Johnson noise in an ideal resistor is white, meaning that the power spectral density is constant throughout the frequency spectrum (except at extremely high frequencies). As the Johnson noise is the results of many independent charge carrier movements, the central limit theorem states that the resulting noise voltage will have a normal or Gaussian distribution.

The most important aspect of Johnson noise from our point of view is that the power of the Johnson noise is directly proportional to absolute temperature. There is no material property or calibration requirement to derive the absolute temperature, just electrical measurements. Therefore, this technique is not subject to sensor drift.


How does measuring Johnson Noise allow you to make a drift free thermometer?

By measuring the Johnson noise in a resistive sensor together with the sensor resistance and measurement bandwidth, the Johnson-Nyquist equation can be used to the determine true thermodynamic temperature of the sensor completely independent of the state of the sensor itself:

Johnson-Nyquist equation

Why aren’t all thermometers based on measuring Johnson noise?

The Johnson noise signal is extremely small (comparable to the electrical noise in the best low-noise amplifiers), making it extremely difficult to measure with sufficient precision and also easily contaminated by electrical noise in the environment. Many attempts to make a practical JNT have been made since the arrival of modern electronics era in the late 1950s, but none have so far led to a commercial product due to the difficulties associated with the low signal levels and the contamination of the signal by external noise.

Metrosol in collaboration with the National Physical Laboratory (NPL) are developing the world’s first practical Johnson Noise Thermometer. This work started in 2014 with a scoping and feasibility project, which lead to a completely new technique for measuring Johnson noise that was then patented and a demonstrator/proof of principle prototype. The demonstrator operated over the range -20 to 120°C, used several commercial instruments in order to make the measurements and weighed in at 35kg in a 70L volume:



Johnson Noise Thermometer



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 Johnson Noise