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Sec. 8–6 Link Budget Analysis 599
TABLE 8–4
ANTENNA GAINS AND EFFECTIVE AREAS
Type of Antenna
Power Gain, G A
(absolute units)
Effective Area,
A e (m 2 )
Isotropic 1 l 2 > 4p
Infinitesimal dipole or loop 1.5 1.5l > 4p
Half-wave dipole 1.64 1.64l > 4p
Horn (optimized), mouth area, A 10A> l 2
0.81A
Parabola or “dish” with face area, A 7.0A> l 2
0.56A
Turnstile (two crossed dipoles fed 90° out of phase) 1.15 1.15l > 4p
where the power density and the field strength are evaluated at the same point in space and
377 Ω is the free-space intrinsic impedance. If the receiving antenna is placed at d meters
from the transmitting antenna, it will act like a catcher’s mitt and intercept the power in an
effective area of (A e ) Rx (m 2 ), so that the received power will be
P Rx = G AT a P Tx
4pd 2 b(A e) Rx
(8–6)
where the gain of the transmitting antenna (with respect to an isotropic antenna), G AT , has
been included. Table 8–4 also gives the effective area for several types of antennas. The gain
and the effective area of an antenna are related by
G A = 4pA e
l 2
(8–7)
where l = cf is the wavelength, c being the speed of light (3 × 10 8 ms) and f the operating
frequency in Hz. An antenna is a reciprocal element. That is, it has the same gain
properties whether it is transmitting or receiving. Substituting Eq. (8–7) into Eq. (8–6),
we obtain
P Rx
P Tx
= G AT a l
4pd b 2
G AR
(8–8)
where the free-space gain is
G FS = a l
4pd b 2
= 1
L FS
(8–9)
and L FS is the free-space path loss (absolute units). The channel gain, expressed in dB, is
obtained by taking 10 log [·] of both sides of Eq. (8–2):
(G channel ) dB = (G AT ) dB - (L FS ) dB + (G AR ) dB
(8–10)