Some of the drawbacks of this method are:

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:

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:

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.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 + TcalComputing (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:

- 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 each time.

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) socalabs=Rabs*Tabs(1.03 - .76*alpha) calsky=Rabs*Tsky(1.40 + 2.50*alpha)

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:

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

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.