# [sdiy] PT1000 (was Re: (no subject))

Roman Sowa modular at go2.pl
Mon Apr 8 12:15:48 CEST 2019

```Ian, you're correct. I have redone from scratch the calculations I did
years ago, and must admit I don't know what was I thinking.
Basicaly what I meant, was that when resistance of PT1000 rises, it
becomes more dominant over the series resistor, so summary equivalent
tempco will rise also resulting in poor compensation. However what I did
now, was to approach it the other way, forgetting about tempco ppm value
at all and focus on actual resistances and voltages. So in detail:

As I'm sure we all know, platinum sensors in temperature above 0C comply
to this law: Rt = R0*(1+ A*t + B*t*t)
where R0 is resistance at 0 degrees C, nominally 100 or 1000 ohms, A is
0.0039083, B is 0.0000005775
Another common knowledge is that 3850ppm standard tempco of platinum
sensor is measured as straight line resistance change between 0C and
100C points, but it's not that simple, reaching slightly over 3900ppm at
low end. So the tempco drops with temperature, which helps a lot in
configuration with series resistor.

Now at the expo converter side, a few also commonly known random facts:
- Ube 1 octave differential voltage is (ln2*k*T)/q (where: k-Boltzman,
T-Kelvin temperature, q-electron charge), which for example at 30C makes
up 18.1mV
- from the same equation, octave drift is 59.73uV per K, and what's most
pleasing, it's linear with temperature (just like dominant A-factor of
platinum sensor)
- commonly claimed 3300ppm tempco of BJT junction is true only if we
assume T=30C as reference.

Since PT1000 is characterized at 0C, let's set that base also for BJT,
linear tempco needed is then about 3663ppm.
Solving equations for additional resistance at 2 different temperatures now:
R1=Rs+1000 (total resistance at 0C, Rs is serial resistor to be found)
R2=Rs+Rt (total resistance at higher temperature)
R2=(1+0.003663T)*R1 (same thing, in another words)
Let's take 80C as high temperature endpoint, so Rs is then merely 54.36
ohms. There will be different results depending on temperature range
chosen, as it's just straight line aproximation of nonlinear function,
but after few numerical examples at 6 different temperatures I found
that 55 ohms actually works pretty well, and creates voltages not that
far from ideal ones, in range of 1 cents if we convert Ube voltage
errors to frequency.

So yes, surprisingly a tiny 55 ohm resistor (when compared to 1k of the
sensor) can make acurate compensating tempco for expo converter out of
typical PT1000 sensor. That of course is only one compensation for one
thing, there's a lot to do in other parts of VCO too to make it stable.
But it was nice experience.
Oh, and by the way, this is with PT1000 + Rs in feedback loop of an
opamp, driven with constant current. If you put this as a part of more
frequently used resistive divider, there's one more nonlinear function
to consider, because divide ratio also changes with temperature.

Correct me if I'm wrong, I'm not as good in maths as Ian is, or buch of
others here. This turned out suspiciously too good.
Comments welcome, like it was 1998 :)

Roman

W dniu 2019-04-06 o 15:12, Ian Fritz pisze:
> Roman --
>
>   I do not understand why the series resistor would not work well. We
> must be calculating differently?
> http://ijfritz.byethost4.com/sy_cir7.htm
> Isn't the resistance PTAT plus a constant?
>
> Ian
>
>
> On Apr 5, 2019, at 3:23 AM, Roman Sowa <modular at go2.pl
> <mailto:modular at go2.pl>> wrote:
>
>> I have used PT1000 once, mostly because I could, and out of curiosity,
>> and because it's the only tempco available in SMD with well defined
>> TCR. Nice thing about it is precise tempco, 3850 every time, while
>> typical cheap tempsos have +/-400ppm tolerance.
>>
>> But whatever math I tried, could not find nice and clean way to make
>> the overal circuit down to 3300ppm from those 3850 in reasonable temp
>> range. You can trim to whatever TCR by adding resistor, but it works
>> only at given temperature. I guess it's still better than random TCR
>> of regular cheap 3300ppm PTC in a small range of temperatures.
>>
>> Roman
>>
>> W dniu 2019-04-04 o 21:55, Mike Beauchamp pisze:
>>> Has anyone used the Platinum RTD mentioned in the PDF? I see Digikey
>>> has quite a few in stock of different values,  ±3850ppm/°C.
>>> Mike
>>> On 3/27/19 1:31 AM, Michael E Caloroso wrote:
>>>> I wish he wasn't anonymous.  He does very good work.
>>>>
>>>> MC
>>>>
>>>> On 3/27/19, Ian Fritz <ijfritz at comcast.net
>>>> <mailto:ijfritz at comcast.net>> wrote:
>>>>> “Guest” has been reporting his results regularly over at Muff’s for
>>>>> the past
>>>>> few years. Very careful and thorough work, IMO.
>>>>>
>>>>> Ian
>>>>>
>>>>>> On Mar 26, 2019, at 10:17 PM, Michael E Caloroso
>>>>>>
>>>>>> Not sure this was already posted, but this is an excellent article
>>>>>> (technical descriptions including the math) on temperature
>>>>>> compensation techniques used in exponential converters for VCO.
>>>>>>
>>>>>>
>>>>>>
>>>>>> MC
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>>>>>
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