Problems
355
transmission and, at the time of this writing, is increasingly being deployed in long-
haul networks.
Problems
5.1
In an experiment designed to measure the attenuation coefﬁcient
α
of optical ﬁber,
the output power from an optical source is coupled onto a length of the ﬁber and
measured at the other end. If a 10-km-long spool of ﬁber is used, the received optical
power is
−
20 dBm. Under identical conditions but with a 20-km-long spool of ﬁber
(instead of the 10-km-long spool), the received optical power is
−
23 dBm. What is
the value of
α
(in dB/km)? If the source-ﬁber coupling loss is 3 dB, the ﬁber-detector
coupling loss is 1 dB, and there are no other losses, what is the output power of the
source (expressed in mW)?
5.2
The following problems relate to simple link designs. Assume that the bit rate on
the link is 1 Gb/s, the dispersion at 1.55
μ
m is 17 ps/nm-km, and the attenuation is
0.25 dB/km, and at 1.3
μ
m, the dispersion is 0 and the attenuation is 0.5 dB/km. (Ne-
glect all losses except the attenuation loss in the ﬁber.) Assume that NRZ modulation
is used.
(a) You have a transmitter that operates at a wavelength of 1.55
μ
m, has a spec-
tral width of 1 nm, and an output power of 0.5 mW. The receiver requires
−
30 dBm of input power in order to achieve the desired bit error rate. What
is the length of the longest link that you can build?
(b) You have another transmitter that operates at a wavelength of 1.3
μ
m, has
a spectral width of 2 nm, and an output power of 1 mW. Assume the same
receiver as before. What is the length of the longest link that you can build?
(c) You have the same 1.3
μ
m transmitter as before, and you must achieve an
SNR of 30 dB using an APD receiver with a responsivity of 8 A/W, a gain of
10, an excess noise factor of 5 dB, negligible dark current, a load resistance of
50
±
, and an ampliﬁer noise ﬁgure of 3 dB. Assume that a receiver bandwidth
of
B/
2
Hz is sufﬁcient to support a bit rate of
B
b/s. What is the length of
the longest link you can build?
(d) Using the same 1.3
μ
m transmitter as before, you must achieve an SNR of
20 dB using a
pin
receiver with a responsivity of 0.8 A/W, a load resistance
of 300
±
, and an ampliﬁer noise ﬁgure of 5 dB. Assume that a receiver
bandwidth of
2
Hz is sufﬁcient to support a bit rate of
B
b/s. What is the
length of the longest link you can build?
5.3
Compute the dispersion-limited transmission distance for links with standard single-
mode ﬁber at 1550 nm as a function of the bit rate (100 Mb/s, 1 Gb/s, and 10 Gb/s)