Thermal noise

Definition

Thermal noise, also known as Johnson-Nyquist noise, is electrical noise caused by the random thermal movement of charge carriers in a conductor or resistor. It occurs independently of external voltage sources and is a fundamental property of all electrical components at temperatures above absolute zero.

Origin

The constant thermal movement of electrons causes small voltage fluctuations that can be measured as a noise signal. Higher temperatures lead to stronger noise.

Mathematical description

The effective noise voltage _VRMS across a resistor R is described by the following formula:

_VRMS=√(_4kB T R Δf)

_kB: Boltzmann constant (1.38 × ^10-23 J/K)
T: Temperature (Kelvin)
R: Resistance (Ohm)
Δf: Frequency bandwidth (Hertz)

Properties

Broadband: Distributed over a large frequency spectrum (white noise).
Temperature-dependent: Increasing temperature increases the noise.
Unavoidable: Is part of the basic characteristic of electronic systems.

Technical significance

Thermal noise sets a fundamental limit for the sensitivity of amplifiers:

Amplifiers
Sensors
Radio receivers
Medical devices (e.g. EEG, ECG)

Differentiation from other types of noise

Shot noise: Arises from discrete charge transports.
1/f noise: Increases at low frequencies.
Quantisation noise: Occurs when analogue signals are digitised.

Summary

Thermal noise is an unavoidable, temperature-dependent form of electrical noise that determines the performance limits of electronic systems.