563489578934

Sec. 8–6 Link Budget Analysis 611
Using Eqs. (8–2) and (8–3), we obtain the received signal power
C Rx = (P EIRP ) G FS G AR
(8–39)
where P EIRP is the EIRP from the transmitter, G FS is the free-space gain, and G AR is the
receiving antenna power gain.
When we use Eq. (8–17), the available noise power at the input to the ideal amplifier in
the model (Fig. 8–24) is
N = kT syst B
(8–40)
where B is the IF equivalent bandwidth. The receiving system noise temperature is
T syst = T AR + T e
(8–41)
where T AR is the noise temperature of the antenna (due to received cosmic noise and Earth
blackbody radiation) and T e is the effective input-noise temperature of the overall receiving
system.
When Eqs. (8–39) and (8–40) are combined, the carrier-to-noise ratio at the detector
input is
C
N = P EIRPG FS G AR
kT syst B
(8–42)
For engineering applications, this formula is converted to decibel units. Using Eq. (8–9)
and taking 10 log [·] of both sides of (8–42), we find that the received carrier-to-noise ratio at
the detector input in decibels is
a C N b dB
= (P EIRP ) dBw - (L FS ) dB + a G AR
b -k dB - B dB
T syst dB
(8–43)
where
(P EIRP ) dBw = 10 log (P EIRP ) is the EIRP of the transmitter in dB above 1 W,
(L FS ) dB = 20 log [(4pd)l] is the path loss, †
k dB = 10 log (1.38 × 10 -23 ) =-228.6,
B dB = 10 log (B)
(B is the IF bandwidth in hertz).
For analog communication systems, the SNR at the detector output can be related to the
CNR at the detector input. The exact relationship depends on the type of detector, as well as
the modulation used. These relationships were developed in Chapter 7. They are summarized
in Table 7–2 and Fig. 7–27 with the use of Eq. (7–85), where CN = (SN) in . Example 8–6
uses Eq. (8–43) to evaluate the performance of a CATV satellite receiving system.
† This free-space path-loss expression can be modified to include effects of a multipath channel within an
urban building environment. [See Eq. (8–47) and (8–67).]