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1 Perspectives on Lightwave Communications
1.8 Convert the following decibel power gains to absolute power gains: −30 dB,
0 dB, 13 dB, 30 dB, 10n dB.
1.9 Convert the following absolute power levels to dBm values: 1 pW, 1 nW, 1
mW, 10 mW, 50 mW.
1.10 Convert the following dBm values to power levels in units of mW: −13, −6,
6, 17 dBm.
1.11 A signal travels along a fiber from point A to point B. (a) If the signal power
is 1.0 mW at point A and 0.125 mW at point B, what is the fiber attenuation in
dB? (b) What is the signal power at point B if the
attenuation is 15 dB?
1.12 A signal passes through three cascaded amplifiers, each of which has a 5 dB
gain. What is the total gain in dB? By what numerical factor is the signal
amplified?
1.13 A 50 km long optical fiber has a total attenuation of 24 dB. If 500 μW of
optical power get launched into the fiber, what is the output optical power
level in dBm and in μW?
1.14 Based on the Shannon theorem, the maximum data rate R of a channel with a
bandwidth B is R = B log2(1 + S/N), where S/N is the signal-to-noise ratio.
Suppose a transmission line has a bandwidth of 2 MHz. If the signal-to-noise
ratio at the receiving end is 20 dB, what is the maximum data rate that this line
can support?
1.15 (a) At the lowest TDM level of the digital service scheme, 24 channels of
64 kb/s each are multiplexed into a 1.544 Mb/s DS1 channel. How much is the
overhead that is added? (b) The next higher multiplexed level, the DS2 rate,
is 6.312 Mb/s. How many DS1 channels can be accommodated in the DS2
rate, and what is the overhead? (c) If the DS3 rate that is sent over a T 3 line
is 44.376 Mb/s, how many DS2 channels can be accommodated on a T 3 line,
and what is the overhead? (d) Using the above results, find how many DS0
channels can be sent over a T 3 line. What is the total added overhead?
Answers to Selected Problems
1.1 1.46, 0.95, 0.83, and 0.80 eV, respectively
1.2 40 kHz, 4.0 MHz, and 8 GHz, respectively
1.3 (a) 2A; (b) 0
1.4 90°
1.5 428, 657, 753, and 781, respectively
1.6 15.6 μs, 200 ns, and 0.1 ns, respectively
1.7 −30, −5.2, 0, 6, 10, 20, 27, and 3n dB, respectively
1.8 10
–3 , 1, 20, 1000, and 10
n , respectively
1.9 −90 dBm, −60 dBm, −30 dBm, 10 dBm, and 17 dBm, respectively
1.10 50 μW, 250 μW, 4 mW, and 50 mW, respectively
1.11 (a) 9 dB; (b) 32 μW
1.12 15 dB. The signal is amplified by a factor 10
1.5
= 31.6.
1.13 −27 dBm, which is equivalent to 2.0 μW
1 Perspectives on Lightwave Communications
1.8 Convert the following decibel power gains to absolute power gains: −30 dB,
0 dB, 13 dB, 30 dB, 10n dB.
1.9 Convert the following absolute power levels to dBm values: 1 pW, 1 nW, 1
mW, 10 mW, 50 mW.
1.10 Convert the following dBm values to power levels in units of mW: −13, −6,
6, 17 dBm.
1.11 A signal travels along a fiber from point A to point B. (a) If the signal power
is 1.0 mW at point A and 0.125 mW at point B, what is the fiber attenuation in
dB? (b) What is the signal power at point B if the
attenuation is 15 dB?
1.12 A signal passes through three cascaded amplifiers, each of which has a 5 dB
gain. What is the total gain in dB? By what numerical factor is the signal
amplified?
1.13 A 50 km long optical fiber has a total attenuation of 24 dB. If 500 μW of
optical power get launched into the fiber, what is the output optical power
level in dBm and in μW?
1.14 Based on the Shannon theorem, the maximum data rate R of a channel with a
bandwidth B is R = B log2(1 + S/N), where S/N is the signal-to-noise ratio.
Suppose a transmission line has a bandwidth of 2 MHz. If the signal-to-noise
ratio at the receiving end is 20 dB, what is the maximum data rate that this line
can support?
1.15 (a) At the lowest TDM level of the digital service scheme, 24 channels of
64 kb/s each are multiplexed into a 1.544 Mb/s DS1 channel. How much is the
overhead that is added? (b) The next higher multiplexed level, the DS2 rate,
is 6.312 Mb/s. How many DS1 channels can be accommodated in the DS2
rate, and what is the overhead? (c) If the DS3 rate that is sent over a T 3 line
is 44.376 Mb/s, how many DS2 channels can be accommodated on a T 3 line,
and what is the overhead? (d) Using the above results, find how many DS0
channels can be sent over a T 3 line. What is the total added overhead?
Answers to Selected Problems
1.1 1.46, 0.95, 0.83, and 0.80 eV, respectively
1.2 40 kHz, 4.0 MHz, and 8 GHz, respectively
1.3 (a) 2A; (b) 0
1.4 90°
1.5 428, 657, 753, and 781, respectively
1.6 15.6 μs, 200 ns, and 0.1 ns, respectively
1.7 −30, −5.2, 0, 6, 10, 20, 27, and 3n dB, respectively
1.8 10
–3 , 1, 20, 1000, and 10
n , respectively
1.9 −90 dBm, −60 dBm, −30 dBm, 10 dBm, and 17 dBm, respectively
1.10 50 μW, 250 μW, 4 mW, and 50 mW, respectively
1.11 (a) 9 dB; (b) 32 μW
1.12 15 dB. The signal is amplified by a factor 10
1.5
= 31.6.
1.13 −27 dBm, which is equivalent to 2.0 μW