Intro

•  Tx   temperature of  x (in kelvins)
• Px    power measured when configure to look at x
• fl     : receiver flange . can be Tfl or Pfl
• h     :  hot config. can be Th or Ph
• c     : cold config. Tc or Pc
• Yx   : ratio of Ph/Pc  for configuration x
• abs : absorber .. usually at 300K
• sky  : contribution from sky 3deg cmb + clouds
• scat: radiation scattered into the feed
• gnd : measurement done with horn on the ground looking up
• ant :  measurement done with the horn mounted on the antenna.
  
• dut  : device under test.
• g     : gain between dut and measurement device (spectrum analyzer)
• KtB : boltzman's contstant time bandwidth
  

deriving the Yfactor equation:

• Measure the power using the hot and cold loads.
• Ph=(Th + Tdut)*gain*KtB
• Pc=(Tc  + Tdut)*gain*KtB
• (Ph/Pc)=Ydut=(Th  + Tdut)/(Tc +Tdut)
• Tdut=(Th - Tc*Ydut)/(Ydut -1)

flange temp: rcvr on ground, rcvr on antenna

    The flange temperature is the temperature at the mouth of the feed. This can be done with the horn on the ground looking up or on the telescope. The flange temperature should be the same in both cases (if you use the correct Tc values).

• You measure the flange temperature using a hot and cold load
• hot load:
  
• absorber.. around 300 Kelvins
• same value for ground and antenna
  
• cold load:
• Tsky: Tcmb + Tclouds. assumes no scattered radiation.
• Tant: Tsky  + Tscat  .. Tscat is the ground radiation scattered into the the feed.
• Ygnd is the Yfactor  measurement done with the horn on the ground looking up:
  
• Tflgnd=(Tabs - Tsky*Ygnd)/(Ygnd -1)
• Tc is just Tsky
• Ygnd is the Ph/Pc measured when rcvr on the ground looking up
• Yant is the Yfactor measured with horn on the antenna
• Tflant=(Tabs -(Tsky +Tscat)*Yant)/(Yant -1)
• Tflant =  Tflgnd (since the flange temperature will not change)

Measuring  Tscat (scattered into the horn on ant)

• Tflant=(Tabs -(Tsky +Tscat)*Yant)/(Yant -1)  or
  
• Tflant= (Tabs - Tsky*Yant)/(Yant -1)  - (Tscat*Yant)/(Yant-1)
• let Tflant' = (Tabs - Tsky*Yant)/(Yant-1)
• This does the  computation with Tc = Tsky, leaving out Tscat.
• Tflant= Tflant' -(Tscat*Yant)/(Yant-1)
  
• Tflant -Tflgnd=0
• Tflant'- Tflgnd= Tflant - Tflgnd  - (Tscat*Yant)/(Yant-1)
• deltaT'=Tflant' - Tflgnd=  Tscat/(1. - 1/Yant)
• Tscat = deltaT'*(1-1/Yant)
• Yant should be about 300/(10+20)=10
  
• so Tscat will be about .*Tflant'
  

Summary

• Tdut=(Th - Tc*Ydut)/(Ydut -1)
• Tflgnd=(Tabs - Tsky*Ygnd)/(Ygnd -1)
• Tflant=(Tabs -(Tsky +Tscat)*Yant)/(Yant -1)
• Tflant=Tflgnd
• Tflant' = (Tabs - Tsky*Yant)/(Yant-1)
• deltaT'=Tflant' - Tflgnd=  Tscat/(1. - 1/Yant)
• Tscat = deltaT'*(1-1/Yant)
• (1-1/yant) will be around .9 If Tabs=300 and (Tsky + Tant)=(10+20)
  

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