Page 100 - Fiber Optic Communications Fund

Optical Fiber Transmission 81

the power at the output of the DCF. Assume a splice loss of 0.5 dB between the transmission fiber and the
DCF. (c) Find the gain of the amplifier such that the signal power at the output of the amplifier is the same as
that at the input.

Solution:
(a) From Eq. (2.234), we have
TF TF
L =− DCF DCF , (2.235)
L
2 2
TF 2 TF
=−21 ps ∕km, L = 80 km, (2.236)
2
2
DCF = 130 ps ∕km, (2.237)
2
TF TF
− L
L DCF = 2 = 12.9 km. (2.238)
DCF
2
(b) The launch power in dBm units is given by Eq. (2.124) as
2mW
P (dBm)= 10 log = 3 dBm. (2.239)
in 10
1mW
Loss budget:
loss in transmission fiber = 0.2 × 80 dB = 16 dB,
loss in DCF = 0.5 × 12.9dB = 6.45 dB,
splice loss = 0.5dB,
total loss = 16 + 6.45 + 0.5dB = 22.95 dB.

The power at the output of the DCF is
P = 3dBm − 22.95 dBm =−19.95 dBm. (2.240)
out,DCF
(c) To keep the signal power at the output of the amplifier the same as the input, the amplifier gain should be
equal to the total loss in the system, i.e.,

amplifier gain = 22.95 dBm. (2.241)

2.9 Additional Examples

Example 2.12
The numerical aperture of a multi-mode fiber is 0.2. Find the delay between the shortest and longest path. Fiber
length = 2 km and core index = 1.45. Assume that the difference between the core index and the cladding
index is small.

Solution:
The NA is given by Eq. (2.9) as
√
NA = n 1 2Δ, (2.242)