity
gain and power gain is given by
G
P
P
=
P
RADG
NET
D (20.31)
where all terms are as previously defined.
Aperture
Antennas obey the law of reciprocity, which means that any given antenna will work as
well receiving as it does transmitting. The function of the receive antenna is to gather
energy from the electromagnetic field radiated by one or more transmit antennas. The
aperture is related to, and often closely approximates, the physical area of the antenna.
But in some designs the effective aperture A e is less than the physical area A, so there is
an effectiveness factor h that must be applied. In general, however, a high-gain transmitter
antenna also exhibits a high receiving aperture, and the relationship can be expressed
as
A η
G = 4 π e
2
λ
(20.32)
where A e = effective aperture
h = aperture effectiveness (h = 1 for a perfect, lossless antenna)
l = wavelength of signal