Noise temperature

The noise temperature of a one- port is the temperature that a real ohmic resistance would have to have in order to generate the same available noise power P at the measurement frequency as the one-port to be characterized:  

${\displaystyle T={\frac {P}{k_{\mathrm {B} }B}}}$

It is

• ${\displaystyle k_{\mathrm {B} }}$the Boltzmann constant
• ${\displaystyle B}$the measurement bandwidth .

The available noise power of an ohmic resistor is proportional to the absolute temperature T and the measurement bandwidth up to very high frequencies  :

${\displaystyle \iff P=k_{\mathrm {B} }\,T\,B}$

The noise temperature of a two-port is the noise temperature that a noise source connected to the input port of the two-port (noisy one-port) would have to have in order to generate the same available noise power at the output of the two-port to be characterized, but then thought to be noise-free, at the measuring frequency as the one to be characterized, Noisy two-port when controlled by a source thought to be noise-free.

Low-noise amplifiers have noise temperatures of 40 K and less.

Designations

The product of temperature and Boltzmann's constant has the dimension of energy, but also that of power per bandwidth. Therefore it is also called spectral noise power density (see also spectral power density ).

At 17 ° C (290 K) it is:

${\displaystyle {\begin{aligned}k_{\mathrm {B} }T&=1{,}3806488\cdot 10^{-23}\,\mathrm {J/K} \cdot 290\,\mathrm {K} \\&\approx 4\cdot 10^{-21}\,\mathrm {J} \\&=4\cdot 10^{-21}\,\mathrm {W/Hz} \\&\approx -204\,\mathrm {dB\cdot W/Hz} .\end{aligned}}}$

Multiplied by the bandwidth, we get the noise power  P and the relationship given above.

Linear amplifiers

Ideal, linear amplifiers would increase the available power of the input signal by the factor of the available power gain without adding additional noise. The signal-to-noise ratio  (SNR) at the input and output would be the same.

Real amplifiers, on the other hand, are made up of components that themselves make noise. As a result, the SNR at the output is smaller than at the input. The ratio of both SNRs leads to the noise figure :

${\displaystyle F={\frac {\mathrm {SNR} _{\mathrm {ein} }}{\mathrm {SNR} _{\mathrm {aus} }}}={\frac {P_{S,\mathrm {ein} }}{P_{N,\mathrm {ein} }}}\cdot {\frac {P_{N,\mathrm {aus} }}{P_{S,\mathrm {aus} }}}}$

The output signal ( ) is separated into a component that is ideally amplified and a noise component that is added by the amplifier: ${\displaystyle P_{\mathrm {aus} }=P_{S,\mathrm {aus} }+P_{N,\mathrm {aus} }\,}$

${\displaystyle {\begin{aligned}P_{\mathrm {aus} }&=GP_{\mathrm {ein} }+P_{R,\mathrm {aus} }\\&=G(P_{\mathrm {ein} }+P_{R,\mathrm {ein} })\end{aligned}}}$

Here,  G the gain .

If there is no signal ( ), the input power is only determined by the noise power, which is calculated using the above equation. The additional noise from the amplifier ( ) corresponds to a noise temperature that is characteristic of the amplifier, but whose feedback and correlation properties also depend on the internal impedance of the controlling source. ${\displaystyle P_{\mathrm {ein} }=P_{N,\mathrm {ein} }}$ ${\displaystyle P_{R,\mathrm {ein} }}$

literature

• Jürgen Detlefsen, Uwe Siart: Basics of high frequency technology. 2nd, expanded edition. Oldenbourg, Munich et al. 2006, ISBN 3-486-57866-9 .
• HT Friis : Noise Figures of Radio Receivers. In: Proceedings of the IRE. Vol. 32, 1944, ISSN  0096-8390 , pp. 419-422, (PDF; 612 kB) .
• Rudolf Müller: Noise. 2nd edition, Springer Verlag, Berlin / Heidelberg 1990, ISBN 978-3-540-51145-8 .
• FR Connor: Noise. Random signals - noise measurement - system comparison, Friedrich Vieweg & Sohn Verlag, Wiesbaden 1986, ISBN 978-3-528-04376-6 .
• Heinz Bittel , Leo Storm: Noise. An introduction to understanding electrical fluctuations. Springer Verlag, Berlin a. a. 1971, ISBN 3-540-05055-8 .

See also

• G / T (reception quality)

Web links

• Investigations on noise sources (accessed on October 13, 2017)
• Lossy Line Noise (accessed October 13, 2017)
• Noise and interference (accessed October 13, 2017)