570
13 Fiber Optic Communication Networks
(c) Show that the shortest cable length is obtained when the star is at the
center of the grid.
13.5 In this problem do not resort to wavelength conversion but assume that wavelengths can be reused in different parts of a network. Show that the minimum
number of wavelengths required to connect N nodes in a WDM network are
as follows:
(a) N − 1 for a star network
(b) N(N − l)/2 for a ring network
13.6 (a) Show that the number of 64-kb/s voice channels that can be carried by
an STM-1, an STM-16, and an STM-64 system are 2322 channels, 37,152
channels, and 148,600 channels, respectively.
(b) Show that the number of 20-Mb/s digitized video channels that can
be transported over these systems are STM-1: 7 channels, STM-16: 118
channels, and STM-64: 475 channels (see Drill Problem 13.3).
13.7 Compare the system margins for 40 and 80-km long-haul OC-48 (STM16) links at 1550 nm for the minimum and maximum source output ranges.
Assume there is a 1.5-dB coupling loss at each end of the link. Use Tables 13.3
and 13.4.
[Answers: Minimum power at 40 km: Margin = +2 dB; maximum power
at 40 km: Margin = +4 dB. Minimum power at 80 km: Margin = −2 dB;
maximum power at 80 km: Margin = +3 dB]
13.8 Verify that the maximum optical powers per wavelength channel given in
Table 13.5 yield a total power level of +17 dBm in an optical fiber.
13.9 Consider the four-node network shown in Fig. 13.49. Each node uses a
different combination of three wavelengths to communicate with the other
nodes, so that there are six different wavelengths in the network. Given that
node 1 uses λ 2 , λ 4 , and λ 6 for information exchange with the other nodes (i.e.,
these wavelengths are added and dropped at node 1, and the remaining wavelengths from other nodes pass through), establish wavelength assignments
for the other nodes.
[Answer: Add/drop wavelengths at node 2: 3, 5, 6; node 3: 1, 2, 3; node 4:
1, 4, 5]
13.10 Suppose an engineer wants to attach a 50-m long standard 50-μm fiber that
has a bandwidth of 500 MHz-km to a 100-m higher-grade 50-μm fiber that
has a bandwidth of 2000 MHz-km. A 10-m length of the lower grade fiber
is used at each end in order to connect to transmission equipment. Show that
this link will not work at 10 Gb/s.
[Answer: From Eq. (13.5), L max = 380 m > OM3 allowed 300-m limit. Thus
the link will not work at 10 Gb/s.]
13.11 Consider an OBS system in which the processing and configuration times
are both 1 ms. Similar to Fig. 13.34, suppose the burst goes between edge
routers A and B through four intermediate OXCs and that all nodes are 10 km
apart. Show that the offset time is 5 ms.
13 Fiber Optic Communication Networks
(c) Show that the shortest cable length is obtained when the star is at the
center of the grid.
13.5 In this problem do not resort to wavelength conversion but assume that wavelengths can be reused in different parts of a network. Show that the minimum
number of wavelengths required to connect N nodes in a WDM network are
as follows:
(a) N − 1 for a star network
(b) N(N − l)/2 for a ring network
13.6 (a) Show that the number of 64-kb/s voice channels that can be carried by
an STM-1, an STM-16, and an STM-64 system are 2322 channels, 37,152
channels, and 148,600 channels, respectively.
(b) Show that the number of 20-Mb/s digitized video channels that can
be transported over these systems are STM-1: 7 channels, STM-16: 118
channels, and STM-64: 475 channels (see Drill Problem 13.3).
13.7 Compare the system margins for 40 and 80-km long-haul OC-48 (STM16) links at 1550 nm for the minimum and maximum source output ranges.
Assume there is a 1.5-dB coupling loss at each end of the link. Use Tables 13.3
and 13.4.
[Answers: Minimum power at 40 km: Margin = +2 dB; maximum power
at 40 km: Margin = +4 dB. Minimum power at 80 km: Margin = −2 dB;
maximum power at 80 km: Margin = +3 dB]
13.8 Verify that the maximum optical powers per wavelength channel given in
Table 13.5 yield a total power level of +17 dBm in an optical fiber.
13.9 Consider the four-node network shown in Fig. 13.49. Each node uses a
different combination of three wavelengths to communicate with the other
nodes, so that there are six different wavelengths in the network. Given that
node 1 uses λ 2 , λ 4 , and λ 6 for information exchange with the other nodes (i.e.,
these wavelengths are added and dropped at node 1, and the remaining wavelengths from other nodes pass through), establish wavelength assignments
for the other nodes.
[Answer: Add/drop wavelengths at node 2: 3, 5, 6; node 3: 1, 2, 3; node 4:
1, 4, 5]
13.10 Suppose an engineer wants to attach a 50-m long standard 50-μm fiber that
has a bandwidth of 500 MHz-km to a 100-m higher-grade 50-μm fiber that
has a bandwidth of 2000 MHz-km. A 10-m length of the lower grade fiber
is used at each end in order to connect to transmission equipment. Show that
this link will not work at 10 Gb/s.
[Answer: From Eq. (13.5), L max = 380 m > OM3 allowed 300-m limit. Thus
the link will not work at 10 Gb/s.]
13.11 Consider an OBS system in which the processing and configuration times
are both 1 ms. Similar to Fig. 13.34, suppose the burst goes between edge
routers A and B through four intermediate OXCs and that all nodes are 10 km
apart. Show that the offset time is 5 ms.