# Online Encyclopedia

# Johnson-Nyquist 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 *P* = 4*k**T* Δ*f* , where *k* is Boltzmann's constant in joules per kelvin, *T* is the conductor temperature in kelvins, and Δ*f* is the bandwidth in hertz. Thermal noise power, per hertz, is equal throughout the frequency spectrum, depending only on *k* and *T* .

Electronics engineers often prefer to work in terms of noise voltage and noise current. These also depend on the electrical resistance, R, of the conductor:

*e*= √ (4_{n}*k*TR Δ*f*)

*i*= √ (4_{n}*k*T Δ*f*) / R

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

## See also

- Harry Nyquist, J. Johnson

## 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