Page 126 - Optical Communications Essentials

Photodiodes and Receivers

116 Chapter Seven

Thermal noise arises from the random motion of electrons that is always
present at any finite temperature.

Noise Calculations
Thermal Noise Consider a resistor that has a value R at a temperature T. If I thermal
is the thermal noise current associated with the resistor, then in a bandwidth or
frequency range B e its variance σ 2 thermal is

2 2 4 kT
B
I B (7.6)
thermal thermal e
R
Here k B 1.38054 10 23 J/K is Boltzmann’s constant, and the symbol x desig-
2
/
nates the mean value of the quantity x. Typical values of the quantity ( I thermal B e ) 1 2 /
are 1pA/ H z . Note that in practice the receiver bandwidth B e varies from 1/(2T bit ) to
1/T bit , where T bit is the bit period.
Shot Noise For a photodiode the variance of the shot noise current I shot in a band-
width B e is
2
2
2
I shot shot 2 qI B M F M() (7.7)
pe
where I p is the average photocurrent as defined in Eq. (7.3), M is the gain of an APD,
and F(M) is the APD noise figure. For a pin photodiode, M and F(M) are equal to 1.
Dark Current If I D is the primary (not multiplied) dark current, then its variance is
given by
2
I D 2 = 2 D = 2 qI M F M B e (7.8)
()
D
Again, for a pin photodiode, M and F(M) are equal to 1.
Signal-to-Noise Ratio Since the various noise currents are not correlated, the total
2
mean-square photodetector noise current I N can be written as
2 2 2 2
+
+
I N = I shot I D I thermal (7.9)
2
2
2
From Eq. (7.3) we know (I P ) (RP 0 ) M is the mean-square signal current. Then by
using Eq. (7.5) the SNR is equal to
2
2
IM 2 IM 2
p
p
SNR (7.10)
( )B +
2
I 2 2 ( qI + I )M F M 4 k TB R
/
N p D e B e
7.5. Summary
The function of an optical receiver is to interpret the information contained in
the optical signal. A receiver consists of a photodetector and various amounts of
electronics. The electronics can range from some simple amplification functions
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