03/11/2020 posted
The definition of thermal noise is, “the electronic noise generated by the thermal agitation of the electrons inside an electrical conductor at equilibrium.” In other words, it means that noise is always generated when a current is passed through the resistor.
Thermal Noise is referred to multiple names, it may also be called Johnson-Nyquist noise, Johnson noise or Nyquist noise. And the noise is called multiple names because it was first detected and measured by Johnson B. Johnson and later explained by Harry Nyquist, however it is often referred as thermal noise in Japan.
In the case of voltage values, the noise level is specified as below:
vn=√4 kTRB（Vrms）
k: Boltzmann constant (1.38 x 10-23 J/K)
T: The resistor's absolute temperature in kelvins (K)
R: The resistor value in ohms (Ω)
B: The Frequency bandwidth (Hz)
The noise is proportional to the square root of the product’s temperature, resistance and frequency bandwidth. The reason why a sample is sometimes cooled to cryogenic temperature in a measurement is to reduce its thermal noise.
Because the noise level is dependent upon the temperature, so we often assume the measurement is under room temperature, which is at absolute temperature 300k (27 °C, 80 °F)
vn = 0.126 √4R (kΩ) x B (kHz) (µVrms)
When the resistor R is 1 kΩ and the frequency bandwidth B is 1 kHz, the noise is 0.126 µV. This value of voltage is inevitable because it is always generated as long as there is resistance. It can be ignored in circuits with a voltage of 5 V or 3.3 V, but it has a large effect on a voltage of several μV. In other words, it is a level that cannot be ignored in small signal measurement, and it is necessary to be aware of the existence of this noise.
