# Tempcos was: Re: New(?) ideas for the new year

Martin Czech martin.czech at intermetall.de
Wed Jan 7 15:13:35 CET 1998

```> Hi Martin, and a happy new year,
Same to you !!

> True, a NTC of that kind has a *exponential* behaviour, that is the resistance
> changes by some *factor* (0.04 = 4%) with temperature. (yep, very nonlinear).
> But -3300ppm/K is also an exponential change, since what ever the value of
> our current

Well, when I measured the NTC I was imidiately disappointed and stopped
the whole idea. Maybe too early ?

Ok, what do we need ?
For the 101th time (please forgive me ! :>)

Exponential generator temperature compensation.
The current out of a matched pair expo converter
looks like this (1st order explanation):

I=Iref*exp{Rl/(Ru+Rl)*Ue/Ut)}

where :

Iref : reference current
Rl   : voltage divider lower leg
Ru   : voltage divider upper leg
Ue   : input voltage fed to divider
Ut   : Kb*T/q or shorter a*T where a ~ 8.625e-5 V/K

This temperature voltage Ut by law of physics is the reason for all
this temperature bla bla.
Example : Ut (273K = 0C  ) : 23.5mV
Ut (373K = 100C) : 32.2mV that's ~36% more!

We could simply put a controlled oven around the expo-converter, to keep
the temperature always say at 50C (what some critical crystal oscillator
applications also do, so this is not so stupid as it may sound).

Or we could make Rl or Ru depend on temperature to compensate for Ut changes.

We need I=Iref*exp{ln(2)*Ue/V} (one Volt per octave)

=>   Rl/(Ru+Rl)*Ue/Ut=ln(2)*Ue
=>   Rl=Ut*ln(2)/(1-Ut*ln(2))*Ru

If we say that Rl should depend on T we get:

a*T*ln(2)
Rl(T)= ---------------- * Ru
1-a*T*ln(2)

If we say that Ru should depend on T we get:
1
Ru(T)= (------------- - 1) * Rl
a*T*ln(2)

OK ??

So we can see that in both cases the needed temparature curve
of Rl or Ru is not linear at all, also the first derivations
are not linear.

But Rl(T) can be aproximated by a linear function with very little
error, e.g. between -40C and 110C only 0.15% error:

Rl(T) ~ R0+r*T , R0 is often measured at room temperature 27C and T is
in this case not the absolute temperature, but the difference to room
temperature.  That is the famous resistor with linear positive tempco
of ~3300 ppm at room temp. Which can be obtained by wirewound resistors
which are very hard to get.

Now the other leg :

Ru(T) can not be well aproximated by a linear function, e.g. the error
is 6% between -40C and 110C. A negative tempco would be required, we don't
have any device with such a negative linear behaviour.

But: As Rene proposed, we have NTC-thermistors, they are cheap and easy to
get. Some suppliers also have low tolerance types which are a bit more
expensive (RS Components, I think).
As Rene said, the behaviour of a NTC is exponential:

R(T)=K1*exp{-K2*T}+R0

Maybe with some non ideal resistance R0.

This seems to be a completely different function than the required

1
Ru(T)= (------------- - 1) * Rl.
a*T*ln(2)

But this is not the question.
The Question is: how good does it approximate the wanted behaviour?
We could also add some fixed value resistor in parallel or series
or both to get the wanted behaviour. This is what Rene proposed.

Now, I'm really courious what K1 and K2 where, when I measured
my NTC. I've got the plot at home.

Rene, do you have values for K1, K2 and R0 ?

Even if it turns out, that the NTC method won't work under all conditions,
it could be good enough to compensate an expo-vca etc.
Maybe I was completely wrong, and NTC is THE solution for the
compensation problem.

Ice water and boiling water is a good idea.
It should be possible to get temperatures in between by mixing
hot and cold water, with specific heat in mind. Energy=T*K*mass.
After mixing, the energy should be the sum of both energies.
On the othrt hand, digital thermometers are cheap these days...

m.c.

------------------------------------------------------------------------
m.c. has made it finally:  3 CDs out now; 72 min. minimum; "1"
(1994-1995),"2" (95-96),"three" (96-97); experimental stuff; mostly
Eimert/Stockhausen style; but also modern popular style

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