AT K5SO

MEASUREMENT OF Tsys

The sensitivity of a radio telescope is often characterized by a parameter referred to as "system temperature", denoted as Tsys.  Tsys may be determined via several methods.  One common method is the so-called  "Y-factor" method wherein two noise measurements are made by the radio telescope, one with the telescope pointing to the ground and the other with the telescope pointing toward "cold sky" (i.e., pointing to a region of sky with few thermal sources).  The results of the two measurements are used to calculate Tsys using a factor termed "Y", defined as:

Y = (ground noise power level) / (cold sky noise power level) = (Tg  + Tsys) / Tcs + Tsys)       (1)

where

Tg = the result of the noise power measured when the telescope is pointing toward the ground

Tcs = the result of the noise power measured when the telescope is pointing toward cold sky

Tsys = system temperature for the radio telescope.

Re-arranging Eqn (1),

Tsys =   (Tg - Y * Tcs) / (Y -1).                                            (2)

Applying this method for determining Tsys for this radio telescope at 1400 MHz is shown below.  The two noise measurements were obtained in a single graph by plotting the output of the telescope as the telescope moved from pointing to a cold sky region (in the constellation Leo in this case) to ground and recording the noise level difference, as shown below:

The relationship of Y to the dB differential shown above is:

dB = 10 log(10)((ground noise power level)/(cold sky noise power level)) =  10 log(Y)      (3)

which may be re-arranged as

Y = 10exp(dB / 10) = 10exp(7.7/10) = 5.89                                                           (4)

Substituting into Eqn (2) with Tg = 294 K and Tcs = 10 K,

Tsys  =   (294 - 5.89 * 10) / (5.89 - 1)   =    48 K 