210 CHAPTER 5. LIGHTWAVE SYSTEMS
Figure 5.10: Chirp-induced power penalty as a function ofBLD∆λcfor several values of the
parameterBtc, where∆λcis the wavelength shift occurring because of frequency chirp andtcis
the duration of such a wavelength shift.
a power loss decreases the SNR at the receiver and results in power penalty. In a simple
model the chirp-induced power penalty is given by [100]
δc=−10 log 10 ( 1 − 4 BLD∆λc), (5.4.11)where∆λcis the spectral shift associated with frequency chirping. This equation ap-
plies as long asLD∆λc<tc, wheretcis the chirp duration. Typically,tcis 100–200 ps,
depending on the relaxation-oscillation frequency, since chirping lasts for about one-
half of the relaxation-oscillation period. By the timeLD∆λcequalstc, the power
penalty stops increasing because all the chirped power has left the bit interval. For
LD∆λc>tc, the productLD∆λcin Eq. (5.4.11) should be replaced bytc.
The model above is overly simplistic, as it does not take into account pulse shap-
ing at the receiver. A more accurate calculation based on raised-cosine filtering (see
Section 4.3.2) leads to the following expression [107]:
δc=−20 log 10 { 1 −( 4 π^2 / 3 − 8 )B^2 LD∆λctc[ 1 +( 2 B/ 3 )(LD∆λc−tc)]}. (5.4.12)The receiver is assumed to contain ap–i–nphotodiode. The penalty is larger for an
APD, depending on the excess-noise factor of the APD. Figure 5.10 shows the power
penaltyδcas a function of the parameter combinationBLD∆λcfor several values of the
parameterBtc, which is a measure of the fraction of the bit period over which chirping
occurs. As expected,δcincreases with both the chirp∆λcand the chirp durationtc.The
power penalty can be kept below 1 dB if the system is designed such thatBLD∆λc<
0 .1 andBtc< 0 .2. A shortcoming of this model is that∆λcandtcappear as free