Resistor Noise

Due to the random thermal motion of charge carriers, we observe thermal noise, voltage and current noise in resistive circuit elements that is proportional to absolute temperature.

Modeling Thermal Noise in Resistors

Consider the noisy resistor in Fig. 1. We can model this as a noiseless resistor in series with a voltage noise generator, or a noiseless resistor in parallel with a current noise generator. Since we cannot predict the voltage or current noise at any point in time, we instead specify the noise voltage or current power:

${\overline {v_{n}^{2}}}=4kTRB$

(1)

${\overline {i_{n}^{2}}}=4kTGB={\frac {4kTB}{R}}$

(2)

Where $k$ is Boltzmann's constant, equal to $8.617\times 10^{-5}\mathrm {\tfrac {eV}{K}}$, and $B$ is the observation bandwidth. Thermal noise has a white power spectral density, as shown in Fig. 2.