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•Types of electrical noises
(i) Johnson Noise
Johnson noise occurs in any device that dissipates power, such as resistor,
hence it is very common. Principle of equipartition of energy states: For a
system in thermal equilibrium with its surroundings : The mean kinetic
energy of each degree of freedom is ½ kT, where
k=Boltzmann’s constant (1.4×10
-23
J/K)
1. 1 joule = 0.2388 calorie. It is named after James Joule. When the point of
application of a force of one Newton moves, in the direction of the force, a
distance of one metre.
2. Boltzmann's constant (k): The number that relates the average energy of a
molecule to its absolute temperature.
3. T = the absolute temperature (thermodynamic temperature): A measure,
in Kelvin (K), proportional to the thermal energy of a given body at
equilibrium.
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Note 1: A temperature of 0 K is called "absolute zero," and coincides with the
minimum molecular activity (i.e. , thermal energy) of matter.
Note 2: Thermal noise power, per hertz, is equal throughout the frequency
spectrum, depending only on k and T .
Note 3: For the general case, the above definition may be held to apply to
charge carriers in any type of conducting medium.
The electrons in a conductor thus have a mean square velocity (in one
direction) that is dependent on temperature and given by
½ mv² = ½ kT
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It can be shown that the power spectrum (in mean squares volts per Hz)
For the Johnson noise in a resistor R is given by
pv ( f )  4 RkT
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which is constant up to very high frequencies, and is refereed as white noise
(ii) Shot noise
Shot noise is less universal than Johnson noise, but occurs in diodes and
hence in transistor. It is often the main source of noise. The effect occurs
since the passage of an electron across the potential barrier in a p-n diode
is a statistical process, leading to the fluctuation of the current.
The expression for the power spectrum (in terms of mean squares per
Hz)
pi ( f )  2eI
where I is the mean current, e the electronic charge( 1.6  10 19 )
i  2eIB
2
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Diode:
An electronic device with two electrodes. In the obsolescent
thermionic diode a heated cathode emits electrons, which
flow across the intervening vacuum to the anode when a
positive potential is applied to it. The device permits flow of
current in one direction only as a negative potential applied to
the anode repels the electrons. This property of diodes was
made use of in the first thermionic radios, in which the diode
was used to demodulate the transmitted signal.
In the semiconductor diode, a p-n junction performs a similar
function. The forward current increases with increasing
potential difference whereas the reverse current is very small
indeed.
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A semiconductor diode consists of a PN junction and has two(2)
terminals, an anode (+) and a cathode(-). Current flows from anode to
cathode within the diode. A diode and schematic representation are
shown below.
Summary:
Current flows in only one direction (anode to cathode
internally). When a forward voltage is applied, the diode
conducts; and when a reverse voltage is applied, there is
no conduction.
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Forward Voltage Drop , Vf
Notice that the diode conducts a
small current in the forward
direction up to a threshold voltage,
0.3 for germanium and 0.7 for
silicon ; after that it conducts as we
might expect. The forward voltage
drop, Vf, is specified at a forward
current, If.
Leakage current
In the reverse direction there is a small leakage current up until the reverse
breakdown voltage is reached. This leakage is undesireable, obviously the
lower the better, and is specified at a voltage less the than breakdown; diodes
are intended to operate below their breakdown voltage.
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Example: A thermal diode is connected in series with a resistor of
10kΩ and carries a current of 0.1mA, as shown in the figure below.
Find the noise voltage at the output in a bandwidth of 1MHz.
The resistor produces Johnson noise
4RKTB in bandwidth B, taking
kT=4×10-21
VJ2  4 RkTB
 4 10  4 10
4
10
 1.6 10 V
 21
10
2
8
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The diode produces a Shot noise, which flows through the
resistor, so the voltage produced is
Vs2  2eIBR 2
 2  1.6  10 19 10  4 10 6 108
 3.2 10 9 V 2
The total noise, the sum of the mean squares values, is
3.4 10 9 V 2 or 5.9 10 5V
( in root mean squre)
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(iii) 1/f noise
It is found that most semiconductor devices produce more noise,
particularly at low frequencies, than is predicted by Johnson or Shot
noise. This is attributed to 1/f noise, which has a power spectrum
inversely proportional to frequency, given by
I2
pv ( f )  K
f
in which I is the current in the device, and K is a constant that
depends on the device.
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A power spectrum for the noise from a typical operational amplifier.
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Homework:
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(i) Explain why Johnson noise increases with temperature. Does it
occur at absolute zero?
(ii) Does Johnson noise depend on the direct current flowing in a
resistor? Does it occur in semiconductors?
(iii) Does shot noise depend on the current, on the temperature or on
both in a semiconductor diode? Does Shot noise occur in a resistor
carrying direct current?
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