TMP006 Calibration Problem

Hello,

We are having a project with TMP006 and having some difficulties in calibrating the sensors.  We have some questions:

1) Calibration calculation

As a recap, the followings are formulas from SBOU107
(1) S = S0 [ 1 + a1 (Tdie-Tref) + a2 (Tdie-Tref)^2 ]
(2) Vos = b0 + b1 (Tdie-Tref) + b2 (Tdie-Tref)^2
(3) fVobj = (Vobj-Vos) + C2 (Vobj-Vos)^2
(4) Tobj = ( Tdie^4 + fVobj / S )^0.25
(5) Calibration Function = fVobj / [ 1 + a1 (Tdie-Tref) + a2 (Tdie-Tref)^2 ]

[ 1 + a1 (Tdie-Tref) + a2 (Tdie-Tref)^2 ] is quite a mouthful, and is used in (1) and (5), so let's define
(kw1) fa = [ 1 + a1 (Tdie-Tref) + a2 (Tdie-Tref)^2 ]

Therefore,
(kw2) S = S0 * fa
(kw3) Calibration function = fVobj / fa
(kw4) Tobj = ( Tdie^4 + fVobj / (S0 * fa) )^0.25

Rearranging (kw4),
(kw5) S0 = fVobj / [ fa * (Tobj^4 - Tdie^4) ]

This means that in the perfect system, to resolve S0, we do not actually need more than one point; just substitute the measured temperature ("Trtd" from another forum thread), substitute it into Tobj in (kw5), and calculate S0 in one go.  If more than one point are measured, all of them should yield the identical S0.

In an imperfect system, if multiple data points are measured, they could yield different S0 (let's call them S0n).  To do the calibration, we can plot S0n over (Trtd^4 - Tdie^4), and find the best fit horizontal line and the vertical value becomes the calibrated S0, and this is pretty much equivalent to plotting Calibration Function over (Trtd^4 - Tdie^4) and finding the slope.

Is my understanding correct?

2) Plotting Calibration Function

From (kw3) and (kw5), it can be resolved that
(kw6) Calibration Function = S0 * (Tobj^4 - Tdie^4)

This should be why plotting the Calibration Function over (Trtd^4 - Tdie^4) and finding the slope would yield S0.

However, (kw6) also suggests that the fitted linear approximation should go through point (0,0).  This means that if the fitted line does not hit (0,0), the system is imperfect, and farther it misses (0,0), worse the system is.  Is this correct?

3) Would you provide a set of "good" sample values so we can make sure our calculation is correct?

Many Thanks,
Kelvin