You'll also get differences between NPN or PNP types because each type has different area and bulk resistance. A transistor temperature sensor can't be expected to have 0.5 K accuracy without calibration.
You didn't clarify if (and how) bulk resistance is compensated with your measurement.
I presume that the used transistor equations still involve some idealization. What's the specified accuracy?
Yes, the equation being used is the ideal diode equation:
T (in Kelvin), q, k, n, Is, and Iforced.
We can hardly discuss the said models and equations without seeing it.The data supports an NPN transistor, but not a PNP. The claim so far is that a PNP is not compatible and I do not agree.
1) NPN: I_in = Ic + Ib
2) PNP: I_in = Ie
Are you trying reinvent electrical circuit theory?in that case order from left side to right side matters.
We can hardly discuss the said models and equations without seeing it.
The equations I'm familiar with (e.g. SPICE model equations) have a certain range for involved constants, so they can give slightly different results for NPN and PNP.
You forgot line 3
Ie = Ic + Ib (by application of Kirchhoff's first law) https://en.wikipedia.org/wiki/Kirchhoff's_circuit_laws
I see several empirical parameters discussed in the paper that are assumed to have a certain value, e.g. the said "nonindeality factor". In so far it's more a guess than certainty that different batches of 2N3904 and 2N3906 always show exactly the same characteristic. The usual transistor sensor application in CPU chip temperature measurements would have no problems with 0.5 (or slightly higher) temperature offsets.
You insist to use the "standard diode equation" but I'd bet you
have nothing for n or Is, which are the primary fitting params.
PNP devices often have inferior collector resistance and since
you want to operate at Vbe(ext)=Vce(ext) you may be running
into onset of saturation at higher temp and higher currents,
with this bending the hFE-vs-Ic curve (which, hFE, is what
linearizes the transdiode relative to what you'd get from the
E-B junction alone - more decades of log-linearity, suppressing
the series resistance).
Switching transistors may employ charge gettering features
in the base and collector which make saturation worse in the
sense of Vce(sat) achievable (and there lies your margin
against Vbe-Ic*Rc, Vbe=Vce(ext)). Shorted-junction plugs
and the like take you away from idealized models at higher
level injection.
It would not be the least bit surprising to see base doping differ
by factors of 2-5 between NPN and PNP, especially when you
are talking about devices that aren't even asserted to be
"complementary" and are not co-processed. Complementary
vertical bipolar technologies at least used to take a stab at
gross matching of Vbe(NPN):Vbe(PNP) but in discrete world,
you'd have to dig.
The unsaid prerequisite is that the used transistor model parameters exactly reproduce the nonideal device behaviour, including the small differences between NPN and PNP. Possible but not neccessary.I did run my own sim in TINA spice using an NPN and a PNP. I do see a difference in delta-Vbe, so this may be something of interest to look into. The currents in the lab being used are very low; <100uA. I don't think saturation of Vce is the issue, but I'll certainly look at it again.
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