7.6 Summary
301
and the photodetector quantum efficiency is 0.65. (a) Show that the power
falling on the photodetector is 2.5 nW. (b) Show that the average number of
electron–hole pairs generated in a time t = 1 ns is N = 10.6. (c) Show that
the probability that fewer than 5 electron − hole pairs will be generated at
the detector in the 1-ns interval is P(n = 5) = 0.05 = 5%.
7.7 If a bit-corrupting noise burst lasts for 2 ms, how many bits are affected at
data rates of 10 Mb/s,100 Mb/s, and 2.5 Gb/s? [Answer: (a) 2 × 10
4 ; (b) 2 ×
10
5 ; (c) 5 × 10
6 .]
7.8 Consider a thermal-noise-limited analog optical fiber system that uses a pin
photodiode with a responsivity of 0.85 A/W at 1310 nm. Assume the system
uses a modulation index of 0.5 and operates in a 5-MHz bandwidth. Let the
mean-square thermal noise current per unit bandwidth for the receiver be 2
× 10
−23 A
2 /Hz. Show that the peak-to-peak signal power to rms noise ratio
at the receiver is 38 dB when the average incident optical power is − 20 dBm
(0.010 mW).
7.9 Consider a shot-noise limited analog optical fiber system that uses a pin photodiode with a responsivity of 0.85 A/W at 1310 nm. Assume the system uses
a modulation index of 0.6 and operates in a 40-MHz bandwidth. Neglecting
detector dark current, show that is the signal-to-noise ratio is SNR = 29.1 dB
when the incident optical power at the receiver is − 15 dBm (0.032 mW).
7.10 Show that if thermal noise dominates then the signal-to-noise ratio given by
Eq. (7.32) is a maximum when the gain is optimized at
M
2+x
opt =
4k B T F t /R eq
q
i p + i D
x
7.11 Consider a Si APD detector that has an excess noise factor related parameter
x = 0.3, a load-resistance/amplifier-noise-figure value of R eq /F t = 10
4
, a
dark current of i D = 6 nA, and a responsivity of 0.55 A/W. If at a temperature
T = 300°K the photodetector is irradiated with a light power level P in = 15
nW, (a) first use Eq. (6.6) to show that the primary photocurrent is i p = 8.25
nA and (b) then use the relationship given in Problem 7.10 to show that the
optimum gain is M opt = 29.6.
References
1. T. V. Muoi, Receiver design for high-speed optical-fiber systems. J. Lightw. Technol. LT-2,
243−267 (1984)
2. M. Brain, T. P. Lee, Optical receivers for lightwave communication systems. J. Lightw. Technol.
LT-3, 1281−1300 (1985)
3. E. Säckinger, Broadband Circuits for Optical Fiber Communications (Wiley, New York, 2005)
4. K. Schneider, H. Zimmermann, Highly Sensitive Optical Receivers (Springer, Berlin, 2006)
5. S.D. Personick, Optical detectors and receivers. J. Lightw. Technol. 26(9), 1005–1020 (2008)
301
and the photodetector quantum efficiency is 0.65. (a) Show that the power
falling on the photodetector is 2.5 nW. (b) Show that the average number of
electron–hole pairs generated in a time t = 1 ns is N = 10.6. (c) Show that
the probability that fewer than 5 electron − hole pairs will be generated at
the detector in the 1-ns interval is P(n = 5) = 0.05 = 5%.
7.7 If a bit-corrupting noise burst lasts for 2 ms, how many bits are affected at
data rates of 10 Mb/s,100 Mb/s, and 2.5 Gb/s? [Answer: (a) 2 × 10
4 ; (b) 2 ×
10
5 ; (c) 5 × 10
6 .]
7.8 Consider a thermal-noise-limited analog optical fiber system that uses a pin
photodiode with a responsivity of 0.85 A/W at 1310 nm. Assume the system
uses a modulation index of 0.5 and operates in a 5-MHz bandwidth. Let the
mean-square thermal noise current per unit bandwidth for the receiver be 2
× 10
−23 A
2 /Hz. Show that the peak-to-peak signal power to rms noise ratio
at the receiver is 38 dB when the average incident optical power is − 20 dBm
(0.010 mW).
7.9 Consider a shot-noise limited analog optical fiber system that uses a pin photodiode with a responsivity of 0.85 A/W at 1310 nm. Assume the system uses
a modulation index of 0.6 and operates in a 40-MHz bandwidth. Neglecting
detector dark current, show that is the signal-to-noise ratio is SNR = 29.1 dB
when the incident optical power at the receiver is − 15 dBm (0.032 mW).
7.10 Show that if thermal noise dominates then the signal-to-noise ratio given by
Eq. (7.32) is a maximum when the gain is optimized at
M
2+x
opt =
4k B T F t /R eq
q
i p + i D
x
7.11 Consider a Si APD detector that has an excess noise factor related parameter
x = 0.3, a load-resistance/amplifier-noise-figure value of R eq /F t = 10
4
, a
dark current of i D = 6 nA, and a responsivity of 0.55 A/W. If at a temperature
T = 300°K the photodetector is irradiated with a light power level P in = 15
nW, (a) first use Eq. (6.6) to show that the primary photocurrent is i p = 8.25
nA and (b) then use the relationship given in Problem 7.10 to show that the
optimum gain is M opt = 29.6.
References
1. T. V. Muoi, Receiver design for high-speed optical-fiber systems. J. Lightw. Technol. LT-2,
243−267 (1984)
2. M. Brain, T. P. Lee, Optical receivers for lightwave communication systems. J. Lightw. Technol.
LT-3, 1281−1300 (1985)
3. E. Säckinger, Broadband Circuits for Optical Fiber Communications (Wiley, New York, 2005)
4. K. Schneider, H. Zimmermann, Highly Sensitive Optical Receivers (Springer, Berlin, 2006)
5. S.D. Personick, Optical detectors and receivers. J. Lightw. Technol. 26(9), 1005–1020 (2008)