In electronics, noise temperature is one way of expressing the level of available noise power introduced by a component or source. The power spectral density of the noise is expressed in terms of the temperature (in kelvins) that would produce that level of Johnson–Nyquist noise, thus:
P N B = k B T {\displaystyle {\frac {P_{\text{N}}}{B}}=k_{\text{B}}T}
where:
P N {\displaystyle P_{\text{N}}} is the noise power (in W, watts)
B {\displaystyle B} is the total bandwidth (Hz, hertz) over which that noise power is measured
k B {\displaystyle k_{\text{B}}} is the Boltzmann constant (1.381×10−23 J/K, joules per kelvin)
T {\displaystyle T} is the noise temperature (K, kelvin) Thus the noise temperature is proportional to the power spectral density of the noise, P N / B {\displaystyle P_{\text{N}}/B} . 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 frequencies.
Noise voltage and current A noisy component may be modelled as a noiseless component in series with a noisy voltage source producing a voltage of vn, or as a noiseless component in parallel with a noisy current source producing a current of in. This equivalent voltage or current corresponds to the above power spectral density P B {\displaystyle {\frac {P}{B}}} , and would have a mean squared amplitude over a bandwidth B of:
v ¯ n 2 B = 4 k B R T i ¯ n 2 B = 4 k B G T {\displaystyle {\begin{aligned}{\frac {{\bar {v}}_{\text{n}}^{2}}{B}}&=4k_{\text{B}}RT\\\\{\frac {{\bar {i}}_{\text{n}}^{2}}{B}}&=4k_{\text{B}}GT\end{aligned}}}
where R is the resistive part of the component's impedance or G is the conductance (real part) of the component's admittance. Speaking of noise temperature therefore offers a fair comparison between components having different impedances rather than specifying the noise voltage and qualifying that number by mentioning the component's resistance. It is also more accessible than speaking of the noise's power spectral density (in watts per hertz) since it is expressed as an ordinary temperature which can be compared to the noise level of an ideal resistor at room temperature (290 K). Note that one can only speak of the noise temperature of a component or source whose impedance has a substantial (and measurable) resistive component. Thus it does not make sense to talk about the noise temperature of a capacitor or of a voltage source. The noise temperature of an amplifier refers to the noise that would be added at the amplifier's input (relative to the input impedance of the amplifier) in order to account for the added noise observed following amplification.
System noise temperature An RF receiver system is typically made up of an antenna and a receiver, and the transmission line(s) that connect the two together. Each of these is a source of additive noise. The additive noise in a receiving system can be of thermal origin (thermal noise) or can be from other external or internal noise-generating processes. The contributions of all noise sources are typically lumped together and regarded as a level of thermal noise. The noise power spectral density generated by any source ( P / B {\displaystyle P/B} ) can be described by assigning to the noise a temperature T {\displaystyle T} as defined above:
T = P B ⋅ 1 k B {\displaystyle T={\frac {P}{B}}\cdot {\frac {1}{k_{\text{B}}}}}
… excerpt ends here. Continue reading the full article.
