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linear circuits arises from (i) a large number of noise sources and (ii)
the aliasing effect. Methods that compute the output noise power di-
rectly from (11.97) is often referred to as the
brute-force
method be-
cause in this approach not only the contribution of each noise source
is computed separately, the contribution of every sideband compo-
nent of the same noise source is also calculated individually.
4.2
Noise Sources
Thermal noise
: Thermal noise, also known as Johnson noise, in recog-
nition of the first observation of the phenomenon by J. B. Johnson
[88], is generated by the random thermal agitation of mobile carri-
ers. It is due to the random departure and return of mobile charges
in thermal equilibrium. The power of thermal noise is directly pro-
portional to temperature. The band width of thermal noise at room
temperature is around 6000 GHz and time samples separated by 0.17
ps are considered to be uncorrelated [89]. In almost all cases, thermal
noise is treated as a stationary process. The distribution of thermal
noise is Gaussian. The power spectral density of the thermal noise
generated by a resistor is given by
where
R
is the resistance of the resistor, is
Boltzmann constant, and
T
is the absolute temperature in degrees
Kelvin. Eq.(11.98) was first derived by Nyquist [90] from thermo-
dynamics and the exchange of energy between resistive elements in
thermal equilibrium and is known as Nyquist law.
Shot noise
: Shot noise of semiconductor devices is caused by the ran-
dom combination of electron-hole pairs and the random diffusion of
minority carriers across depletion region [91]. This phenomenon is
depicted by a stochastic process representing the sum of a large
number of independent events occurring at random time instants with
an average rate
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