he noise figures, Fi, are similar in value and the gains, Gi, are greater than unity, equation 6.5 predicts that the first term, F1, makes the dominant contribution and the influence of the other elements decreases along the chain. The conse- quence for network design is that, where possible, the first amplifier in a chain should have the lowest noise figure. It is another implication of the noncommutative nature of the Friis formula. A fourth deduction arises by applying equation 6.4 to a loss element, such as a fiber span, plus an amplifier. When the loss exp(-aL) is between the transmitter and the ampli- fier, the total noise figure is Flot= Famp exp(+aL) (6.6) Alternatively, if the amplifier precedes the loss, Ftot=Famp+[exp(+aL)-1]/Gamp (6.7) In all cases of practical interest, where Gamp is greater than unity, equation 6.6 yields a significantly higher value than equation 6.7. This is another important consequence of the noncommutative nature of the Friis cascade formula. When converted to decibels, equation 6.6 states that FdB =Fdb + AdB and one way in which this is often expressed is to say that any loss, AdB, that comes before an amplifier's gain medium adds to the global noise figure "decibel for decibel." Equations 6.6 and 6.7 have several practical implications. In terms of amplifier devices or subsystems, it is essential to minimize the losses that precede the gain element. For example, any components such as filters, couplers, and isolators that are required in an EDFA should ideally be located after the doped fiber. (Refer to the discussion of GEFs in an earlier section on channel power equalization and the discussion of amplification in Chapter 6 Optical Fiber Transmission dispersion-compensating modules in the section Optical Dispersion Compensation.) Another example of the importance of loss in front of the gain is in the SOA, where the gain medium is a waveguide of rectangular cross-section and a much higher refractive index than glass. Thus, there is a large semiconductor-to-fiber-coupling los