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
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
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
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 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
To compute the cal values, the temperature
contributions to Tsys of various things needs to be estimated or
measured. Typical values are:
||sky + scattered ground radiation
||3 + 15=18K
||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
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
The various configurations measured are:
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=
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))
Some assumptions we normally make are:
We can eliminate Trcvr (here i assume alpha is 0) , with:
The match into the horn is good (gamma is small so G2 = 1).
Alpha is zero
Where gamma(f) is the voltage reflection coefficient for the horn/omt.
(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)
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
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:
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.
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)
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).
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
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:
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.
caldeflection/absorberDeflection increases so Tcalmeasured increases
caldeflection/skyDeflection decreases so Tcalmeasured decreases
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:
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.