the loss parame- ter 8 is very small. The impurity parameter has the dimension of a length (we can measure it in meters) and it can be considered as an impurity characteristic length. Technology for Telecommunications: Optical Fibers, Amplifiers, and Passive Devices In the approximation of small 8 (i.e., 8go<<<1), Equation 4.81 can be solved with the pertur- bation method with respect to 8, and the first perturbation term is sufficient to model the effect of the scattering imperfections. The equation of the first-order perturbation is simple giving p 1 = Substituting the expression of the output power in the signal to noise ratio after ampli- fication and detection and using again the definition (Equation 4.74) of NF, the expression of NF formally does not change, but for a multiplication factor that, in the hypothesis of first-order approximation in 8, is written as (1-0.58g)L). As anticipated, the noise factor itself depends on the amplifier gain when amplifier imperfections are considered. What we have obtained means that the factors Vi in Equation 4.80 are no more constant, but depends on the gain of the corresponding stage. In particular, using the expression of the global unsaturated gain Go, it comes out that (4.82) where all has been expressed as a function of the saturated gain exploiting Equation 4.67. Let us now try the amplifier optimization by minimizing the expression of the noise in a realistic parameters configuration described in Table 4.8. The behavior of the noise curves (the normalized noise is represented) versus the gain of the second stage G2 is reported in Figure 4.21; from the figure, it is evident that a minimum of the noise power for a value of G2 is different from zero, thus confirming the experience that the optimum amplifier does not have only one stage. The optimum gain G2 in the case of an overall amplifier gain of 26 dB is shown in Figure 4.22 versus 8 for different values of the interstage loss. From the figure, the presence of a sort of threshold value of 8 is also seen that dep