J

#### Jon Kirwan

- Jan 1, 1970

- 0

Not in my experience. (but my experience is fiarly limited... a few

transitors tested.)

I always got a number that was a bit off ~0.3%, so about 1 degree at

room temp. I always assumed the error was due to the transistor

beta... Since the current is Ic and Ib. (I think I got a temperature

that was always a bit high, but I'd have to check my notebook.) You

could add some beta 'fudge factor'.... but then beta changes with

temperature too.

It also depended a bit on the collector current. (1 uA to 10uA were

'nice' currents)

Hi, George. I posted up a link to Linear's AN45 elsewhere

under this topic. See page 7 there. But I take your

experiences here seriously and wanted to think about this,

not at the 'charged gas' theory level but at the higher (and

more usual for an EE) device modeling level.

The two-current pulse method, using say 1X and 10X currents,

depends upon the following:

dV = (k/q) * ln( 1+Ic/Is ) dT

Although k and q are known, the entire factor that includes

the ln( 1+Ic/Is ) part isn't knowable in advance. But if one

assumes that the +1 term is negligible then the two pulsed

currents results in:

dV1/dT = (k/q) * ln( Ic1 ) - (k/q) * ln( Is )

dV2/dT = (k/q) * ln( Ic2 ) - (k/q) * ln( Is )

Subtracting dV1/dT from dV2/dT yields:

dV1 - dV1 = (k/q) * ln( Ic2/Ic1 ) ) dT

And if the ratio of Ic2/Ic1 is known a priori then the entire

factor, (k/q) * ln( Ic2/Ic1 ) ), is also known. And as a

consequence could be used to measure temperature without

having to calibrate the system. Or so it seems at first

blush.

But it's also the case that the value of the saturation

current, Is, is itself a rather complex function of T:

Is(T) = Is(Tn) * (T/Tn)^3 * e^( -(q*Eg/k) * (1/T-1/Tn) )

Where Tn is some chosen T(nominal).

In fact, this particular component is what overwhelms the

first equation (which is positive vs temperature) and yields

the usually quoted -2mV/K figure (very approximately.) So, in

fact, Is(T) is the dominant factor in Vbe change over T and

in no possible way is it a simple function of T!

(Even the above Is(T) equation itself is a simplification.

The power ((T/Tn)^3) for example is an approximation and not

strictly true in practice. Same with Eg, which itself is also

taken as a single approximation value.)

Just as a guess, the idea of ln( Is ) being cancelled

entirely out of the equation by ratiometry, even assuming

that the die is at thermal equilibrium, would make me worry a

little. (I accept that pulsing the 1X/10X current change fast

enough or that using low enough currents, like the 1uA and

10uA you mention, would yield a near-equilibrium state.) I'm

just not sure that at this level of modeling, that _Is_

remains dead stable as a modeling parameter when facing a 10X

current change. There is a lot of linearity over orders of

magnitude change, as a broad statement. But exactly how

linear is it when provided a two point ratio a decade apart,

vs device variation?

I wonder that some temperature error is swept under this

Is(T) rug and hidden from the analysis, so to speak. Even

assuming thermal equilibrium. Because it may really be that

Is(V,T), not Is(T), as both the power (^3) and Eg are taken

as simple constants for simplification when they aren't, in

fact, invariant at this level of modeling.

You mention base currents as a possible error. I've ignored

that so far. The equation:

dV = (k/q) * ln( 1+Ic/Is ) dT

in the diode connected case refers to Ic. The currents

through it, on whole, are (beta+1)/beta times as much. If you

cobble up precision current sources at exactly 1X and 10X,

the ratio of Ic2/Ic2 would still be 10, even though you are

driving Ie, I think. However, beta itself changes vs Ic. So

there is that to account for, if you were only using a beta

level model. But the:

dV1 - dV1 = (k/q) * ln( Ic2/Ic1 ) ) dT

method doesn't use or rely upon beta. So I'm not imagining a

problem there because (1) the ratio is still 10X and (2) beta

isn't used in the analysis method.

Interesting problem getting past a certain level of accuracy,

though. There must be several papers that go beyond the AN45

app note I'd posted up earlier. I haven't seen one, yet.

Jon