Question

A fiber has a loss of 0.5 dB/km at a wavelength of 1550 nm. How much power is transmitted through such a fiber (at a wavelength of 1550 nm) if the length of the fiber is 1 km, 10 km, or 100 km if 5 mW is coupled into the fiber?

Answer 1

Fibre loss at a wavelength of 1550nm = 0.5db/km

Converting 5mW in dB we get the input power coupled (in dB) :

10×log(5×10^(-3)) = 10log(5) + 10log(10^(-3) = 6.989 - 30 = -23.01dB

1. Now loss for fibre of 1km length = 0.5dB/km × 1km = 0.5dB

So power recieved at the end of this fibre =

Input power coupled (dB) - fibre loss (dB) = -23.01 - 0.5 = -23.51dB

Or 10log(Precieved) - 30 = -23.51

=> Precieved (for 1km fibre) = 10^((-23.51 + 30)/10) = 4.4565 mW

2. Now loss for fibre of 10km length = 0.5dB/km × 10km = 5dB

So power recieved at the end of this fibre = -23.01 - 5 = -28.01dB

Or 10log(Precieved) -30 = -28.01

=> Precieved (for 10km fibre)= 10^((-28.01+30)/10) = 1.5812 mW

3. Now loss for fibre of 100km length = 0.5dB/km × 100km = 50dB

So power recieved at the end of this fibre = -23.01 - 50 = -73.01dB

Or 10log(Precieved) - 30 = -73.01

=>Precieved (for 100km fibre)= 10^((-73.01+30)/10) = 5×10^(-5) mW