Page 413 - Satellite Communications, Fourth Edition

The Space Link 393

2 2
This can be simplified on dividing through by M R to get:
2
S I ph

N 4kT 2qI in 2qI tr 1 (2 CB) 2 (12.73)
c2qIF 2 2 2 2 a 2 bdB
M R M M g m R 3

Example 12.22 An optical receiver utilizes an APD for which R 0 0.65 A/W,
M 100, F 4, I in 0, gm 3000 mS and I tr 0.15 mA. The dark current may
be neglected. The input load consists of a 600 Ω 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.
Solution The photocurrent is I ph 0.65 10 6 0.65 A. The individual terms
in the denominator are, with I d 0 and I in 0:
2
2qIF 6.408 10 25 A/Hz
4kT 25 2
0.027 10 A/Hz
2
M R
2qI tr 1 (2 CB) 2 25 2
a b 0.011 10 A/Hz
2 2
M g m R 2 3
6 2
S (0.65 10 ) 10 25

N (6.408 0.027 0.011) 25 10 6
2.622 10 4

In decibels this is 44.2 dB

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.