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Wire and Wireless Communication Applications Chap. 8
Baseband
signal in
m(t)
Transmitter
Transmitting
antenna gain
Channel
Free space
gain
Receiving
antenna gain
Baseband
s(t)
G AT G FS G AR
r(t)
signal out
m(t) ∼
Transmitter
P Tx
P EIRP PRx
To display
Figure 8–16
Block diagram of a communication system with a free-space transmission channel.
A block diagram of a communication system with a free-space transmission channel is
shown in Fig. 8–16. The overall power gain (or power transfer function) of the channel is
P Rx
P Tx
= G AT G FS G AR
(8–2)
where P Tx is the signal power into the transmitting antenna, G AT is the transmitting antenna
power gain, G FS is the free-space power gain † (which is orders of magnitude less than one in
typical communication systems), G AR is the receiving antenna power gain, and P Rx is the signal
power into the receiver.
To use this relationship, these gains should be expressed in terms of useful antenna and
free-space parameters [Kraus, 1986]. Here, G AT and G AR are taken to be the power gains with
respect to an isotropic antenna. ‡ The EIRP is
P EIRP = G AT P Tx
(8–3)
The antenna power gain is defined as
radiation power density of the actual antenna
in the direction of maximum radiation
G A = radiation power density of an isotropic antenna
with the same power input
where the power density (measured in Wm 2 ) is evaluated at the same distance, d, for both
antennas. The gains are for some practical antennas is given in Table 8–4.
The power density (Wm 2 ) of an isotropic antenna at a distance d from the antenna is
transmitted power
power density at d =
(8–4)
area of a sphere with radius d = P EIRP
4pd 2
The FCC and others often specify the strength of an electromagnetic field by the field intensity,
(Vm), instead of power density (Wm 2 ). The two are related by
power density = 2
377
(8–5)
† A gain transfer function is the output quantity divided by the input quantity, whereas a loss transfer function
is the input quantity divided by the output quantity.
‡ An isotropic antenna is a nonrealizable theoretical antenna that radiates equally well in all directions and is
a useful reference for comparing practical antennas.