Page 92 - Fiber Optic Communications Fund

Optical Fiber Transmission 73

Using Eq. (2.176), we find

P (dBm)= P (dBm)− loss(dB)
in
out
= 3dBm − 16 dB
=−13 dBm. (2.182)

Note that using dBm units, multiplication (Eq. (2.180)) is replaced by subtraction (Eq. (2.182)). Using
Eq. (2.125), we find
P (mW)= 10 −13∕10 mW = 0.05 mW. (2.183)
out

Example 2.9

Consider a fiber-optic system consisting of a fiber with loss F followed by an amplifier of gain G (see
Fig. 2.35). The launch power is P . Calculate the output power of the amplifier in dBm units.
in
Solution:

Fiber-out
Fiber loss (dB) = F(dB)=−10 log . (2.184)
10
P
in
Fiber-out
Fiber loss in linear units,F = . (2.185)
P
in
Fiber-out = FP . (2.186)
in
Similarly, the amplifier output power is
P = GFP . (2.187)
out in
From Eq. (2.124), we find
P(mW)
P(dBm)= 10 log 10 . (2.188)
1mW
Suppose that P and P in Eq. (2.187) are given in units of mW. Divide Eq. (2.187) by 1 mW and take
out in
logarithms on both sides to obtain
[ ]
P out GFP in
10 log = 10 log , (2.189)
10 10
1mW 1mW
Fiber Amplifier
Fiber-out = Amp-in P
P in out
F G

Figure 2.35 A fiber-optic link consisting of a fiber and an amplifier.