Noise mechanisms

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 experimentally found that thermal noise variance was proportional to the absolute temperature. His colleague at the AT&T Bell labs, H. Nyquist explained this. At constant temperature, the generation of thermal noise is a stationary and ergodic process.

The thermal noise in resistors can be modeled with a noise voltage source \(V_{n}\) in series with a noise-free resistor or with a noise current source \(I_{n}\) in parallel with a noise-free resistor.

Resistor noise models

Fig. 6 Resistor noise models:

A: A noise-free resistor in series with a noise voltage source

B: A noise-free resistor in parallel with a noise current source

These thermal noise sources have a Gaussian amplitude distribution density function and, up to very high frequencies, a uniform power spectral density (white noise). The power spectral densities of \(V_{n}\) and \(I_{n}\) of a resistor with value \(R\) are:

\[\begin{split}\begin{align} S_{V_{n}} & =4kTR\qquad\text{[V}^{2}\text{/Hz],}\\ S_{I_{n}} & =4kTG\qquad\text{[A}^{2}\text{/Hz],}% \end{align}\end{split}\]

where \(T\) represents the absolute temperature in K, and \(k\) Boltzmann’s’ constant: \(k=1.38\cdot10^{-23}\) J/K.


Shot noise

Excess noise