# Limitations of Noise temperature of Antenna, Feeder cable and LNA

Read in a study guide: 'Since the noise temperature of the antenna and the feeder could not be reduced below a limit, noise temperature of LNA is kept as low as possible.' I am trying to look for a definite answer why the antenna noise temperature and feeder noise temperature have limitations in their reductions? I have read that antenna elevation angle is a factor for antenna noise temperature with inverse proportionality. So can it be said as a reason, that as antenna elevation angle of earth stations are fixed w.r.t satellite's position in space its noise temperature can't be reduced a certain value? So my questions are:

1) Why can't the noise temperature of antenna and feeder cable be reduced a certain limit or in other words its limitations?

2) Does that mean LNA's noise temperature can be reduced by some technique. Its certain even then a limit is there. What are its limitations?

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The 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/B = Kb*T


where: P is the power (in watts)

B is the total bandwidth (Hz) over which that noise power is measured

Kb is the Boltzmann constant (1.381×10−23 J/K, joules per kelvin)

T is the noise temperature (K)

The noise temperature (not actual temperature) is a function of frequency. To limit this noise you would have to reduce the power level and/or the bandwidth with the resultant degrading of the signal - hence a limitation on what you can do.

In an ideal resistor its the actual temperature of the resistor at all frequencies which controls the noise generated and this can be reduced by cooling.

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@Andy yes you are right, I missed the word certain. By your answer, I got the limitation in not able to reduce the antenna noise temp below a certain limit but what is it for the feeder cable. And also the second question ie about the LNA? –  sk1 Oct 2 '13 at 19:48
@sk1 was this comment for me? –  Andy aka Oct 2 '13 at 22:11

I'm not 100% sure what you are driving at because what you've written seems to miss the word "below" like here: -

1) Why can't the noise temperature of antenna and feeder cable be reduced a certain limit or in other words its limitations?

Is the word "below" missing between "reduced" and "a"? If it is then here's my attempt at an answer.

If what the antenna receives is non-man-made background noise, that noise will be at a power level dependant on the temperature of the stuff that made it. This means that you can cool your antenna and feeder as much as you want but you'll still end up with the noise from what you receive.

It's Planck's law that dictates the total power per Hz emitted from an object at temperature T: -

$P_V = \dfrac{2\pi h f^3}{C^2} \times\dfrac{1}{e^{\frac{h f}{kT}}-1}$

Where h is Planck's constant, f is frequency, K is Boltzmann's constant, T is temperature in kelvin and c is speed of light.

I don't 100% know if this answers your question given the word I've added to make sense of it. Please let me know if it isn't and I'll try and correct it.

This also seems to be quite a good paper on the subject. It's called "Noise in antennas" but I can't seem to fathom out who wrote it.

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@ Andy aka. Hi yes the comment was for you. I did miss the word certain. By your answer, I got the limitation in not able to reduce the antenna noise temp below a certain limit but what is it for the feeder cable. And also the second question ie about the LNA? –  sk1 Oct 3 '13 at 9:14
@sk1 - I think you missed out the word "below" actually. Feeder cable or LNA both produce self-noise which is determined by their own temperature. –  Andy aka Oct 3 '13 at 12:34