RTD temperature equations

[JimatHA]

Morning

I am looking for equations that solve for temperature in terms of RTD
resistance. I find lots of references to equations that only include
the lower order terms or that solve for resistance.

I am writing firmware for a temperature measurement instrument. The
instrument will work with 100pt, 1000pt, 120ni, and 10cu type RTDs and
cover below zero ranges. I have found second order equations that
solve for temperature for Platinum and Nickel. I have found just a
first order equation for Copper. It looks like I need to include
higher order terms for accuracy below zero.

Any ideas where to look
Thanks
Jim

 

[John Larkin]

On Thu, 22 Jan 2009 06:20:26 -0800 (PST), JimatHA <j.hall@air2app.com>
wrote:

Morning

I am looking for equations that solve for temperature in terms of RTD
resistance. I find lots of references to equations that only include
the lower order terms or that solve for resistance.

I am writing firmware for a temperature measurement instrument. The
instrument will work with 100pt, 1000pt, 120ni, and 10cu type RTDs and
cover below zero ranges. I have found second order equations that
solve for temperature for Platinum and Nickel. I have found just a
first order equation for Copper. It looks like I need to include
higher order terms for accuracy below zero.

Any ideas where to look
Thanks
Jim

http://en.wikipedia.org/wiki/Callendar-Van_Dusen_equation

Copper is pretty linear, and nobody makes precision copper RTDs, so a
2nd or even 1st order fit is probably good enough.

We usually use lookup tables and interpolation.

John

 

[Joe]

In article <np9in4labv1shgviqh1cqiuqpqp2kk2nub@4ax.com>, John Larkin
<jjlarkin@highNOTlandTHIStechnologyPART.com> wrote:

On Thu, 22 Jan 2009 06:20:26 -0800 (PST), JimatHA <j.hall@air2app.com
wrote:

Morning

I am looking for equations that solve for temperature in terms of RTD
resistance. I find lots of references to equations that only include
the lower order terms or that solve for resistance.

I am writing firmware for a temperature measurement instrument. The
instrument will work with 100pt, 1000pt, 120ni, and 10cu type RTDs and
cover below zero ranges. I have found second order equations that
solve for temperature for Platinum and Nickel. I have found just a
first order equation for Copper. It looks like I need to include
higher order terms for accuracy below zero.

Any ideas where to look
Thanks
Jim

http://en.wikipedia.org/wiki/Callendar-Van_Dusen_equation

Copper is pretty linear, and nobody makes precision copper RTDs, so a
2nd or even 1st order fit is probably good enough.

We usually use lookup tables and interpolation.

John

Here are a few comments based on my experience as a mathematically
inclined hobbyist, but certainly not an electronics professional.

In the past, I looked up some information about negative temperature
coefficient thermistors, and came across an article containing some
equations for resistance versus temperature.

I was disappointed from a purely scientific viewpoint when I realized that
the equations, tagged with the names of people who developed or promoted
them, were simply the result of curve fitting some measured calibration
data to, typically, a third degree polynomial. There is NO scientific
content in the derivation of those equations, at least from what I saw.

The equations are simply ad hoc, ex post facto, or purely empirical (take
your pick of adjectival phrases).

The article,
http://en.wikipedia.org/wiki/Callendar-Van_Dusen_equation
that John Larkin mentioned is quite in the same vein as the thermistor
article that I came across, except that the Callendar-Van_Dusen_equation
article is a mere stub.

John's comment
"We usually use lookup tables and interpolation"
seems to me to be at least as good an "explanation" as any of the equations.

--- Joe

 

[John Larkin]

On Fri, 23 Jan 2009 03:02:43 -0800, none@given.now (Joe) wrote:

In article <np9in4labv1shgviqh1cqiuqpqp2kk2nub@4ax.com>, John Larkin
jjlarkin@highNOTlandTHIStechnologyPART.com> wrote:

On Thu, 22 Jan 2009 06:20:26 -0800 (PST), JimatHA <j.hall@air2app.com
wrote:

Morning

I am looking for equations that solve for temperature in terms of RTD
resistance. I find lots of references to equations that only include
the lower order terms or that solve for resistance.

I am writing firmware for a temperature measurement instrument. The
instrument will work with 100pt, 1000pt, 120ni, and 10cu type RTDs and
cover below zero ranges. I have found second order equations that
solve for temperature for Platinum and Nickel. I have found just a
first order equation for Copper. It looks like I need to include
higher order terms for accuracy below zero.

Any ideas where to look
Thanks
Jim

http://en.wikipedia.org/wiki/Callendar-Van_Dusen_equation

Copper is pretty linear, and nobody makes precision copper RTDs, so a
2nd or even 1st order fit is probably good enough.

We usually use lookup tables and interpolation.

John

Here are a few comments based on my experience as a mathematically
inclined hobbyist, but certainly not an electronics professional.

In the past, I looked up some information about negative temperature
coefficient thermistors, and came across an article containing some
equations for resistance versus temperature.

I was disappointed from a purely scientific viewpoint when I realized that
the equations, tagged with the names of people who developed or promoted
them, were simply the result of curve fitting some measured calibration
data to, typically, a third degree polynomial. There is NO scientific
content in the derivation of those equations, at least from what I saw.

Welcome to the real world. Most transmission-line impedance equations
are the same, accidental coincidences of shape that were tweaked to
work. It's just like fitting a polynomial to experimental data, but
using any old equation that looks good. Such fits tend to produce
insane results out of their sweet spots, like negative impedances for
wide pcb traces.

Incidentally, there are NIST polynomials for thermocouple voltages, up
to something absurd like 14th order, also probably free of deep
theory.

The equations are simply ad hoc, ex post facto, or purely empirical (take
your pick of adjectival phrases).

I doubt that theory exists to calculate RTD or thermocouple R:T curves
from first principles, to millikelvin accuracy. And don't even think
about thermistors.

The article,
http://en.wikipedia.org/wiki/Callendar-Van_Dusen_equation
that John Larkin mentioned is quite in the same vein as the thermistor
article that I came across, except that the Callendar-Van_Dusen_equation
article is a mere stub.

John's comment
"We usually use lookup tables and interpolation"
seems to me to be at least as good an "explanation" as any of the equations.

It's a lot faster to compute. I usually work in bare-metal assembly
language, so interpolation is easier than high-order polynomial
expansion or whatever. The tables can be generated directly from the
NIST polynomials with a little BASIC program, and the resulting source
file tossed into the assembly program.

I'm an engineer. I don't have to understand it, I only have to make it
work.

I did these:

http://www.highlandtechnology.com/DSS/V450DS.html

http://www.highlandtechnology.com/DSS/V470DS.html

This one also does cryogenic diode sensors, where there's even less
theory to explain what's going on:

http://www.highlandtechnology.com/DSS/V460DS.html


John

 

[John Larkin]

http://www.omega.com/temperature/Z/pdf/z251.pdf

http://www.omega.com/temperature/Z/pdf/z252-254.pdf

 

[Joe]

In article <2jnjn4dnfg4dmqk3ct3hstda4qg2pmjlr2@4ax.com>, John Larkin
<jjlarkin@highNOTlandTHIStechnologyPART.com> wrote:

http://www.omega.com/temperature/Z/pdf/z251.pdf

http://www.omega.com/temperature/Z/pdf/z252-254.pdf

Here is a longer wikipedia article that mentions the

Callendar-Van Dusen equation:

http://en.wikipedia.org/wiki/Resistance_Temperature_Detector

--- Joe

 

[whit3rd]

On Jan 23, 7:07 am, John Larkin
<jjlar...@highNOTlandTHIStechnologyPART.com> wrote:

On Fri, 23 Jan 2009 03:02:43 -0800, n...@given.now (Joe) wrote:
In article <np9in4labv1shgviqh1cqiuqpqp2kk2...@4ax.com>, John Larkin
jjlar...@highNOTlandTHIStechnologyPART.com> wrote:

On Thu, 22 Jan 2009 06:20:26 -0800 (PST), JimatHA <j.h...@air2app.com
wrote:

Morning

I am looking for equations that solve for temperature in terms of RTD
resistance. I find lots of references to equations that only include
the lower order terms or that solve for resistance.

I am writing firmware for a temperature measurement instrument. The
instrument will work with 100pt, 1000pt, 120ni, and 10cu type RTDs and
cover below zero ranges. I have found second order equations that
solve for temperature for Platinum and Nickel. I have found just a
first order equation for Copper.

The Drude theory of metals says that a pure (non-alloy) metal
has resistance proportional to Kelvin temperature. It works
for copper, platinum, and lead pretty well (Heike Kammerling-Ohnes
found something surprising at very low temperatures for lead,
though). Alas, lead and copper tarnish (the calibration would
shift, which is ... inconvenient), and most thin-film resistors
have strains which arise from mismatched thermal expansion
with the substrate. Strain is just like an impurity, it
invalidates the Drude model. All real metals have some
strains when you bend/wind/plate resistors out of them...

We usually use lookup tables and interpolation.

Incidentally, there are NIST polynomials for thermocouple voltages, up
to something absurd like 14th order, also probably free of deep
theory.

Yes, that's right. Thermocouples are designed around alloys
(like constantan) that were commercially available in highly
controlled prescriptions, like for low-tempco resistance wire.
As long as the alloy is EXACTLY prescribed, the thermocouple
is repeatable. I've used thermocouples where 0.07% of iron
content was the difference between the (+) and (-) thermocouple
wire; that has to be 0.07% plus/minus .0001% or so.