Page 59 - Photodetection and Measurement - Maximizing Performance in Optical Systems

Fundamental Noise Basics and Calculations

52 Chapter Three

TABLE 3.3 Contributions to Noise in the Bias Box
1mA Photocurrent
20MHz Bandwidth 1kW Load 1MW Load

Mean DC signal 1mV 1V
Dark DC offset voltage 30mV 30mV
Thermal noise of load 4nV/ Hz or 18mV rms 126nV/ Hz or 0.56mV rms
Shot noise due to 30nA leakage 0.098nV/ Hz or 0.44mV rms 98nV/ Hz or 0.44mV rms
Shot noise due to photocurrent 0.57nV/ Hz or 2.5mV rms 0.57mV/ Hz or 2.5mV rms
Total noise 18.2mV rms 2.6mV rms
Signal-to-Noise 55 385

It is clear that a higher value of load resistor gives more thermal noise.
However, the larger load also gives a much larger signal, with the result that
the S/N improves with the square root of the increasing load. With 1kW the
detection S/N is limited by thermal noise in the resistor, the largest of the noise
contributions of Table 3.3. With 1MW, however, the S/N is limited by the pho-
tocurrent shot noise. The system is “shot-noise limited.” The greater the pho-
tocurrent, the greater is the noise but the greater the S/N. The only way to
remove the signal shot noise contribution is to switch off the optical signal;
however, this is not recommended!
It is generally our goal to design the measurement system to be shot-noise
limited. This is not to say that the S/N will of necessity be adequate for our
measurement, just that we are making best use of the optical power available.
From Table 3.1 we can see that if we have high received optical power, then to
be shot-noise limited should bring high resolution and perhaps precision. We
can easily see whether a simple system is shot-noise limited by measuring the
voltage on the load resistor due to photocurrent. To see this, compare shot and
thermal noise voltage densities produced by a photocurrent I p flowing through
a simple load resistor R:

Thermal noise voltage density 4kTR V Hz (3.9)

Shot noise voltage density R 2qI p V Hz (3.10)
Equating these two expressions, we can calculate the product:

V o = I R = 2 kT q (3.11)
p
Hence if the signal voltage V o due to I p flowing in R is bigger than about
2kT/q = 52mV the measurement should be limited by the shot-noise statis-
tics. We say “should” because other interfering signals may actually form the
limit to S/N. If V o < 52mV, thermal noise in the load resistor should define the
limit to S/N. This was the justification for not bothering to calculate the load
resistor noise contributions in the TRY IT! on shot noise.

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)
Copyright © 2004 The McGraw-Hill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.