176 CHAPTER 4. OPTICAL RECEIVERS
propagation. In fact, the increasing curvature of BER curves indicates that the BER of
10 −^9 would be unreachable after a distance of 2600 km. This behavior is typical of
most lightwave systems. The eye diagram seen in Fig. 4.24 is qualitatively different
than that appearing in Fig. 4.13. This difference is related to the use of the RZ format.
The performance of an optical receiver in actual lightwave systems may change
with time. Since it is not possible to measure the BER directly for a system in opera-
tion, an alternative is needed to monitor system performance. As discussed in Section
4.3.3, the eye diagram is best suited for this purpose; closing of the eye is a measure
of degradation in receiver performance and is associated with a corresponding increase
in the BER. Figures 4.13 and 4.24 show examples of the eye diagrams for lightwave
systems making use of the NRZ and RZ formats, respectively. The eye is wide open
in the absence of optical fiber but becomes partially closed when the signal is trans-
mitted through a long fiber link. Closing of the eye is due to amplifier noise, fiber
dispersion, and various nonlinear effects, all of which lead to considerable distortion
of optical pulses as they propagate through the fiber. The continuous monitoring of the
eye pattern is common in actual systems as a measure of receiver performance.
The performance of optical receivers operating in the wavelength range 1.3–1.6μm
is severely limited by thermal noise, as seen clearly from the data in Fig. 4.23. The use
of APD receivers improves the situation, but to a limited extent only, because of the
excess noise factor associated with InGaAs APDs. Most receivers operate away from
the quantum limit by 20 dB or more. The effect of thermal noise can be considerably
reduced by using coherent-detection techniques in which the received signal is mixed
coherently with the output of a narrow-linewidth laser. The receiver performance can
also be improved by amplifying the optical signal before it is incident on the photode-
tector. We turn to optical amplifiers in the next chapter.
Problems
4.1 Calculate the responsivity of ap–i–nphotodiode at 1.3 and 1.55μm if the quan-
tum efficiency is 80%. Why is the photodiode more responsive at 1.55μm?
4.2 Photons at a rate of 10^10 /s are incident on an APD with responsivity of 6 A/W.
Calculate the quantum efficiency and the photocurrent at the operating wave-
length of 1.5μm for an APD gain of 10.
4.3 Show by solving Eqs. (4.2.3) and (4.2.4) that the multiplication factorMis given
by Eq. (4.2.7) for an APD in which electrons initiate the avalanche process. Treat
αeandαhas constants.
4.4 Draw a block diagram of a digital optical receiver showing its various compo-
nents. Explain the function of each component. How is the signal used by the
decision circuit related to the incident optical power?
4.5 The raised-cosine pulse shape of Eq. (4.3.6) can be generalized to generate a
family of such pulses by defininghout(t)=sin(πBt)
πBtcos(πβBt)
1 −( 2 βBt)^2