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18
Because of the discrete nature of the charge carriers, electric current has noise. Noise is generated in the current since there
is always some non-uniformity in the electron flow. This noise is called shot noise. It appears as voltage noise when
current is passed through a resistor, or as noise in a current measurement.
If the effect between carriers is ignored, the shot noise or current noise is given by:
2
/
1
)
2
(
B
qI
I
dc
where q is the electron charge of 1.6
×
10
-19
Coulomb, I
dc
is the DC current and B is the bandwidth. If I
dc
is 1 A and B is 10
kHz, then, I is 57 nA which is about 0.000006% of I
dc
. The smaller the current, the larger the relative noise ratio. For
example, if I
dc
is 1
μ
A and B is still 10 kHz, then, I is about 0.006% or -85 dB. If I
dc
is 1 pA, then, I is about 5.6% or 56 fA.
In fact, shot noise is one kind of the white noise. Its power spectrum density is given by:
)
/
(
2
)
(
2
Hz
A
qld
f
S
sl
The equation is based on the assumption that carriers in the current do not interact with each other. This assumption is
valid, for example, for the diffusion current in the junction diode. However, for the commonly used metal, this equation
cannot be used because the cross effect between carries cannot be ignored.
Flicker Noise (1/f Noise)
In 1925, Johnson first found 1/f noise in the current of Vacuum tubes. The power spectrum function of this noise is
proportional to 1/f. The lower the frequency, the more serious the noise. Thus, it is also called low frequency noise.
Microscopically, 1/f noise is caused by the random value of contact resistance between two conductors. The current
amplitude of 1/f noise follows the Gaussian distribution, and the power spectrum density is proportional to 1/f which is
given by:
)
/
(
)
(
2
2
Hz
V
f
KI
f
S
d
1/f noise is also called flicker noise due to the random fluctuation of the power spectrum density in active devices. It
broadens the bandwidth near the center frequency and reduces the value of Q of oscillators. 1/f noise must be considered
near the center frequency.
Total Noise
Johnson noise and shot noise are unreducible. Any resistors with a same resistance have the same Johnson noise. Shot
noise relies on the special manufacture of resistors, including its material and package technology and so on. For example,
among winding resistor, metal film, carbon resistor and pure carbon, the winding resistor has the minimum resistance. The
metal film resistor and carbon resistor have larger resistances. The pure carbon resistor has the maximum resistance of
these four. All of these noises are incoherent. The total random noise is the square root of the sum of the squares of all the
incoherent noise sources.
