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

Rene Schmitz uzs159 at uni-bonn.de
Tue Jan 6 00:03:32 CET 1998

```Hi Martin, and a happy new year,

At 08:42 05.01.1998 +0100, you wrote:
>> The other thing is: I calculated a method of temperature compensation with
>> cheap negative tempco resistors. (Those who look similar to ceramic caps)
>> Most of them have a negative exponential behaviour, with a tempco of -4%
/ deg
>
>Mhh, I bought some thermistors a while ago (looking like a nut&bolt, I
>think they where for motor protection etc. and also "cap" like) and
>then I put them into a thermostream.  Since these are semiconductor
>elements (like all cheap tempco stuff) the R/T behaviour is very
>nonlinear. A "tempco" of -4%/K will only be valid at one temperature,
>the "tempco" will decrease with temperature.

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
in our transistor may be, at one degree higher its 0.9967 *times* that value.
So an exponential factor is needed! When we use a "linear" PTC tempco
in a voltage dividers lower leg, that is exactly what we get, the attenuation
changes by a factor. (I know that log, exp stuff is very confusing.)
I hope you see the difference, if I had said like 50 Ohm per degree,
you would be right. Ohms per degree would be more accurate for Q81 and the like.
(Actually its 0.0033*1Kohm per degree)
Its a completely different thing the tempco of a
metallic conductor and the exponential "tempfactor" of a NTC.

Above I put the linear in doublequotes since I used to study physics for
some time,
and I know for *sure* (I did measurements on both kind of resistors in my
education)
that a PTC has a nonlinear behaviour as well, the tempco value we refer to
is just
the first order term of a taylor series of a function describing the exact
behaviour over temperature. I bet the second order coeff. can be found in
some datasheets
and manufacturers try to make it as small as physically possible.
The exponential behaviour of the NTCs is pretty good.
The *only* point that I see is that a series connection of a fixed resistor
and a
NTC produces errors at high temperatures, since the NTC can't make the fixed
resistor
smaller than it is. In other words for T -> +infinity: R -> Rfixed, and not
zero.
But what are we talking about maybe a max temp range of 30 maybe even 40
degrees, that
would be playing outdoors in winter, and on the beach in summer, really who
does that?

>in a limited range of
>temperature it may be possible to lower the overall sytem error.  These
>thermistors have large tolerances for "inital" resistance, i.e.
>resistance say at  25C. This would mean to adapt the whole network for
>the right scale AND for the right tempco. This could turn out a bit
>too difficult for DIY, since you need some kind of temperature chamber.

Nope, I confirmed the 4%/C by two simple measurements (had the value from a
textbook,
did it before, and just wanted to be sure), ice and water mixture,
gives zero degrees, and boiling water, hundred degrees. Plot it logarithmically
using some cheap maths shareware programs, and read out the value at 25
degrees if you
want it very precise.
Otherwise I would not worry about that, even a deviation of 20% is scaled down
to less 2%, because we have a resistor of eleven times the nominal value of
the NTC
in series, so the "error propagation law" must be applied. (Remember physics)
(2% of 3300ppm is 66ppm I guess we could live with that...)

>It is doubtfull if the proposed method will compensate temperature
>errors,

I analysed it, and did simulations that showed that this could be used
in a temp range of 7 to 47 degrees with
almost the performance of a (ideally) linear tempco.
Hey, you might want to judge by yourself, I put the results of my simuls
on a webpage, and you can take a look, just without compensation, the common
resistor (TC=0.0033), and a NTC+resistor, in the same exponiator.
I put the simulator file there as well, for those who have MicroCap IV
(free running demo is at http://www.spectrum-soft.com)
the adress for the files will be
http://titan.cs.uni-bonn.de/~schmitz/results.html
(I never accessed it from outside the universities-network (DFN),
and it might be down.... so contact me if you have trouble.
I can't put it on my other site, since its packed to the limits :-< )

>I feel they might even get worse.
If my eyes are OK, (and the simulator is right) the opposite is true.

>------------------------------------------------------------------------
>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
congrats!

Rene

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