204 CHAPTER 5. LIGHTWAVE SYSTEMS
5.4.2 Dispersive Pulse Broadening
The use of single-mode fibers for lightwave systems nearly avoids the problem of inter-
modal dispersion and the associated modal noise. The group-velocity dispersion still
limits the bit rate–distance productBLby broadening optical pulses beyond their allo-
cated bit slot; Eq. (5.2.2) provides the limitingBLproduct and shows how it depends on
the source spectral widthσλ. Dispersion-induced pulse broadening can also decrease
the receiver sensitivity. In this subsection we discuss the power penalty associated with
such a decrease in receiver sensitivity.
Dispersion-induced pulse broadening affects the receiver performance in two ways.
First, a part of the pulse energy spreads beyond the allocated bit slot and leads to
intersymbol interference (ISI). In practice, the system is designed to minimize the effect
of ISI (see Section 4.3.2). Second, the pulse energy within the bit slot is reduced when
the optical pulse broadens. Such a decrease in the pulse energy reduces the SNR at
the decision circuit. Since the SNR should remain constant to maintain the system
performance, the receiver requires more average power. This is the origin of dispersion-
induced power penaltyδd. An exact calculation ofδdis difficult, as it depends on
many details, such as the extent of pulse shaping at the receiver. A rough estimate
is obtained by following the analysis of Section 2.4.2, where broadening of Gaussian
pulses is discussed. Equation (2.4.16) shows that the optical pulse remains Gaussian,
but its peak power is reduced by a pulse-broadening factor given by Eq. (2.4.17). If we
define the power penaltyδdas the increase (in dB) in the received power that would
compensate the peak-power reduction,δdis given by
δd=10 log 10 fb, (5.4.1)wherefbis the pulse broadening factor. When pulse broadening is due mainly to a wide
source spectrum at the transmitter, the broadening factorfbis given by Eq. (2.4.24),
i.e.,
fb=σ/σ 0 =[ 1 +(DLσλ/σ 0 )^2 ]^1 /^2 , (5.4.2)
whereσ 0 is the RMS width of the optical pulse at the fiber input andσλis the RMS
width of the source spectrum assumed to be Gaussian.
Equations (5.4.1) and (5.4.2) can be used to estimate the dispersion penalty for
lightwave systems that use single-mode fiber together with a multimode laser or an
LED. The ISI is minimized when the bit rateBis such that 4Bσ≤1, as little pulse
energy spreads beyond the bit slot (TB= 1 /B). By usingσ=( 4 B)−^1 , Eq. (5.4.2) can
be written as
fb^2 = 1 +( 4 BLDσλfb)^2. (5.4.3)
By solving this equation forfband substituting it in Eq. (5.4.1), the power penalty is
given by
δd=−5 log 10 [ 1 −( 4 BLDσλ)^2 ]. (5.4.4)
Figure 5.7 shows the power penalty as a function of the dimensionless parameter
combinationBLDσλ. Although the power penalty is negligible (δd= 0 .38 dB) for
BLDσλ= 0 .1, it increases to 2.2 dB whenBLDσλ= 0 .2 and becomes infinite when
BLDσλ= 0 .25. TheBLproduct, shown in Fig. 5.4, is truly limiting, since receiver