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about 1 and 10 GHz. This represents the residual background radiation in the universe. Above about 10 GHz, two peaks in temperature are observed, resulting from resonant losses in the earth s atmosphere. These are seen to coincide with the peaks in atmospheric absorption loss shown in Fig. 4.2. Any absorptive loss mechanism generates thermal noise, there being a direct connection between the loss and the effective noise temperature, as shown in Sec. 12.5.5. Rainfall introduces attenuation, and therefore, it degrades transmissions in two ways: It attenuates the signal, and it introduces noise. The detrimental effects of rain are much worse at Ku-band frequencies than at C band, and the downlink rain-fade margin, discussed in Sec. 12.9.2, must also allow for the increased noise generated. Figure 12.2 applies to ground-based antennas. Satellite antennas are generally pointed toward the earth, and therefore, they receive the full thermal radiation from it. In this case the equivalent noise temperature of the antenna, excluding antenna losses, is approximately 290 K. Antenna losses add to the noise received as radiation, and the total antenna noise temperature is the sum of the equivalent noise temperatures of all these sources. For large ground-based C-band antennas, the total antenna noise temperature is typically about 60 K, and for the Ku band, about 80 K under clear-sky conditions. These values do not apply to any specific situation and are quoted merely to give some idea of the magnitudes involved. Figure 12.3 shows the noise temperature as a function of angle of elevation for a 1.8-m antenna operating in the Ku band.
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12.5.2 Ampli er noise temperature
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Consider first the noise representation of the antenna and the low noise amplifier (LNA) shown in Fig. 12.4a. The available power gain of the amplifier is denoted as G, and the noise power output, as Pno. For the
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Antenna noise temperature as a function of elevation for 1.8-m antenna characteristics. (Andrew Bulletin 1206; courtesy of Andrew Antenna Company, Limited.)
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Figure 12.4 Circuit used in finding equivalent noise temperature of (a) an amplifier and (b) two amplifiers in cascade.
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moment we will work with the noise power per unit bandwidth, which is simply noise energy in joules as shown by Eq. (12.15). The input noise energy coming from the antenna is N0,ant kTant (12.16)
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The output noise energy N0,out will be GN0,ant plus the contribution made by the amplifier. Now all the amplifier noise, wherever it occurs in the amplifier, may be referred to the input in terms of an equivalent input noise temperature for the amplifier Te. This allows the output noise to be written as N0,out Gk(Tant Te) (12.17)
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The total noise referred to the input is simply N0,out /G, or N0,in k(Tant Te) (12.18)
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Te can be obtained by measurement, a typical value being in the range 35 to 100 K. Typical values for Tant are given in Sec. 12.5.1.
12.5.3 Ampli ers in cascade
The cascade connection is shown in Fig. 12.4b. For this arrangement, the overall gain is G G1G2 (12.19)
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The noise energy of amplifier 2 referred to its own input is simply kTe2. The noise input to amplifier 2 from the preceding stages is G1k(Tant Te1), and thus the total noise energy referred to amplifier 2 input is N0,2 G1k(Tant Te1) kTe2 (12.20)
This noise energy may be referred to amplifier 1 input by dividing by the available power gain of amplifier 1: N0,1 N0,2 G1 kaTant Te1 Te2 G1 b (12.21)
A system noise temperature may now be defined as TS by N0,1 kTS (12.22)
and hence it will be seen that TS is given by TS Tant Te1 Te2 G1 (12.23)
This is a very important result. It shows that the noise temperature of the second stage is divided by the power gain of the first stage when referred to the input. Therefore, in order to keep the overall system noise as low as possible, the first stage (usually an LNA) should have high power gain as well as low noise temperature. This result may be generalized to any number of stages in cascade, giving TS
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