8.9. Electronics Noise 513
Note that these expressions do not represent total noise, only the noise density
or noise per unit bandwidth. The noise voltage and current can be obtained by
multiplying the above relations by the system bandwidth f,thatis
Ij^2 =4 kBT
Rf (8.9.6)and Vj^2 =4kBTR f. (8.9.7)A point worth mentioning here is that the Johnson noise associated with a resistor
in series can be modeled by a voltage noise source. A parallel resistor, on the other
hand, can be modeled by a current noise source.
The expressions above reveal an important fact about the Johnson noise. That
is, the noise power is proportional to the bandwidth of the system. This implies
that the noise power for a bandwidth of 0 to 2Hzwould be the same as for a
bandwidth of 40000 to 40002Hz. In other words, the noise power is independent
of the frequency. This kind of noise is generally referred to aswhite noise.
Example:
Determine the thermal noise voltage in a 200 Ω resistor at 27^0 Cfor a system
having a bandwidth of 0 to 500MHz.Solution:
The noise voltage can be calculated from equation 8.9.7.Vj =4kBTR f
=[
(4)
(
1. 38 × 10 −^23
)
(300) (200)
(
500 × 106
)] 1 / 2
=40. 7 μV. (8.9.8)A.2 ShotNoise
The current in a conductor is always carried by discrete charges. In most cases these
charges are injected into the system in such a way that their behavior isstochastically
independent, meaning that creation or arrival of a new charge is independent of its
predecessors. Due to the inherent statistical nature of the underlying phenomena,
the numbers of these charges at any time fluctuates from a mean value. This fluc-
tuation causes the electrical current to randomly fluctuate around its mean value.
Shot noise corresponds to these random fluctuations. It has Gaussian characteristics
both in time and frequency domains and belongs to the category or white noise.
The power density of shot noise at a particular frequency is given by
p^2 s≡dPnoise
df=2eV. (8.9.9)