Thermal noise is the random voltage signal created by the Brownian motion of charge carriers in a conductor. Thermal noise is responsible for the hiss of audio systems and the "snow" of analog televisions. The noise was first explained by H. Nyquist, J.B. Johnson, and W. Schottky in the 1920s. In their honor, thermal noise is also referred to as Johnson noise or Nyquist noise.

For most engineering applications, it is safe to assume that thermal noise power is constant across all frequencies. The root-mean-square, open circuit noise voltage of an element in an electrical circuit is well-approximated by (4kTRΔf)1/2, where k is Boltzmann's constant, Δf is the bandwidth of the circuit, and R is the element's resistance. Given this noise voltage, simple circuit analysis shows that the available noise power, the maximum power that a noise source can deliver to a load, is kTΔf. Since the thermal noise is (almost) constant with frequency, it is often called white noise, because white light is light with power distributed equally across the visible spectrum.

The thermal noise voltage created by a device in an electrical circuit is of considerable interest, since such a voltage is added to the true signal of interest. Thermal noise imposes a minimum allowable signal level on electronic systems. A very common measurement of the effect of noise on a circuit is called signal-to-noise ratio, which is defined as 20log10(Vsignal/Vnoise). For some applications, such as detection of tiny electromagnetic signals from the universe, circuits are cryogenically cooled to reduce thermal noise. Also, the formulas for thermal noise show that filters with low bandwidth (and correspondingly high quality factor) are desirable if noise is a problem.

Reference: The Design of CMOS Radio-Frequency Integrated Circuits by Thomas H. Lee