Introduction#
In any physical information-processing system, noise is added to the signals. Noise is a collective noun for all undesired current and voltage fluctuations in a circuit. Hence, DC offset voltages and currents including their temperature fluctuations, as well as uncertainty of device parameters including their temperature dependency and ageing effects, can be regarded as noise. All of these effects have in common that they increase the uncertainty that the circuit’s current and voltage variations arise from information-carrying signals only. In this way, all these effects limit the amount of information that can be processed by the circuit.
In this section, we will introduce the main physical mechanisms for noise generation and introduce noise-modeling techniques for amplifiers.
Thermal noise#
The noise caused by the thermal movement of electrons in conductive elements is called thermal noise or Johnson noise. In 1928, J.B. Johnson [55] experimentally found that thermal noise variance was proportional to the absolute temperature. His colleague at the AT&T Bell labs, H. Nyquist [56] explained this. At constant temperature, the generation of thermal noise is a stationary and ergodic process.
The thermal noise in resistors can be modeled by a noise voltage source
Fig. 587 Models for noisy resistors (A and B) and for a noise-free resistor (C).#
These thermal noise sources have a Gaussian amplitude distribution density
function and a uniform \ or white power spectral density up to very
high frequencies. The power spectral densities of
where
Shot noise#
Variations in the transport of charge carriers across a potential barrier is
the cause of so-called shot noise. Currents through PN
junctions have an associated shot noise current. Shot noise current sources
have a Gaussian distribution density function and a uniform spectral density,
as long as the junction transit time is small with respect to the reciprocal
value of the frequency. The spectral density of a shot noise current
associated with a DC junction current
where
Excess noise#
Fluctuations in conduction mechanisms give rise to so-called excess noise. Excess noise is found in resistors, in electrolytic capacitors and in semiconductor devices. The amplitude distribution function of excess noise sources is Gaussian, and the spectral density is inversely proportional to the frequency.
In resistors, the spectral density is usually modeled as proportional to the
squared voltage
where
Excess noise in resistors is usually specified in
from which we obtain
The excess noise figure
The
It follows that
in which
Example
We will evaluate
With the aid of expression (245), we obtain
The power dissipation in the resistor
In semiconductors, excess noise is caused by energy traps in the depletion
layer of PN junctions or in the oxide of MOS structures. For
PN junctions, it is modeled with a noise current source
in which
Noise temperature#
The noise power of a source is sometimes defined with the aid of its noise
temperature. The noise temperature
in which
,