Noise temperature

From Wikipedia, the free encyclopedia

In electronics, noise temperature is a temperature (in kelvins) assigned to a component such that the noise power delivered by the noisy component to a noiseless matched resistor is given by

P R L = k B T s B n

in watts, where:

$\scriptstyle k_B$ is the Boltzmann constant (1.381×10⁻²³ J/K, joules per kelvin)
$\scriptstyle T_{s}$ is the noise temperature (K)
$\scriptstyle B_{n}$ is the noise bandwidth (Hz)

Engineers often model noisy components as an ideal component in series with a noisy resistor. The source resistor is often assumed to be at room temperature, conventionally taken as 290 K (17 °C, 62 °F).^[1]

[edit] Applications

A communications system is typically made up of a transmitter, a communications channel, and a receiver. The communications channel may consist of any one or a combination of many different physical media (air, coaxial cable, printed wiring board traces…). The important thing to note is that no matter what physical media the channel consists of, the transmitted signal will be randomly corrupted by a number of different processes. The most common form of signal degradation is called additive noise.^[2]

The additive noise in a receiving system can be of thermal origin (thermal noise) or can be from other noise-generating processes. Most of these other processes generate noise whose spectrum and probability distributions are similar to thermal noise. Because of these similarities, the contributions of all noise sources can be lumped together and regarded as thermal noise. The noise power generated by all these sources ( $\scriptstyle P_{n}$ ) can be described by assigning to the noise a noise temperature ( $\scriptstyle T_{n}$ ) defined as:^[3]

T n = P n / (k B n)

In a wireless communications receiver, $\scriptstyle T_{n}$ would equal the sum of two noise temperatures:

T n = (T a n t + T s y s)

$\scriptstyle T_{ant}$ is the antenna noise temperature and determines the noise power seen at the output of the antenna. The physical temperature of the antenna has no affect on $\scriptstyle T_{ant}$ . $\scriptstyle T_{sys}$ is the noise temperature of the receiver circuitry and is representative of the noise generated by the non-ideal components inside the receiver.

[edit] Noise factor and noise figure

An important application of noise temperature is its use in the determination of a component’s noise factor. The noise factor quantifies the noise power that the component adds to the system when its input noise temperature is $\scriptstyle T_{0}$ .

$F = \frac{T_{0} + T_{sys}}{T_{0}}$

The noise factor (a linear term) can be converted to noise figure (in decibels) using:

$F_{dB} = 10 \ \log_{10} (F)$

[edit] Noise temperature of a cascade

If there are multiple noisy components in cascade, the noise temperature of the cascade will be limited by the noise temperature of the first component in the cascade. The gains of the components at the beginning of the cascade have a large effect on the contribution of later stages to the overall cascade noise temperature. The cascade noise temperature can be found using:^[1]

$T_{cas} = T_{1} + \frac{T_{2}}{G_1} + \frac{T_{3}}{G_1 G_2} + \dots + \frac{T_{n}}{G_1 G_2 G_3 \dots G_{n-1}}$

where

$\scriptstyle T_{cas}$ = cascade noise temperature
$\scriptstyle T_{1}$ = noise temperature of the first component in the cascade
$\scriptstyle T_{2}$ = noise temperature of the second component in the cascade
$\scriptstyle T_{3}$ = noise temperature of the third component in the cascade
$\scriptstyle T_{n}$ = noise temperature of the nth component in the cascade
$\scriptstyle G_1$ = linear gain of the first component in the cascade
$\scriptstyle G_2$ = linear gain of the second component in the cascade
$\scriptstyle G_3$ = linear gain of the third component in the cascade
$\scriptstyle G_{n-1}$ = linear gain of the (n-1) component in the cascade

[edit] Measuring noise temperature

The direct measurement of a component’s noise temperature is a difficult process. Suppose that the noise temperature of a low noise amplifier (LNA) is measured by connecting a noise source to the LNA with a piece of transmission line. From the cascade noise temperature it can be seen that the noise temperature of the transmission line ( $\scriptstyle T_{1}$ ) has the potential of being the largest contributor to the output measurement (especially when you consider that LNA’s can have noise temperatures of only a few Kelvin). To accurately measure the noise temperature of the LNA the noise from the input coaxial cable needs to be accurately known. ^[4] This is difficult because poor surface finishes and reflections in the transmission line make actual noise temperature values higher than those predicted by theoretical analysis. ^[1]

Similar problems arise when trying to measure the noise temperature of an antenna. Since the noise temperature is heavily dependent on the orientation of the antenna, the direction that the antenna was pointed during the test needs to be specified. In receiving systems, the system noise temperature will have three main contributors, the antenna ( $\scriptstyle T_{A}$ ), the transmission line ( $\scriptstyle T_{L}$ ), and the receiver circuitry ( $\scriptstyle T_{R}$ ). The antenna noise temperature is considered to be the most difficult to measure because the measurement must be made in the field on an open system. One technique for measuring antenna noise temperature involves using cryogenically cooled loads to calibrate a noise figure meter before measuring the antenna. This provides a direct reference comparison at a noise temperature in the range of very low antenna noise temperatures, so that little extrapolation of the collected data is required.^[5]

[edit] References

^ ^a ^b ^c McClaning, Kevin, and Tom Vito. Radio Receiver Design. Atlanta, GA: Noble Publishing Corporation, 2000. ISBN 1-884932-07-X.
^ Proakis, John G., and Masoud Salehi. Fundamentals of Communication Systems. Upper Saddle River, New Jersey: Prentice Hall, 2005. ISBN 0-13-147135-X.
^ Skolnik, Merrill I., Radar Handbook (2nd Edition). McGraw-Hill, 1990. ISBN 978-0-07-057913-2
^ Hu, Robert. “Analysis of the Input Noise Contribution in the Noise Temperature Measurements.” Microwave and Wireless Components Letters, IEEE. Volume 15, Issue 3. pp 141-143. March 2005. 23 April 2008 <http://ieeexplore.ieee.org>.
^ Schuster, D., C. Stelzried, and G. Levy. “The Determination of Noise Temperatures of Large Paraboloidal Antennas.” Antennas and propagation, IEEE Transactions on. Volume 10, Issue 3. pp 286-291. May 1962. 23 April 2008 <http://ieeexplore.ieee.org>.

[mcclaning-0] McClaning, Kevin, and Tom Vito. Radio Receiver Design. Atlanta, GA: Noble Publishing Corporation, 2000. ISBN 1-884932-07-X.

[1] Proakis, John G., and Masoud Salehi. Fundamentals of Communication Systems. Upper Saddle River, New Jersey: Prentice Hall, 2005. ISBN 0-13-147135-X.

[2] Skolnik, Merrill I., Radar Handbook (2nd Edition). McGraw-Hill, 1990. ISBN 978-0-07-057913-2

[3] Hu, Robert. “Analysis of the Input Noise Contribution in the Noise Temperature Measurements.” Microwave and Wireless Components Letters, IEEE. Volume 15, Issue 3. pp 141-143. March 2005. 23 April 2008 <http://ieeexplore.ieee.org>.

[4] Schuster, D., C. Stelzried, and G. Levy. “The Determination of Noise Temperatures of Large Paraboloidal Antennas.” Antennas and propagation, IEEE Transactions on. Volume 10, Issue 3. pp 286-291. May 1962. 23 April 2008 <http://ieeexplore.ieee.org>.

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Noise temperature

From Wikipedia, the free encyclopedia

Contents

[edit] Applications

[edit] Noise factor and noise figure

[edit] Noise temperature of a cascade

[edit] Measuring noise temperature

[edit] References

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