6.1. BASIC CONCEPTS 229
Figure 6.2: Saturated amplifier gainGas a function of the output power (normalized to the
saturation power) for several values of the unsaturated amplifier gainG 0.
6.1.2 Gain Saturation.........................
The origin of gain saturation lies in the power dependence of theg(ω)in Eq. (6.1.1).
Sincegis reduced whenPbecomes comparable toPs, the amplification factorGde-
creases with an increase in the signal power. This phenomenon is called gain saturation.
Consider the case in which incident signal frequency is exactly tuned to the gain peak
(ω=ω 0 ). The detuning effects can be incorporated in a straightforward manner. By
substitutinggfrom Eq. (6.1.1) in Eq. (6.1.5), we obtain
dP
dz=
g 0 P
1 +P/Ps. (6.1.9)
This equation can easily be integrated over the amplifier length. By using the initial
conditionP( 0 )=Pintogether withP(L)=Pout=GPin, we obtain the following implicit
relation for the large-signal amplifier gain:
G=G 0 exp(
−
G− 1
G
Pout
Ps)
. (6.1.10)
Equation (6.1.10) shows that the amplification factorGdecreases from its unsatu-
rated valueG 0 whenPoutbecomes comparable toPs. Figure 6.2 shows the saturation
characteristics by plottingGas a function ofPout/Psfor several values ofG 0. A quantity
of practical interest is the output saturation powerPouts , defined as the output power for
which the amplifier gainGis reduced by a factor of 2 (or by 3 dB) from its unsaturated
valueG 0. By usingG=G 0 /2 in Eq. (6.1.10),
Pouts =G 0 ln 2
G 0 − 2
Ps. (6.1.11)