Tsys measurement, C/X CA03/4 2010-06-15

## Procedure

• Jock was at antenna, I was controlling the correlator
• Jock placed hot box to cover the main window of the focus room; the antenna was in park position
• Attenuators were set on the correlator to get GTP in default tvchannels to a level of around 700
• A 3 minute (18 cycles) run was made for each frequency setup of (IF1/IF2 centre freq) 5500/9000, 5000/8500, 6000/9500
• After taking data while looking at the hot box, the hot box was removed and its temperature measured
• Data was recorded while looking at sky
• The hot box was replaced, and data was recorded
• The hot box was again removed and its temperature measured, and sky data was recorded

### Schedule

The schedule used was ste616_cband_tsys.sch. It has 6 scans:

• tsys_c_sky1 : Sky load, IF config 5500/9000
• tsys_c_hot1: Hot load, IF config 5500/9000
• tsys_c_sky2: Sky load, IF config 5000/8500
• tsys_c_hot2: Hot load, IF config 5000/8500
• tsys_c_sky3: Sky load, IF config 6000/9500
• tsys_c_hot3: Hot load, IF config 6000/9500

### Files

• 2010-06-14_2321.C999
• hot box in position on CA03, Thot=295.4 K
• 2010-06-14_2333.C999
• looking at sky on CA03
• 2010-06-14_2345.C999
• hot box in position on CA03, Thot=296.9 K
• 2010-06-14_2358.C999
• looking at sky on CA03
• 2010-06-15_0107.C999
• hot box in position on CA04, Thot=298.2 K
• 2010-06-15_0120.C999
• looking at sky on CA04
• 2010-06-15_0132.C999
• hot box in position on CA04, Thot=298.2 K
• 2010-06-15_0144.C999
• looking at sky on CA04

## Analysis

### Theory

The simplest way of expressing the relation between the power received and the system temperature is:

(1)
\begin{align} P = A \times T_{sys} \end{align}

That is, if no power is being input into the system, the power received is just some factor multiplied by the system temperature. In this equation, $P$ is power in Jy, and $T_{sys}$ is the system temperature in Kelvin.

When the antenna is observing a load with some brightness temperature $T_{load}$, the power becomes:

(2)
$$P= A ( T_{sys} + T_{load} )$$

For our situation we observe two different loads, each of which has a different $T_{load}$, while we assume that $T_{sys}$ remains constant.

(3)
$$P_{hot} = A (T_{sys} + T_{hot})$$
(4)
$$P_{sky} = A (T_{sys} + T_{sky})$$

Assuming that the hot load has a higher temperature than the sky, we can rearrange this equation to solve for $A$ in terms of measurable quantities:

(5)
$$P_{hot} - P_{sky} = A (T_{hot} - T_{sky})$$
(6)
\begin{align} A = \frac{(P_{hot} - P_{sky})}{(T_{hot} - T_{sky})} \end{align}

Here it should be noted that both $P$ and $T_{sys}$ are frequency dependent, however because we expect both the hot box and the sky to be blackbodies, $T_{hot}$ and $T_{sky}$ do not change with frequency.

We now have a way of obtaining $T_{sys}$:

(7)
\begin{align} T_{sys} = \frac{P_{hot}}{A} - T_{hot} \end{align}
(8)
\begin{align} T_{sys} = \frac{P_{hot}(T_{hot}-T_{sky})}{(P_{hot}-P_{sky})} - T_{hot} \end{align}

The receivers have a noise diode that is injected into the feed horn in addition to the signal already coming in. It is designed to be approximately 1/20th as "warm" as the system temperature.

Let the noise diode temperature be $T_{cal}$ and the power received with the noise diode on be $P_{cal-on}$. Then $T_{cal}$ can be solved for in the following way:

(9)
$$P_{cal-on} = P + P_{cal}$$
(10)
$$P_{cal-on} = A(T_{sys} + T_{load} + T_{cal})$$
(11)
\begin{align} T_{cal}=\frac{P_{cal-on}}{A} - (T_{load} + T_{sys}) \end{align}

### Data Reduction

The first step is to extract the data from each RPFITS file and generate text logs of the autocorrelation power spectra. The script make_logs.pl does this. At the end of this script, log files tsys_c_{hot,sky}[1-3]_freq_ca0[34]_{xx,yy}_{off,on}_data[1-8].log are created. Here, the hot,sky signifies the load, 1-3 signifies the frequency config, and freq is the actual centre frequency in MHz, [34] is the antenna, xx,yy is the polarisation, off,on signifies whether the data is with the noise diode off or on, and [1-8] is the experiment number.

With these logfiles created, the system temperatures can be calculated by the calc_systemps.pl Perl script. It is used in the following way:

calc_systemps.pl Thot Tsky hot_spectrum.log sky_spectrum.log cal_spectrum.log

where Thot is the temperature of the hot load (K), Tsky is the temperature of the sky load, hot_spectrum.log is a logfile that represents the power while observing the hot load, sky_spectrum.log is a logfile that represents the power while observing the sky (and must have the same configuration as the hot load log), and cal_spectrum.log is a logfile that represents the power while the noise diode is switched on and the hot load is being observed.

The sky temperature Tsky is assumed to be the CMB temperature of 2.725 K (http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation). No correction for atmospheric absorption is applied here, as Burke & Graham-Smith ("An introduction to Radio Astronomy", S7.11) state that:

At radio frequencies below about 10 GHz atmospheric absorption is small and often negligible…

This script then calculates the system temperature as a function of frequency using the equations shown above. It also makes a plot of system temperature vs frequency and noise diode temperature vs frequency. It also writes out a logfile systemps.log that has 3 columns, the first being frequency in GHz, the second being the system temperature in K, and the third being the noise diode temperature in K.

For example, the command:

calc_systemps.pl 295.4 2.725 logs/tsys_c_hot1_5500_ca03_xx_off_data1.log logs/tsys_c_sky1_5500_ca03_xx_off_data2.log logs/tsys_c_hot1_5500_ca03_xx_on_data1.log

gives the plot output:

In this image, the green line is the system temperature, and the blue line is the noise diode temperature.

The shell script run_through_systemps.sh automatically goes through all the log files generated before and runs calc_systemps.pl accordingly. The output logs are named systemps_freq_{xx,yy}_ca0[34]_data[1,3,5,7].log.

These logs can be plotted and smoothed by the Perl script plot_systemps.pl. The shell script make_systemp_plots1.sh takes care of generating the plots from the individual log files. For example, the command:

plot_systemps.pl logs/systemps_5500_xx_ca03_data1.log logs/systemps_5000_xx_ca03_data1.log logs/systemps_6000_xx_ca03_data1.log —minfreq 4.1 —logplot —title "CA03 6cm X Polarisation" —plot ca03_6cm_x_polarisation_run1.png/png —avgout ca03_6cm_x_polarisation_run1.avg

makes the plot:

In this plot, the coloured lines are the system temperatures that were found in the files listed on the command line; the colours are in PGPLOT order representing the order that the logs were given on the command line. The white dashed line is the smoothed average of these coloured lines. In this case, the system temperature values have been smoothed over an 8 MHz interval (the default smoothing). This smoothed averaged system temperature data is written out to the file ca03_6cm_x_polarisation_run1.avg.

The shell script make_systemp_plots1.sh goes through all the appropriate log files and generates the averages using plot_systemps.pl.

Finally, the plot_averages.pl script is used to plot the smoothed and averaged system temperatures and noise diode temperatures against each other for meaningful comparison.

## Results

### Consistency between experiments

These plots of CA03's system temperatures at 6cm wavelengths show that between the two independent experiments, there is only a small difference in the results.

### Polarisation differences

#### 6 cm

Here we can see that the system temperatures are slightly different between the two orthogonal polarisations on both CA03 and CA04. More significant differences are observed on the "wings" of the band where the system temperature rises significantly.

#### 3cm

The differences between the polarisations are more pronounced at 3cm than for 6cm, and even the shapes of the bands differ significantly.

### Overall comparison

These two figures suggest that the 6cm receiver is far more consistent between polarisations and antenna than the 3cm receiver, although the differences in temperature scale may be partly responsible for that impression.

### Noise diode temperatures

page revision: 53, last edited: 21 Jun 2010 23:03