Nyquist Formula

Nyquist Formula


(or Nyquist theorem), a relationship that determines the magnitude of thermal fluctuations of voltage or current in an electric circuit. It was obtained by the American physicist H. Nyquist in 1928.

According to the Nyquist formula, the mean square voltage across the ends of a conductor with a resistance R is equal to

(1) V̅2 = 4RkTΔv

if the conductor is in a state of thermal equilibrium at the absolute temperature T; here, k is Boltzmann’s constant and Δ v is the frequency band within which the voltage fluctuations are measured. For low temperatures and for sufficiently high frequencies (such that hv > kT, where v is the frequency and h is Planck’s constant), formula (1) must be replaced by the more general expression

(2) V̅2 = 4RkT coth (hv/2kT) Δv

The Nyquist formula is widely used in calculations of thermal noise in measuring and radio engineering devices.


Kittel, C. Elementarnaia statisticheskaia fizika. Moscow, 1960. (Translated from English.)
MacDonald, D. Vvedenie v fiziku shumov i fluktuatsii. Moscow, 1964. (Translated from English.)