Characterize lasers for DWDM transmission--derivation of Equation 6

Measurements tell engineers how well a communication system will work.

Bita Nosratieh, Agilent Technologies, Santa Rosa, CA -- Test & Measurement World, 1/1/2001

This is a companion piece to Characterize lasers for DWDM transmission which appeared in our January 2001 issue.

Shot noise and average power depend on the average current from the photodiode, and you can calculate their values. Shot noise power (N_q ) in a 1-Hz band is:

N_q = (2qI_dc) R_L (A)

where:

q is the electron charge (1.60 x 10^-19 coulomb),

I_dc is the average current out of photodiode due to average optical power input, and

R_L is the load resistance of the input amplifier on the microwave spectrum analyzer.

You can calculate the average current (I_dc) from the measured average power at the amplifier input using the following equation:

P_AVG = I_dc ²R_L

Dividing both sides of Equation A by P_AVG yields the shot noise ratio:

N_q / P_AVG = (2qI_dc) R_L / I_dc²R_L = 2q / I_dc

You can substitute the equality above for the N_q / P_AVG term in the equation given below (Equation 5), for the RIN of the laser (1-Hz bandwidth):

RIN_Laser = N_L / P_AVG = RIN_System - N_q / P _AVG - N_th / P_AVG

to convert it to:

RIN_Laser = RIN _System - N_th / P_AVG - 2q / I_dc (C)

Then, by using the relationships:

P_AVG = I_dc ² R_L

and

I_dc = r P_AVG(opt)

You can write the equation for P _AVG as:

P_AVG = (r P_AVG(opt) )²R_L

Substituting these variables into Equation C yields the relationship below that appears in the main article as Equation 6:

RIN_Laser = RIN _System - N_th / (r P_AVG(opt))² R_L - 2q / r P_AVG(opt)