III. Gm-C Filtering - Epublications - Université de Limoges
III. Gm-C Filtering - Epublications - Université de Limoges
III. Gm-C Filtering - Epublications - Université de Limoges
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A.2 The Various Origins of Noise<br />
A.2.a Origins of Noise<br />
There are three main origins of noise in electronic systems [A.3].<br />
Thermal noise comes from the thermal Brownian motion of electrons, or any other<br />
charged particles, in an electrical component like a resistor for instance. This kind of noise is<br />
proportional to the absolute temperature. In<strong>de</strong>ed, since there would be no motion at the<br />
absolute zero temperature, this would mean the absence of noise.<br />
Thermal noise power are given by the following formulas:<br />
2<br />
vn = 4kTRB<br />
(A.4)<br />
2 1<br />
in = 4kT<br />
B<br />
(A.5)<br />
R<br />
where, k is the Boltzmann constant, T the absolute temperature given in Kelvin, B the<br />
effective noise bandwidth and R the resistance of the material in Ω.<br />
Shot noise originates from the corpuscular nature of the energy transport. The finite<br />
number of charged particles, electrons for example, creates a quantized random current flow<br />
which can be <strong>de</strong>scribed by a Poisson distribution. It can be <strong>de</strong>monstrated that it gives the<br />
following shot noise power:<br />
i = 2qI<br />
B<br />
(A.6)<br />
2<br />
n d<br />
Flicker noise is a low-frequency phenomenon, also called “1/f noise”. It is due to<br />
conductivity variations of the material where the current flows, like the presence of<br />
contaminants and of <strong>de</strong>fects in the crystal structure of the semiconductor material. The<br />
equivalent noise power is given by:<br />
α<br />
2 I<br />
in = K B<br />
(A.7)<br />
β<br />
f<br />
K being a constant, α and β being coefficients.<br />
A.2.b Available Input and Output Noise Powers<br />
Input noise NI is <strong>de</strong>fined as the thermal noise generated in the resistance of the signal<br />
source. The available noise power from a resistor is then:<br />
2<br />
v n<br />
N I = = kTB<br />
(A.8)<br />
4R<br />
The available output noise can also be <strong>de</strong>fined and will be referred as NO in the following.<br />
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