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約翰克勞斯《天線》一書的一道習題

文章來源: 互聯(lián)網(wǎng) 錄入: mweda.com

在第二章的習題里面，有道關(guān)于火星地球間無線通信的題，不會做，我覺得題目比較有意思，很想弄清楚到底怎么分析，我認為題目好像條件不夠啊，連天線是哪種類型都沒說清楚，不過感覺可能指的是螺旋天線，因為后面有類似題目中就提到了。
題目我貼上來了，麻煩大家?guī)臀铱纯窗伞?nbsp;

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本書課后完整版答案：
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2-11-4. Mars and Jupiter links.
(a) Design a two-way radio link to operate over earth-Mars distances for data and picture transmission with a Mars probe at 2.5 GHz with a 5 MHz bandwidth. A power of 10-19
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W Hz-1 is to be delivered to the earth receiver and 10-17 W Hz-1 to the Mars receiver. The Mars antenna must be no larger than 3 m in diameter. Specify effective aperture of Mars and earth antennas and transmitter power (total over entire bandwidth) at each end. Take earth-Mars distance as 6 light-minutes. (b) Repeat (a) for an earth-Jupiter link. Take the earth-Jupiter distance as 40 light-minutes.
2-11-4. continued
Solution:
(a)
1961317611(earth)10510510 W(Mars)10510510 WrrPP−−−−=××=×=××=×
Take )5.0( m 5.31.5(1/2)Mars)(ap22===επeA
Take kW 1Mars)(=tP
Take )5.0( m 35051(1/2)earth)(ap22===επeA
MW 9.63505.312.0)103360(105)earth(Mars)(earth)(Mars)()earth(2281122=××××==−tetetrtPAArPPλ
To reduce the required earth station power, take the earth station antenna
22m 392750 )2/1(==πeA (ans.)
so
62(earth)6.910(15/50)620 kW ()tPans.=×=
W10812.0)103360(39305.310earth)(Mars)(Mars)()earth(14228322−×=×××==λrAAPPerettr
which is about 16% of the required 5 x 10−13 W. The required 5 x 10−13 W could be obtained by increasing the Mars transmitter power by a factor of 6.3. Other alternatives would be (1) to reduce the bandwidth (and data rate) reducing the required value of Pr or (2) to employ a more sensitive receiver.
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As discussed in Sec. 12-1, the noise power of a receiving system is a function of its system temperature T and bandwidth B as given by P = kTB, where k = Boltzmann’s constant = 1.38 x 10−23 JK−1.
For B = 5 x 106 Hz (as given in this problem) and T = 50 K (an attainable value),
2-11-4. continued
The received power (8 x 10−14 W) is about 20 times this noise power, which is probably sufficient for satisfactory communication. Accordingly, with a 50 K receiving system temperature at the earth station, a Mars transmitter power of 1 kW is adequate.
(b) The given Jupiter distance is 40/6 = 6.7 times that to Mars, which makes the required transmitter powers 6.72 = 45 times as much or the required receiver powers 1/45 as much.
Neither appears feasible. But a practical solution would be to reduce the bandwidth for the Jupiter link by a factor of about 50, making B = (5/50) x 106 = 100 kHz.