# System temperature versus za.

#### july,2000

I've gone through the telescope data sets taken with the correlator (april thru july 2000) and extracted all of the cal on/off pairs (about 15000).The system temperature in the calOff portion of the cycle was computed using the tabulated cal values.
The plots can be found at:

#### Computing Tsys using the cal onoff pairs.

calOn/Off pairs typically track a position on the sky  for 10 seconds with the cal on and then continue tracking the same position (on the sky) for another 10 seconds with the cal off.  If the observer was position switching then the sequence is: positionOn, positionOff, calOn,calOff where the calOn/calOff pair tracks the off source position.

The system temperature is computed using the total power information (0 lag).  If [K] is kelvins and [corTP] are
correlator total power units (linear in power but arbitrary) then:

delta[corTP]= calOn[corTP] - calOff[corTP]  gives the size of the cal in [corTP] units
calTPtoK      = calSize[K]/(delta[corTP]  is the size of the cal in K / size of the cal in  [corTP]  so it
will  convert [corTP] to kelvins
Tsys[K]          = calOff[corTP] * calTPtoK is the system temperature.

Tsys is computed for the calOff scan so  that the cal is not included. When computing (calOn - calOff)  we assume that the difference is only do to the cal. For small cals and high zenith angle, there is a small change  from tsys(za) dependance since we continue to track the same position in the sky for the calon and caloff.

#### Fitting the system temperature za dependance:

The beam should start to spill over the dish at 15 deg za and start to leave the ground screen at 17 degrees. Looking at the data there is a linear increase out to 15 degrees za and then it turns up. I fit a linear term to za 0-20 and then a 2nd and 3rd order term for za > 14 degrees. To remove outliers, I did the fit, removed all points greater than N sigma (this is labeled on the plot) and then refit the data.

• There are two plots for each data set. One has the data labeled with + polA,  * polB .  The second plot has both Pols labeled with a period so you can see the fit to the data.
• The 3rd order fit is: Tsys[za] = c0 + c1*za + c2*(za-14)^2 + c3*(za-14)^3  where  za is in degrees and the last two terms are only included for za > 14.  The polA coefficients are in column 1 and those for polB are in column 2.
• The sigmas for the final iteration of the fit is in degrees kelvins.
• the number of points started with and the number of points used in the final fit.
• what sigma value was used to iterate the fit.
• The bandwidth * integration time is of order 10Mhz*10 seconds so 1/sqrt(b*tau)  or .01 %.  For system temperatures of 30-40 K  this is 3milliKelvins. The fit rms of  order .5 kelvins for lband is most likely from confusion .

#### lband narrow 1400-1425 Mhz

1400 through 1425 Mhz were kept giving 2157 samples. There is only 1 tabulated cal value near 1400 Mhz. The outliers for pol A + occurred when the receiver was warmed up and then cooled down during the first part of july. polA came back 4 degrees K higher than before the cycle. The solid line in the second plot is the fit. The dashed line is the fit to data taken in jul98 normalized to match this data at 10 degrees za. The edges are different but the slope 5 to 15 degrees is the same.

#### lband wide 1300-1425 Mhz then 1650-1670 Mhz

lband wide was broken into two sets 1300-1425 and then 1650-1670 Mhz (OH). The scatter in the OH may be from the galaxy in the off position raising the system temperature. Both of these bands show the linear increase in tsys 0 to 15 degrees. Also note that Tsys(1665) is about 2 degK < Tsys(1400) for lbw. The lbw OMT provides linear polarization. There is a hybrid after the dewar (switch selectable) that converts this to circular polarization. This data was taken in circular mode. The tabulated cals are for the linear mode. The cal values used here are the average of the polA,polB linear values.

#### sband narrow

sband narrow shows a flat tsys(za) out to 15 degrees za and then curves up.

#### cband

The cband data comes from a single observer who used 4.1,5,5.9 Ghz. Each frequency has a separate curve. This could be the receiver or the cal (we need to check the sefd plots for the calibrators the user had). Each individual curve looks pretty flat out to 15 degrees za.

• The Tsys(za) curve is not flat for 0 to 15 degrees for lbw,lbn. It is flag for sbn and cband. These receivers differ in the horns illumination of the tertiary. If this is a tertiary spillover problem then we still need to find a reason why the spillover is a function of za. It might be a good idea to revisit the reasons why we wanted to overilluminate the tertiary with these horns.

•
• The Tsys(za) curve turns up at 15 degrees rather than 17 degrees. Is this from the taper of the beam illumination on the dish, diffraction, or is the ground screen seeing some of the ground?

#### Tsys vs za polynomials:

The polynomial fits to Tsys vs zenith angle are listed below. The ^2 and ^3 order terms are only used for za > 14 degrees. The za is in degrees.

• lbn 1400-1425 Mhz

• polA Tsys(za)=29.474 + .13599*za + .215752*(za-14)^2  - .020024*(za-14)^3
polB  Tsys(za)=27.315 + .12809*za + .207750*(za-14)^2 - .019014*(za-14)^3

• lbw 1300-1425 Mhz circular polarizations

• polA Tsys(za)=36.550 + .12215*za + .237660*(za-14)^2 - .015145*(za-14)^3
polB  Tsys(za)=35.739 + .14101*za + .197705*(za-14)^2 - .007744*(za-14)^3

• lbw 1650-1670 Mhz

• polA Tsys(za)=34.556 + .10924*za + .215577*(za-14)^2 - .017823*(za-14)^3
polB  Tsys(za)=34.382 + .09409*za + .241162*(za-14)^2 - .020710*(za-14)^3

• sbn

• polA Tsys(za)=26.000 - .00016*za + .078998*(za-14)^2 + .005007*(za-14)^3
polB  Tsys(za)=25.127 - .00738*za + .061695*(za-14)^2 + .009357*(za-14)^3
`processing: x101/tsys/Readme for a description`
`plotting  : x101/tsys/plotall.plt`
` home_~phil`