An antenna absorbs power from the radio waves that fall on it.
This power is also usually specified in temperature units, i.e. degrees Kelvin.
To motivate these units, consider a resistor placed in a thermal bath at a
temperature . The electrons in the resistor undergo random thermal motion,
and this random motion causes a current to flow in the resistor. On the
average there are as many electrons moving in one direction as in the
opposite direction, and the average current is zero. The power in the
resistor however depends on the square of the current and is not zero.
From the equipartition principle one could compute this power as a function
of the temperature, and in the radio regime the power per unit frequency
is well approximated by the Nyquist formula:
The system temperature when looking at blank sky is a measure of the
total random noise in the system and hence it is desirable to make the
system temperature as low as possible. Noise from the various sub systems
that make up the radio telescope are uncorrelated and hence add up linearly.
The system temperature can be very generally written as
is the contribution of the background sky brightness. For example the galaxy is a strong emitter of non thermal3.10 continum radiation, which at low frequencies usually dominates the system temperature. At all frequencies the sky contributes at least 3K from the cosmic background radiation.3.11
The feed antenna is supposed to collect the radiation focused by the reflector. Often the feed antenna also picks up stray radiation from the ground ( which radiates approximately like a black body at 300 K ) around the edge of the reflector. This added noise is called spillover noise, and is a very important contribution to the system temperature at a telescope like Arecibo. In Figure 3.8 is shown (schematically) the system temperature for the (pre-upgrade) Arecibo telescope at 12cm as a function of the zenith angle at which the telescope is pointed. At high zenith angles the feed radiation spills over the edge of the dish and picks up a lot of radiation from the surrounding hills and the system temperature changes from under 40 K to over 80 K. If a reflecting screen were to be placed around the telescope edges, then, the spill over radiation will be sky radiation reflected by the screen, and not thermal radiation from the ground. At cm wavelengths, , so such a ground screen would significantly reduce the system temperature at high zenith angles3.12.
Any lossy element in the feed path will also contribute noise ( ) to the system. This follows from Kirchoff's law which states that good absorbers are also good emitters, and that the ratio of emission to absorption in thermodynamic equilibrium is given by the Planck spectrum at the absorber's physical temperature. This is the reason why there are rarely any uncooled elements between the feed and the first amplifier. Finally, the receiver also adds noise to the system, which is characterized by . The noise added after the first few stages of amplification is usually an insignificant fraction of the signal strength and can often be ignored.
The final, increasingly important contributor to the system temperature is terrestrial interference. If the bandwidth of the interference is large compared to the spectral resolution, the interference is called broad band. Steady, broad band interference increases the system temperature, and provided this increase is small its effects are relatively benign. However, typically interference varies on a very rapid time scale, causing a rapid fluctuation in the system temperature. This is considerably more harmful, since such fluctuations could have harmonics which are mistaken for pulsars etc. In aperture synthesis telescopes such time varying effects will also produce artifacts in the resulting image3.13. Interference whose bandwidth is small compared to the spectral resolution is called narrow band interference. Such interference, provided it is weak enough will corrupt only one spectral channel in the receiver. Provided this spectral channel is not important (i.e. does not coincide with for eg. a spectral line from the source) it can be flagged with little loss of information. However, if the interference is strong enough, the receiver saturates, which has several deleterious effects. Firstly since the receiver is no longer in its linear range, the increase in antenna temperature on looking at a cosmic source is no longer simply related to the source brightness, making it difficult, and usually impossible to derive the actual source brightness. This is called compression. Further if some other spectral feature is present, perhaps even a spectral line from the source, spurious signals are produced at the beat frequencies of the true spectral line and the interference. These are called intermodulation products. Given the increasingly hostile interference environment at low frequencies, it is important to have receivers with large dynamic range, i.e. whose region of linear response is as large as possible. It could often be the case, that it is worth increasing the receiver temperature provided that one gains in dynamic range. For particularly strong and steady sources of interference (such as carriers for nearby TV stations), it is usually the practice to block such signals out using narrow band filters before the first amplifier3.14.