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Thermal noise in an ideal resistor is approximately white, meaning that its power spectral density is nearly constant throughout the frequency spectrum (Figure 2). When limited to a finite bandwidth and viewed in the time domain (as sketched in Figure 1), thermal noise has a nearly Gaussian amplitude distribution. [1]
Thus the noise temperature is proportional to the power spectral density of the noise, /. That is the power that would be absorbed from the component or source by a matched load . Noise temperature is generally a function of frequency, unlike that of an ideal resistor which is simply equal to the actual temperature of the resistor at all ...
An approximate formula for the noise-equivalent power (NEP) due to phonon noise in a bolometer when all components are very close to a temperature T is =, where G is the thermal conductance and the NEP is measured in /. [2]
It occurs in the definitions of the kelvin (K) and the gas constant, in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy and heat capacity.
Thermal noise is approximately white, meaning that its power spectral density is nearly equal throughout the frequency spectrum. The amplitude of the signal has very nearly a Gaussian probability density function. A communication system affected by thermal noise is often modelled as an additive white Gaussian noise (AWGN) channel.
Thermal noise results from the motion of charge carriers (usually electrons) in an electrical circuit generated by their thermal motion. Thermal noise is white noise meaning that the power spectral density is constant throughout the frequency spectrum. The root mean square value of the thermal noise in a resistor is given by [22]
Here, k ≈ 1.38 × 10 −23 J/K is the Boltzmann constant and kT 0 is the available noise power density (the noise is thermal noise, Johnson noise). As a numerical example: A receiver has a bandwidth of 100 MHz, a noise figure of 1.5 dB and the physical temperature of the system is 290 K.
Thermal noise can be a fundamental standard. A resistor at a certain temperature has a thermal noise associated with it. A noise generator might have two resistors at different temperatures and switch between the two resistors. The resulting output power is low.