514 Chapter 8. Signal Processing
The power density can be used to define the spectral shot noise current densityi^2 s
and spectral shot noise voltage densityvs^2 as follows.
i^2 s ≡dI^2 noise
df=2eI (8.9.10)vs^2 ≡dVnoise^2
df=2eRV (8.9.11)As with the Johnson noise, here also the above expressions must be multiplied
by the system bandwidth to determine the absolute noise current or voltage, that is
Is =√
2 eI f (8.9.12)
and Vs =√
2 eRV f. (8.9.13)These expressions reveal why shot noise is called a white noise: the noise power is
dependent on the bandwidth and not on the frequency itself. Or in other words the
noise power at a bandwidth of 2 to 3Hzwould be the same as at a bandwidth of
200002 to 200003Hz.
Example:
Compute the total noise current in a semiconductor based detection system
having a bandwidth from 0 to 500kHzif a current of 0.5μAflows through
it.Solution:
The detector can be assumed to be a current noise source. the magnitude of
the current can be computed from the equation 8.9.12 as follows.Is =√
2 eI f
=[
(2)
(
1. 602 × 10 −^19
)(
0. 5 × 10 −^6
)(
500 × 103
)] 1 / 2
=0. 28 nA (8.9.14)A.3 1/fNoise
One overfnoise corresponds to a number ofnon-randomnoise sources in a detection
system. Its name derives from the fact that its power spectrum has an approximate
1 /fdependence, that is
pf≡dPnoise
df∝
1
fα, (8.9.15)
where the exponentαis approximately equal to unity for most systems. Since power
is proportional to the square of the voltage, therefore the noise voltage density can
be written as
v^2 f=A
fα