160 CHAPTER 4. OPTICAL RECEIVERS
Figure 4.16: Excess noise factorFAas a function of the average APD gainMfor several values
of the ionization-coefficient ratiokA.
The dimensionless parameterkA=αh/αeifαh<αebut is defined askA=αe/αhwhen
αh>αe. In other words,kAis in the range 0<kA<1. Figure 4.16 shows the gain
dependence ofFAfor several values ofkA. In general,FAincreases withM. However,
althoughFAis at most 2 forkA=0, it keeps on increasing linearly (FA=M) when
kA=1. The ratiokAshould be as small as possible for achieving the best performance
from an APD [87].
If the avalanche–gain process were noise free (FA=1), bothIpandσswould in-
crease by the same factorM, and the SNR would be unaffected as far as the shot-noise
contribution is concerned. In practice, the SNR of APD receivers is worse than that
ofp–i–nreceivers when shot noise dominates because of the excess noise generated
inside the APD. It is the dominance of thermal noise in practical receivers that makes
APDs attractive. In fact, the SNR of APD receivers can be written as
SNR=
Ip^2
σs^2 +σT^2=
(MRPin)^2
2 qM^2 FA(RPin+Id)∆f+ 4 (kBT/RL)Fn∆f, (4.4.19)
where Eqs. (4.4.9), (4.4.16), and (4.4.17) were used. In the thermal-noise limit (σs
σT), the SNR becomes
SNR=(RLR^2 / 4 kBTFn∆f)M^2 Pin^2 (4.4.20)and is improved, as expected, by a factor ofM^2 compared with that ofp–i–nreceivers
[see Eq. (4.4.13)]. By contrast, in the shot-noise limit (σsσT), the SNR is given by
SNR=RPin
2 qFA∆f=
ηPin
2 hνFA∆f