Measuring cals using sky and absorber on the telescope


     The cals on a receiver can be measured using absorber and sky as the hot and cold load. Ideally it can be done on the antenna test range (where there is little scattered ground radiation). It can also be done on the telescope but you then need to figure out the value of scattered radiation to include when looking at the sky. The good things about measuring the cals on the telescope are:
  • The cabling is the same as normal operations. You don't need to disconnect/reconnect anything.
  • You can use the correlator to get frequency information for resonances in the omt and rfi.
  • You can cover the entire band rapidly since you can put the cals, correlator, and lo's under computer control.

  • Some of the drawbacks of this method are:
  • Since the absorber is 300K it's hard to measure the small cals.
  • Rfi coming bothers you while on the sky (and occasionally on the absorber).
  • You don't know the scattered radiation value (although you can make some educated guesses).

  •    The procedure is to fire the cal on/off with the absorber  in place and then repeat this on blank sky.  You should also use a thermometer to measure the temperature of the absorber. If possible, measure the receiver temperature (Tamp + Tomt) on the test range prior to doing this experiment.
        Some receivers have up to 8 different cals (hi correlated, hi uncorrelated, hi correlated 90deg phase shift, low ....). We normally measure the high correlated cal using the sky and absorber. Later we track blank sky and measure the ratio of the other cals to the one measured on the sky,absorber.

        The correlator  is  setup as 4 subcorrelators of 25 Mhz by 256 lags. The integration time is set to 5 seconds cal off followed by 5 seconds cal on.  To cover the entire frequency range of the receiver the LO needs to be stepped by 100 Mhz increments. We normally repeat the entire receiver frequency range 3 times to make sure we don't have any interference. The measurement is automated and takes about 8 minutes to measure a 1 Ghz band 3 complete times (on absorber or on sky). For this bandwidth and integration time the radiometer equation on the absorber for calon/caloff gives: 300K*sqrt(2)/sqrt(25e6*5secs) which is less then .04 kelvins. Cals run from 2 K to 60 K so .04 kelvins is no greater than 2% error.

         To compute the cal values, the temperature contributions to Tsys  of various things needs to be estimated or measured. Typical values are:
    typical temperatures
    Tamp from amplifiers  8K
    Tomt orthomode transducer 4 K
    Tabs absorber temperature 300 K
    Tsky sky + scattered ground radiation 3 + 15=18K
    Trcvr Tamp+Tomt 8 + 4 = 12K

    Tabs can be measured with a thermometer. Trcvr can be measured on the antenna test range. The major uncertainty is Tsky (the scattered radiation component).

        Another problem is the  match of the signal from the sky/absorber into the amplifier.  The reflection coefficient (gamma) is the fraction of the voltage that gets reflected. If the absorber temperature is Tabs then (1-gamma^2)*Tabs actually makes it to the OMT. Lets call G2=(1-gamma^2). G2(f) is a function of frequency.
        If there is a fractional loss alpha in the OMT (resonances, etc) then alpha*Tinput is lost while alpha*Tomt is added.
        For the receiver systems that we use the amplifiers tend to be wider band than the polarizers (omt's) and the cals are injected after the polarizers. So the Tsky,Tabs are affected by G2 but Tcal,Trcvr is not.

    The various configurations measured are:

    Trcvr + Tabs*G2(1-alpha) + Tomt*alpha  and   Trvcr + Tabs*G2(1-alpha) + Tomt*alpha + Tcal
    Trcvr + Tsky*G2(1-alpha) + Tomt*alpha  and   Trcvr + Tsky*G2(1-alpha) + Tomt*alpha + Tcal
    Computing (CalOn-CalOff)/CalOff gives the measured Ratios:
    Rabs= Tcal/(Trcvr + Tabs*G2(1-alpha) + Tomt*alpha)
    Rsky= Tcal/(Trcvr + Tsky*G2(1-alpha) + Tomt*alpha)
    CalAbs=Rabs*Tabs(Trcvr/Tabs + G2(1-alpha) + alpha(Tomt/Tabs) or
    CalAbs=Rabs*Tabs(G2 + Trcvr/Tabs + alpha(Tomt/Tabs - G2))
    CalSky=Rsky*Tsky(G2 + Trcvr/Tsky + alpha(Tomt/Tsky - G2))
    The major uncertainties in the Cal  values are Trcvr, Tsky (actually Tscattered),  G2, and alpha. When using the absorber the relative error in the rcvr temperature is at most 5 deg K or about 2%. On the sky the error in the scattered radiation may be 5 degrees. This is a 5/18= 30% error.
        Some  assumptions we normally make are:
    1. The match into the horn is good (gamma is small so G2 = 1).
    2. Alpha is zero
    We can eliminate Trcvr (here i assume alpha is 0) , with:
    (Rabs - Rsky) = Tcal*G2( Tsky - Tabs) / ((Trcvr+Tsky*G2)*(Trcvr+Tabs*G2))
    Rabs*Rsky     = (Tcal)^2 / ( Trcvr+Tsky*G)*(Trcvr+Tabs*G2)
    (Rabs*Rsky)/(Rabs - Rsky) = Tcal / (G2*( Tsky - Tabs))
    Tcal=  (Rabs*Rsky)  * G2 * ( Tabs - Tsky) / (Rsky - Rabs)
    Where gamma(f) is the voltage reflection coefficient for the horn/omt.
    We've measured all of the ratios (R's) and we have a measurement of Tabs from a thermometer.  We then only have to estimate Tsky (main beam plus scattered radiation) and assume gamma is zero.
    note: Engineers will talk about the Y factor when doing the above ratio. I can never remember which way it goes so i just rederive the equation each time.

    Figuring out Tsky and Trcvr:

       If the correct temperature values have been used and both gamma and alpha are zero, then  the cal value computed using just the absorber, just the sky, and the ratio of the two should all agree.  You can use this to determine Tsky and Trcvr (unless electronics has measured Trcvr versus frequency for you).
  • Use the receiver frequency range where gamma and alpha should be the smallest.
  • Since Tabs >> Trcvr , CalAbs is not very sensitive to Trcvr. CalRatio is not a function of Trcvr. So pick a reasonable value for Trcvr and then adjust Tsky so CalAbs and CalRatio agree.
  • Using Tsky from above, adjust Trcvr so that CalSky agrees with CalAbs,CalRatio. You may want to iterate this process once.
  • Trying to get a handle on alpha.

        Alpha affects CalAbs (computed from the absorber) and calSky (computed from the sky) differently. Most of our receivers have an OMT at 70K (although the higher  frequency ones are coolled to 20K).  If we use typical numbers for the temperatures (Tabs=300, Tsky=20,  Trcvr=8,Tomt=70) and G2 =1 the cal equations become:
    CalAbs=Rabs*Tabs(1 + 8/300 + alpha(70/300 - 1)
    CalSky=Rabs*Tsky(1 + 8/20. + alpha(70/20. - 1) so
    calabs=Rabs*Tabs(1.03 -  .76*alpha)
    calsky=Rabs*Tsky(1.40 + 2.50*alpha)
    If the computation sets alpha to zero then CalAbs will be too Big, and  calSky will be too small. As an example let alpha be .1. Then CalAbs will be CalSky will be 15% too small. So alpha will have a larger affect on calSky. For receivers with Tomt=20K, alpha will not affect calSky at all and it will have a large affect on CalOmt.

    Learning about the receiver:

        The results from the cal can also tell you something about the receiver system, in particular gamma (the reflection coefficient)  and alpha (the absorptive loss).

        The  cal value is  Tcal =(1-gamma^2)*Tabs*(caldeflection/loaddeflection). We've assumed that gamma is zero so the measuredTcal will be larger than normal if gamma is nonzero. The increase in Tcalmeasured should occur for bothTcalabs and Tcalsky.

        If alpha (the absorbption) is non zero (say a resonance in the OMT where Tomt=70K) then (1-alpha) of Tomt will replace (1-alpha) of Tabs or Tsky. The absorberdeflection will decrease (Tomt<Tabs) while the skydeflection will increase (Tomt>Tsky). The measured ratios are then:

    caldeflection/absorberDeflection increases so Tcalmeasured increases
    caldeflection/skyDeflection      decreases so Tcalmeasured decreases
        If you see Calabs and Calsky diverging, then it may be because of losses. You could also go to a resonance in the OMT and measure Calabs and Calsky to give you a value for the size of alpha.


    The following problems have occurred while doing this:
  •  Interference in Tsky. Since you've measured the same frequency band 3 times you will see rfi as scatter in the 3 measurements. You can look at the spectra and attempt to excise it (as long as things have remained linear). Beware that you can also get interference with the absorber in place. If rfi is bad only in the sky measurements, you can use the absorber measurements to interpolate across this region. Many of the radars have 10 to 12 second rotation periods. If the integration time for cal on or cal off is 5 seconds then you may get the radar pointing at us only in the cal on or only in the cal off. It's probably better to make the cal integration time a multiple of the rotation period so the cal on, cal offs are not biased by the radar.
  •  Resonances in the OMT. These tend to be a few Mhz wide. You can use the spectra to excise them or just interpolate between adjacent 25 Mhz bands. This can be a problem if the receiver temperature was measured up on the test range and was taken as total power measurements.
  • The match of the absorber into the horn is not good. You can move the absorber up and down a few inches and see how the power output changes.
  • Don't take the absorber out of the air conditioned turret room and start measuring immediately. If water starts to condense on the absorber, it's reflection properites change. This also happened when there was a gap between the receiver and the rotary floor. Cold air from the turret room blew down on the absorber and caused problems.

  •     The results not agreeing over a particular part of the frequency range of the receiver is probably pointing to a problem in the receiver.

    Measuring the other cals using the ratio of the sky/absorber cal.

        We measure the temperature of the high correlated cal using the above procedure. To get the other cal values, we track blank sky and run the sequence:
  • hcorcal(on,off)
  • hcal(on,off),hxcal(on,off),h90cal(on,off)
  • hcorcal(on,off)
  • lcorcal(on,off),lcal(on,off),lxcal(on,off),l90cal(on,off)
  • hcorcal(on,off)

  •     Each cal transition is for 5 seconds. These 10 measurements are repeated in 100 Mhz junks across the entire band. The cal values in Tsys units are  computed at 100 mhz spacing after filtering the cal on/off spectra. The ratio is taken with the hcorcal (interpolating between the 3 hcorcal measurements to correct for tsys variation with za). The cal in kelvins is formed by multiplying the ratio by the measured hcorcal value from the sky, absorber.
        Since the sky << absorber temperature, it is easier to measure the low cals using this method.