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where T e is the equivalent temperature, considering the contributions fromLNA <strong>and</strong> other devices, as seen at the LNA input (at the dotted line point <strong>of</strong>Fig. 3.15):T e ¼ T e2 þ T e3G 2ð3:56ÞBy substituting (3.56) <strong>and</strong> (3.54) in (3.55), we see that the system noisetemperature isT ¼ T aþ T 0ðL 1L 1L 11Þþ T e2 þ T e3G 2ð3:57ÞWith the gain expressions developed for different kinds <strong>of</strong> antennas in Sec. 2.7<strong>and</strong> the system noise temperature in (3.57), we can establish the earth stationsensitivity G=T.Example 3.3: A 20-m Cassegrain antenna, having a receive antenna gain <strong>of</strong>54.53 dB at 11.2 GHz <strong>and</strong> an ambient temperature <strong>of</strong> 275 K, is characterizedby the following parameters:Antenna noise temperature ¼ 60 K.Waveguide loss ¼ 0.3 dB.Low-noise amplifier (LNA) with 20-dB gain <strong>and</strong> 350 K effective noisetemperature.Effective noise temperature <strong>of</strong> the downconverter ¼ 1500 K.Estimate (1) the earth station system noise temperature <strong>and</strong> (2) the antennagain referred to the input <strong>of</strong> the LNA.SolutionL 1 ¼ 10 0:03 ¼ 1:0715 G 2 ¼ 20 dB ¼ 10 2 ¼ 100T a ¼ 60 T 0 ¼ 275 T e3 ¼ 1500 T e2 ¼ 3501. Using (3.57), we can calculate the earth station temperature asT ¼ 601:0715275 0:0715þ þ 350 þ 15001:0715100 ¼ 439:345 K2. Antenna gain referred to the input <strong>of</strong> LNA: G a ¼ð54:53 0:3Þ ¼54:50 dB.Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.

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