# Johnson-Nyquist noise

(Redirected from Thermal noise)

Johnson-Nyquist noise (sometimes thermal noise, Johnson noise or Nyquist noise) is the noise generated by the equilibrium fluctuations of the electric current inside an electrical conductor, which happens without any applied voltage, due to the random thermal motion of the charge carriers (the electrons).

It is to be distinguished from shot noise, which consists of additional current fluctuations that occur when a voltage is applied and a macroscopic current starts to flow. For the general case, the above definition applies to charge carriers in any type of conducting medium (e.g. ions in an electrolyte).

The thermal noise power, P, in watts, is given by [itex]P = { 4 k_B T \Delta f }[itex], where kB is Boltzmann's constant in joules per kelvin, T is the conductor temperature in kelvins, and Δf is the bandwidth in hertz. Thermal noise power, per hertz, is equal throughout the frequency spectrum, depending only on kB and T. It is white noise, in other words.

In communications, noise power is often used. Thermal noise at room temperature can be estimated in decibels as:

[itex]

P = -174 + 10 log(\Delta f) [itex]

Where P is measured in dBm (0 dBm = 1 mW) and Δf is bandwidth in Hz. For example:

Bandwidth Power
1 Hz -174 dBm
10 Hz -164 dBm
1000 Hz -144 dBm
5 kHz -137 dBm
1 MHz -114 dBm
6 MHz -106 dBm

Electronics engineers often prefer to work in terms of noise voltage across the resistor (en) and noise current (in) going through the resistor. These also depend on the electrical resistance, R, of the conductor:

[itex]

e_n = \sqrt { 4 k_B T R \Delta f } [itex]

[itex]

i_n = \sqrt {{ 4 k_B T \Delta f } \over R} [itex]

Thermal noise is intrinsic to all resistors and is not a sign of poor design or manufacture, although resistors may also have excess noise.

## References

• J. Johnson, "Thermal Agitation of Electricity in Conductors", Phys. Rev. 32, 97 (1928) -- the experiment
• H. Nyquist, "Thermal Agitation of Electric Charge in Conductors", Phys. Rev. 32, 110 (1928) -- the theory
• adapted in part from Federal Standard 1037C and from MIL-STD-188

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