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(12.71)
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(MIphR) c a2qIM F
(12.72) g2 m a1 (2 RCB) 3
4kT R
2qIin bR
2qItr
The Space Link
This can be simplified on dividing through by M 2R2 to get: S N
2 Iph
c2qIF
4kT M 2R
2qIin M
2qItr
M gm
1 R2
(2 CB)2 3
(12.73)
Example 12.22
An optical receiver utilizes an APD for which R0 0.65 A/W, M 100, F 4, Iin 0, gm 3000 mS and Itr 0.15 mA. The dark current may be neglected. The input load consists of a 600 resistor in parallel with a 10pF capacitance. The signal bandwidth is 25 MHz and equalization is employed. Calculate the resultant signal-to-noise ratio for an input signal power of 1 W. The photocurrent is Iph 0.65 10 in the denominator are, with Id 0 and Iin 0: 2qIF 4kT M R 2qItr
2 M 2gm 2
Solution
0.65 A. The individual terms
6.408 0.027 b
10 10
A2/Hz A2/Hz
(2 CB)2 3 (0.65
0.011 10 6)2 0.011)
A2/Hz
S N (6.408 2.622 In decibels this is 44.2 dB
0.027 104
12.13 Problems and Exercises
Note: In problems where room temperature is required, assume a value of 290 K. In calculations involving antenna gain, an efficiency factor of 0.55 may be assumed. 12.1. Give the decibel equivalents for the following quantities: (a) a power ratio of 30:1; (b) a power of 230 W; (c) a bandwidth of 36 MHz; (d) a frequency ratio of 2 MHz/3 kHz; (e) a temperature of 200 K. 12.2. (a) Explain what is meant by EIRP. (b) A transmitter feeds a power of 10 W into an antenna which has a gain of 46 dB. Calculate the EIRP in (i) watts; (ii) dBW. 12.3. Calculate the gain of a 3-m parabolic reflector antenna at a frequency of (a) 6 GHz; (b) 14 GHz.
Twelve
12.4. Calculate the gain in decibels and the effective area of a 30-m parabolic antenna at a frequency of 4 GHz. 12.5. An antenna has a gain of 46 dB at 12 GHz. Calculate its effective area.
12.6. Calculate the effective area of a 10-ft parabolic reflector antenna at a frequency of (a) 4 GHz; (b) 12 GHz. 12.7. The EIRP from a satellite is 49.4 dBW. Calculate (a) the power density at a ground station for which the range is 40,000 km and (b) the power delivered to a matched load at the ground station receiver if the antenna gain is 50 dB. The downlink frequency is 4 GHz. 12.8. Calculate the free-space loss as a power ratio and in decibels for transmission at frequencies of (a) 4 GHz, (b) 6 GHz, (c) 12 GHz, and (d) 14 GHz; the range being 42,000 km. 12.9. Repeat the calculation in Prob. 12.7b allowing for a fading margin of 1.0 dB and receiver feeder losses of 0.5 dB. 12.10. Explain what is meant by (a) antenna noise temperature, (b) amplifier noise temperature, and (c) system noise temperature referred to input. A system operates with an antenna noise temperature of 40 K and an input amplifier noise temperature of 120 K. Calculate the available noise power density of the system referred to the amplifier input. 12.11. Two amplifiers are connected in cascade, each having a gain of 10 dB and a noise temperature of 200 K. Calculate (a) the overall gain and (b) the effective noise temperature referred to input. 12.12. Explain what is meant by noise factor. For what source temperature is noise factor defined 12.13. The noise factor of an amplifier is 7:1. Calculate (a) the noise figure and (b) the equivalent noise temperature. 12.14. An attenuator has an attenuation of 6 dB. Calculate (a) its noise figure and (b) its equivalent noise temperature referred to input. 12.15. An amplifier having a noise temperature of 200 K has a 4-dB attenuator connected at its input. Calculate the effective noise temperature referred to the attenuator input. 12.16. A receiving system consists of an antenna having a noise temperature of 60 K, feeding directly into a LNA. The amplifier has a noise temperature of 120 K and a gain of 45 dB. The coaxial feeder between the LNA and the main receiver has a loss of 2 dB, and the main receiver has a noise figure of 9 dB. Calculate the system noise temperature referred to input.
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