to acquire a Pt100 I set up a board with INA326. Full bridge: the upper resistors are 100k (say R1 and R2), the lower 100R (R(t) and R3). The INA326 is programmed to gain 10 (4k and 200k). Supply voltage is 3.3V.
The start equation is:
R(t) = R0(1 + At + Bt^2)
My output is:
Vo(t) = G(V+ - V-)
where G is the INA326 gain, V+ and V- both arms of the bridge. Thus:
Vo(t) = G[Vs*R(t)/(R1+R(t)) - k]
where k is the reference voltage from the fixed network divider.
Well, but I need t(Vo)! Inverting the formula leads to a quite complex expression, and I need to fit it into a small AVR.
This is the right way or there is something else that I'm missing?
Convert the equation into a polynomial in R instead of T.
Cheers
Phil Hobbs
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Dr Philip C D Hobbs
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Don't forget that you can cancel out the square term with a bit of feedback. IIRR, increasing the current through the Pt100 sensor - increasing with voltage drop across the bridge - with increasing temperature can save you from having to calculate the square term in the AVR.
I invented this for myself back in 1979, but the guy that took over the project claimed that any positive feedback would lead to oscillation (it won't if the positive feedback gain is less than one, and it really isn't anywhwere near it in this application). Honeywell are reputed to use it in their Pt100 sensing modules.
The traditional fix is to add a bit of v-squared to the voltage measurement value. I usually diddle it numerically, rather than doing all the algebra. The v-squared will pretty much fix up both the RTD curve and the small additional curvature caused by the bridge loading.
Of course, you don't really need a bridge, or a diffamp. If you want, you can excite, amplify, and linearize with just an opamp or two.
if the needed temperature range is small and the resolution is large, a small lookup table will do. You may use a stepwise linear aproximation of the formula for a larger temperature range and smaller resolution.
Can you tell me, why you want to go such a complicated way to convert a resistor value to a voltage, that have to be measured via AD, when you have a µC that can very easy count timings? You just need a few low ohmic switches (power-Mosfets or simple relais will do a great job) and one capacitor, one digital input and three digital outputs and last not least one stable resistor (piece of constantan wire).
discharge the cap charge capacitor with reference resistor up to the voltage the input recognises 1 and count the timer ticks that are going by (time 1). discharge the cap again and charge your cap via PT100 counting timer ticks (time 2) The time 1 /time 2 = R1 / R2
The rest is simple mathematics ;-) Hint, AVRs dont like floating point aritmetic. It may be easier to do fixed pont artimetic with integers. Second hint. You may select a big cap or interlace the accumulating of time 1 and time 2 using smaller a capacitor.
Nice, if the Pt100 can be mounted in a well-shielded area, ideally inside a grounded screen.
Temperature sensors are often used to measure temperatures of places outside of the electronics, and an average voltage across the Pt100 which can be low-pass-filtered is generally more useful.
Thats quite complicated. What accuracy do you need? Better use a pt1000 element. Feed from 3.3V through a 2.2k resistor and read with an ADC.
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Assuming you're in no hurry for the results, you can do a binary search using the Callendar-Van Dusen equation and get EXTREMELY good results. Just loop the evaluations for a fixed number of iterations-- it really won't take much code at all.
Best regards, Spehro Pefhany
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"it's the network..." "The Journey is the reward"
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There is something weird that bugs me about those RTD equations.... How is it possible that a different equation applies to "positive" and "negative" temperatures?
The same equation is used in the Callendar-Van Dusen equations- but one of the coefficients is different. That's a bit odd, but it's not unusual to have different equations valid over different regions.
BTW, I don't think that ADC sample code could be written in a more inefficient way. Horrible, even considering it's free.
Best regards, Spehro Pefhany
--
"it's the network..." "The Journey is the reward"
speff@interlog.com Info for manufacturers: http://www.trexon.com
Embedded software/hardware/analog Info for designers: http://www.speff.com
The physics of the sensor does not have any discontinuities at 0 C. The different constants are used to keep the error funnel at its narrowest around zero C.
But the 0 degrees C point is totally artifical, and seems to bear no relation to anything physical - unless we are talking about water which we are not!
On the Kelvin scale one equation describing the resistance of platinum suddenly takes over from another when we get to 273.15K?
Would you rather have the change made at 12.3456C? 0C seems to be a pretty good place to make a "fit" change, to me (as long as there isn't a discontinuity there). Easy on the algorithm, anyway.
That just shows how "fishy" the Kelvin scale is. ;-) It would look pretty messy on the Rankin scale, too.
To be fair they do show the way the positive model function goes pearshaped at around -20C on their graph Fig4 of errors at negative T.
Their algebra is a bit ropey too. There is no need at all for Z4 it can be divided out of the numerator terms as a constant and the problem can with care be recast in fixed point arithmetic.
BTW if your hardware has a fast integer divide then it is worth considering rational approximations to the inverse function which have smaller errors than polynomials using the same number of coefficients.
Perhaps it does seem so. It's a useful division point because many applications (eg. comfort heating) only need to work above 0°C, so the simpler version can be used. The reasons are historical and practical.
The RTD resistance is specified at 0°C and 100°C. Callendar came up with an equation that used measurements at an additional (higher) point (eg. freezing point of pure Zn). That agrees very well with actual resistance over the range of 0..600°C at least (and doesn't go all squirrely outside the optimal range like typical higher order least squares polynomial fits- it's still quite good at more than
800°C). Subsequently, Van Deusen added the higher order terms to reduce the error at very low temperatures, the determination of which involves using another convenient low temperature point such as the boiling point of pure O2.
The equations are written in terms of degrees C, so the effect of all three coefficients is zero at T = 0°C-- so it's a natural place to make a transition. Kind of arbitrary, but it fits really well and is convenient (and it matches the IEC standard exactly).
BTW, if T is constrained to be >= 0° it's possible to exactly solve for T (R) using the CvD equations (Actually just C's contribution-- it's just a quadratic in T)-- so multiplications, divisions and a square root. It's also pretty close at temperatures a bit below zero, if a fudge works for you. I never get that lucky, but others might..
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