8.2 Concepts of Link Power Penalties
325
(c) When external modulation is used, the spectral width of the signal is proportional to the bit rate. For example, using a factor of f = B, a 10-Gb/s externally
modulated signal would have a spectral width of f = 10 GHz. To view this
particular spectral width in terms of wavelength, differentiate the basic equation c = f λ to get λ = (c/f
2 )f = (λ
2 /c) f . Substituting σ λ = λ =
(λ
2 /c)B into Eq. (8.19) yields (for a 2-dB power penalty)
D C D B
2 L C D λ
2
/c ≤ 0.491. Using the parameter values D C D = 18 ps/(nm km)
at λ = 1550 nm yields B
2 L C D ≤ 3406(Gb/s)
2 km
Thus, at B = 2.5 Gb/s the transmission distance limit is 545 km, whereas at
B = 10 Gb/s the transmission distance limit is 34 km when using a G.652 fiber
at 1550 nm. This condition for the chromatic dispersion-limited repeaterless transmission distances L CD is plotted as a function of the bit rate in the top curve in
Fig. 8.9.
Drill Problem 8.4 Repeat the exercise given in Example 8.6 for the case when
the maximum allowed pulse dispersion with a 1-dB penalty requires that the
product D C D L C D σ λ is less than or equal to 0.306 of the bit period 1/B.
[Answers: (a) B L CD ≤ 17 Gb/s km; (b) 85 Gb/s km; (c) B
2 L CD ≤ 2123
(Gb/s)
2 km.]
8.2.2 Power Penalties Arising from PMD
As Sect. 3.2 describes, polarization-mode dispersion (PMD) results from the fact
that light-signal energy at a given wavelength in a single-mode fiber actually occupies two orthogonal polarization states or modes. Figure 3.12 shows this condition.
PMD arises because the two fundamental orthogonal polarization modes travel at
slightly different speeds owing to fiber birefringence. That is, each polarization mode
encounters a slightly different refractive index in the fiber. The resulting difference
in propagation times between the two orthogonal polarization modes will result in
pulse spreading. This PMD effect cannot be mitigated easily and can be a very serious
impediment for links operating at 10 Gb/s and higher.
PMD is not a fixed quantity but fluctuates with time due to factors such as temperature variations and stress changes on the fiber [20–22]. Because these external stresses
vary slowly with time, the resulting PMD also fluctuates slowly. PMD varies as the
square root of distance and thus is specified as a maximum value in units of ps/
√
km.
A typical PMD value for a fiber is D PMD = 0.05 ps/
√
km, but the cabling process
can increase this value. The PMD value does not fluctuate widely for cables that are
325
(c) When external modulation is used, the spectral width of the signal is proportional to the bit rate. For example, using a factor of f = B, a 10-Gb/s externally
modulated signal would have a spectral width of f = 10 GHz. To view this
particular spectral width in terms of wavelength, differentiate the basic equation c = f λ to get λ = (c/f
2 )f = (λ
2 /c) f . Substituting σ λ = λ =
(λ
2 /c)B into Eq. (8.19) yields (for a 2-dB power penalty)
D C D B
2 L C D λ
2
/c ≤ 0.491. Using the parameter values D C D = 18 ps/(nm km)
at λ = 1550 nm yields B
2 L C D ≤ 3406(Gb/s)
2 km
Thus, at B = 2.5 Gb/s the transmission distance limit is 545 km, whereas at
B = 10 Gb/s the transmission distance limit is 34 km when using a G.652 fiber
at 1550 nm. This condition for the chromatic dispersion-limited repeaterless transmission distances L CD is plotted as a function of the bit rate in the top curve in
Fig. 8.9.
Drill Problem 8.4 Repeat the exercise given in Example 8.6 for the case when
the maximum allowed pulse dispersion with a 1-dB penalty requires that the
product D C D L C D σ λ is less than or equal to 0.306 of the bit period 1/B.
[Answers: (a) B L CD ≤ 17 Gb/s km; (b) 85 Gb/s km; (c) B
2 L CD ≤ 2123
(Gb/s)
2 km.]
8.2.2 Power Penalties Arising from PMD
As Sect. 3.2 describes, polarization-mode dispersion (PMD) results from the fact
that light-signal energy at a given wavelength in a single-mode fiber actually occupies two orthogonal polarization states or modes. Figure 3.12 shows this condition.
PMD arises because the two fundamental orthogonal polarization modes travel at
slightly different speeds owing to fiber birefringence. That is, each polarization mode
encounters a slightly different refractive index in the fiber. The resulting difference
in propagation times between the two orthogonal polarization modes will result in
pulse spreading. This PMD effect cannot be mitigated easily and can be a very serious
impediment for links operating at 10 Gb/s and higher.
PMD is not a fixed quantity but fluctuates with time due to factors such as temperature variations and stress changes on the fiber [20–22]. Because these external stresses
vary slowly with time, the resulting PMD also fluctuates slowly. PMD varies as the
square root of distance and thus is specified as a maximum value in units of ps/
√
km.
A typical PMD value for a fiber is D PMD = 0.05 ps/
√
km, but the cabling process
can increase this value. The PMD value does not fluctuate widely for cables that are