9.2 Concept of Carrier-to-Noise Ratio
367
where P t is the optical output power at the bias current level and the modulation
index m is defined by Eq. (4.56). In terms of optical power, the modulation index is
given by
m =
P peak
P t
(9.3)
where P peak and P t are defined in Fig. 9.2. Typical values of m for analog applications
range from 0.25 to 0.50.
For a sinusoidal received signal, the carrier power C at the output of the receiver
(in units of A
2 ) is
C =
1
2
m R M P
2
(9.4)
where R is the unity gain responsivity of the photodetector, M is the photodetector
gain (M = 1 for pin photodiodes), and ¯
P is the average received optical power.
9.2.2 Photodetector and Preamplifier Noises
The expressions for the photodiode and preamplifier noises are given by Eqs. (6.14)
and (6.15), respectively. These expressions then yield the following total mean-square
photodetector noise current
i
2
N
= σ
2
N = 2q
i p + i D
M
2 F(M)B e
(9.5)
Here, as defined in Chap. 6, i p = R ¯
P is the primary photocurrent, i D is the
detector dark current, M is the photodiode gain with F(M) being its associated noise
figure, and B e is the receiver bandwidth. Then, the CNR for the photodetector only
is CNR det = C/σ
2
N
Generalizing Eq. (6.15) for the preamplifier noise gives
i
2
th
= σ
2
th =
4k B T
R eq
B e F t
(9.6)
Here, R eq is the equivalent resistance of the photodetector load and the preamplifier, and F t is the noise factor of the preamplifier. Then, the CNR for the preamplifier
only is CNR preamp = C/σ
2
th .
Drill Problem 9.1 A 20-km analog optical fiber link has a fiber attenuation
of 1.0 dB/km. Assume the transmitting laser diode injects an average power of
367
where P t is the optical output power at the bias current level and the modulation
index m is defined by Eq. (4.56). In terms of optical power, the modulation index is
given by
m =
P peak
P t
(9.3)
where P peak and P t are defined in Fig. 9.2. Typical values of m for analog applications
range from 0.25 to 0.50.
For a sinusoidal received signal, the carrier power C at the output of the receiver
(in units of A
2 ) is
C =
1
2
m R M P
2
(9.4)
where R is the unity gain responsivity of the photodetector, M is the photodetector
gain (M = 1 for pin photodiodes), and ¯
P is the average received optical power.
9.2.2 Photodetector and Preamplifier Noises
The expressions for the photodiode and preamplifier noises are given by Eqs. (6.14)
and (6.15), respectively. These expressions then yield the following total mean-square
photodetector noise current
i
2
N
= σ
2
N = 2q
i p + i D
M
2 F(M)B e
(9.5)
Here, as defined in Chap. 6, i p = R ¯
P is the primary photocurrent, i D is the
detector dark current, M is the photodiode gain with F(M) being its associated noise
figure, and B e is the receiver bandwidth. Then, the CNR for the photodetector only
is CNR det = C/σ
2
N
Generalizing Eq. (6.15) for the preamplifier noise gives
i
2
th
= σ
2
th =
4k B T
R eq
B e F t
(9.6)
Here, R eq is the equivalent resistance of the photodetector load and the preamplifier, and F t is the noise factor of the preamplifier. Then, the CNR for the preamplifier
only is CNR preamp = C/σ
2
th .
Drill Problem 9.1 A 20-km analog optical fiber link has a fiber attenuation
of 1.0 dB/km. Assume the transmitting laser diode injects an average power of