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Wire and Wireless Communication Applications Chap. 8
In Eq. (8–10), the free-space loss † is
(L FS ) dB = 20 log a 4pd
l
b dB
(8–11)
For example, the free-space loss at 4 GHz for the shortest path to a synchronous satellite from
Earth (22,300 miles) is 195.6 dB.
Note that from Eq. (8–8), the received power increases as the square of the wavelength
(free space condition). That is, if the carrier frequency is reduced by a factor of 2, then the
received power will increase by a factor of 4. This is equivalent to the loss decreasing by 6 dB
as shown by Eq. (8–11).
Thermal Noise Sources
The noise power generated by a thermal noise source will be studied because the receiver noise
is evaluated in terms of this phenomenon. A conductive element with two terminals may be
characterized by its resistance, R ohms. This resistive, or lossy, element contains free electrons
that have some random motion if the temperature of the resistor is above absolute zero. This
random motion causes a noise voltage to be generated at the terminals of the resistor. Although
the noise is small, when the noise is amplified by a high-gain receiver it can become a problem.
(If no noise were present, we could communicate to the edge of the universe with infinitely
small power, since the signal could always be amplified without having noise introduced.)
This physical lossy element, or physical resistor, can be modeled by an equivalent circuit
that consists of a noiseless resistor in series with a noise voltage source. (See Fig. 8–17.)
From quantum mechanics, it can be shown that the (normalized) power spectrum corresponding
to the voltage source is [Van der Ziel, 1986]
v (f) = 2Rc h ƒ f ƒ
2
+
h ƒ f ƒ
d
e hƒfƒ>(kT) - 1
(8–12)
Physical
resistor
R
Noiseless
resistor
Equivalent
noise
source
R
v(t)
p v (f)
(a) A Lossy Circuit Element
Characterized by Its
Resistance
Figure 8–17
(b) Thevenin Equivalent
Circuit Model of the
Lossy Circuit Element
Thermal noise source.
† This free-space path loss expression can be modified to include effects of a multipath channel within an
urban building environment. [See Eq. (8–67).]