Noise thermometry is based on the Nyquist formula for the thermal noise ΔU of the electrical voltage drop U across a resistor with resistance R and temperature T. While the mean value vanishes, the square of the noise voltage occurring in a narrow frequency band Δν around the frequency ν is:
The usual approximate expression on the right can be used whenν/T << k/h ≈ 20 GHz/K. The Nyquist formula is a special case of the general fluctuation dissipation theorem for the thermal fluctuations of macroscopic quantities.
From the statistical nature of the measured quantity, long measuring times arise. One of the main problems is the accurate measurement of the very small noise voltages, avoiding extraneous sources of noise and maintaining a constant bandwidth and gain of the amplifiers.