Page 279 - Fiber Optic Communications Fund

260 Fiber Optic Communications

6.5.5 Amplifier Noise Figure
The noise figure is commonly used to characterize the noise added by an amplifier. It is defined as the ratio
of the electrical SNR at the amplifier input to that at the amplifier output [3, 4],
(SNR) in
F = . (6.90)
n
(SNR) out
See Fig. 6.7. Since (SNR) out can never exceed (SNR) , the noise figure is greater than unity. Note that the
in
SNRs appearing in the above equation are measured in the electrical domain using photodetectors at the input
and output of the amplifiers, and measuring the electrical signal and noise powers. To minimize the parameters
of the measurement unit entering into the definition of F , ideal photodetectors with 100% quantum efficiency
n
are used, and thermal noise is ignored. Let us first consider (SNR) . When the incident power is P ,the
in
in
photocurrent is
I = RP , (6.91)
in
in
where responsivity is given by Eq. (5.17),
q
R = = , (6.92)
hf 0 hf 0
assuming = 1. Here, f is the carrier frequency. The electrical signal power delivered to a load resistor R is
0 L
2
S = I R . (6.93)
in in L
We assume that there is no noise in the optical signal before the amplifier. The noise power at the output of
PD is due to the shot noise and is given by Eq. (5.79),
1
N = 2qI R B . (6.94)
shot in L e
Here, we have ignored the dark current. Therefore, we have
S in RP in
SNR = = . (6.95)
in
N 2qB
shot e
Next, consider SNR . The output optical power of the amplifier is
out
P out = GP , (6.96)
in

P in P out SNR out
G
PD 2

SNR in
PD 1

Figure 6.7 Measurement of the amplifier noise figure.