4.4. RECEIVER NOISE 161
Figure 4.17: Optimum APD gainMoptas a function of the incident optical powerPinfor several
values ofkA. Parameter values corresponding to a typical 1.55-μm InGaAs APD receiver were
used.
and is reduced by the excess noise factorFAcompared with that ofp–i–nreceivers [see
Eq. (4.4.15)].
Optimum APD Gain
Equation (4.4.19) shows that for a givenPin, the SNR of APD receivers is maximum
for an optimum valueMoptof the APD gainM. It is easy to show that the SNR is
maximum whenMoptsatisfies the following cubic polynomial:
kAMopt^3 +( 1 −kA)Mopt=4 kBTFn
qRL(RPin+Id). (4.4.22)
The optimum valueMoptdepends on a large number of the receiver parameters, such as
the dark current, the responsivityR, and the ionization-coefficient ratiokA. However,
it is independent of receiver bandwidth. The most notable feature of Eq. (4.4.22) is
thatMoptdecreases with an increase inPin. Figure 4.17 shows the variation ofMopt
withPinfor several values ofkAby using typical parameter valuesRL=1kΩ,Fn=2,
R=1 A/W, andId=2 nA corresponding to a 1.55-μm InGaAs receiver. The optimum
APD gain is quite sensitive to the ionization-coefficient ratiokA.ForkA=0,Mopt
decreases inversely withPin, as can readily be inferred from Eq. (4.4.22) by noting that
the contribution ofIdis negligible in practice. By contrast,Moptvaries asPin−^1 /^3 for
kA=1, and this form of dependence appears to hold even forkAas small as 0.01 as
long asMopt>10. In fact, by neglecting the second term in Eq. (4.4.22),Moptis well