Intro

The 12meter has the following cal diodes:

xband: temperature stabilized single diode feeding polA and polB

08nov21 xb diode temperature stabilized.
06jun22 new xb diode to make room for sb diode in peltier cooler. no attn
907jun22 added 7,7 db atten to output of peltier xb box. Should have been 3,2 db

sband: temperature stabilized single diode feeding polA and polB

08apr22 installed but no temperature stabilized
06jun22 sb diode temp stabilized but no attenuators
07jun22 : added 3,2 db attens. (should have been 7,7)

The model to get Tcal from the sky, absorber measurements

Let gamma (g) be the reflection coef (voltage) from the horn and omt (I'm assuming the amp is perfect..)

If the input temperature (sky or absorber) is T
T*(1- gamma^2) will get to the next stage. Let (1-gamma^2)=G2 . G2(f) should be a function of frequency.

Let alpha be the absorption by the omt (say a resonance or dielectric).

If we have Tinput to the OMT then

Tinput*alpha is lost and
Tomt*alpha is added to the temp

The calon,off, sky , absorber measurements then measure

	CalOn	CalOff
abs	Trcv + TabsG2(1-alpha) +Tomt*alpha + Tcal	Trcv + TabsG2(1-alpha) +Tomt*alpha
sky	Trcv + TskyG2(1-alpha) +Tomt*alpha + Tcal	Trcv + TskyG2(1-alpha) +Tomt*alpha

The calRatio= (CalOn - CalOff)/CalOff can be computed for the abs and the sky measurements:

(1). calRatioAbs= Tcal / (Trcv + Tabs*G2*(1-alpha) + Tomt*alpha)
(2). calRatioSky= Tcal / (Trcv + Tsky*G2*(1-alpha) + Tomt*alpha)

solving (1) (2) for Tcal_xxx gives:

(3.) Tcal_abs= calRatioAbs*Tabs*(Trcv/Tabs + G2*(1-alpha) + Tomt*alpha)
(4.) Tcal_sky= calRatioSky*Tsky*(Trcv/Tsky + G2*(1-alpha) + Tomt*alpha)

Using (1) (2) you can eliminate Trcv: (I've shortened calRatioAbs to Rabs, calRatioSky to Rsky).

(1/Rabs) - (1/Rsky) = (1./Tcal) * (1-alpha)*G2*(Tabs - Tsky) or:
(5). Tcal= (Rabs*Rsky)/(Rsky - Rabs) * [(1-alpha)*G2*(Tabs - Tsky)

The parameters needed to compute the cal value are:

Measured:Rabs,Rsky, Tabs,

guess: Tsky at sband may be 8 K plus some scattered radiation and clouds.

Unknowns:

G2=(1-gamma^2)
alpha
Trcv if we use (1.) or (2.).

the amp spec says it is about 50K. there could be some additions from things after the amp.

When using (1) or (2) to compute Tcal

Trcv does not affect Tcal_abs because Tabs is much larger
Trcv will affect Tcal_sky a lot more since Tsky is smaller that Trcv.

How big would we expect G2 (1-gamma^2) and alpha to be?

For the 305 meter cals we assumed that gamma was close to 0 (G2=1) and that alpha was 0 (no absorption)
Those assumptions may not be valid for the dual frequency s-x feed on the 12meter. The omt contains some dielectric and Trcv is much higher than the cooled amps of the 305m receivers.
For most of the 305m receivers we also had a separate measurement of the rcvr temperature taken with the horn pointing up at blank sky.

What I ended up doing was playing with Trcv, gamma and alpha till i could get the 3 different measurements of Tcal (3.) (4.) and (5.) to agree.
This was possible since the 3 measurements were affected differently by gamma and alpha. I really should have just written a nonlinear fit to get the best values of Trcv, alpha , and gamma (maybe next time :)

Cal measurements:

date	rcvr	measurement	measurements installed	valid dates
				start	end
230520	wb	cooled receiver, 4" shims	230620,230727	230620	current
230530	wb	cooled receiver, 2" shims		230516	230520
220624	sb	switch cal attenuators 3,2 -> 7,7 db	220628	220624	230301
220624	xb	Switch cal attenuators:7,7->3,2db	220627	220624	230301
220607	xb	new diode, attenuators installed on polA,B outputs (7,7)db	220607	220607	220623
220607	sb	attenuators installed on polA,B outputs (3,2)db	220607	220607	220623
220606	sb	diode now on peltier cooler.attns not installed, no measurements done
220527	sb	sb diode with no temperature stabilization.	220601	220408	220606
220117	xb	measured cals using sky and absorber peltier cooler installed 08nov21.	220120	211108	220607

12 meter cal diode values

Intro

The model to get Tcal from the sky, absorber measurements

Cal measurements: