# DeltaT circuit using 10K thermistors to output 2-10vdc control voltage

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#### weekendguy

##### New Member
I need some help with a simple circuit - I want to convert the difference between 2 resistors (actually 10K thermistors) into a linear 2-10 vdc voltage output. If the resistances are the same, the output voltage is low, the greater the difference the higher the output voltage up to 10vdc. I am picturing using a comparator but I'm just not clear on the approach.

I'd need to be able to set upper and lower output voltage limits (may need to tweak actual output range to be 4-8vdc for example). And same on the input side - would need to tweak range of what difference is considered high and low.

Thermistors will provide resistance in the range of 750-5000 ohms.

The output goes to a motor speed control to set a pump motor speed - lower difference, lower speed; higher difference, higher speed.

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#### alec_t

##### Well-Known Member
Welcome to ETO!
Thermistors are non-linear, so if you really want a linear output proportional to the difference of their resistances (temperatures?) then you would probably need a look-up table in a microprocessor to correct for non-linearity. However, for your particular application I would have thought that true linearity was unimportant. Over a limited temperature range an approximately linear response would be attainable by analogue means (an opamp) and should be sufficient?

#### AnalogKid

##### Well-Known Member
If the temperature difference always is in one direction (that is, T1 always is greater than T2), then an analog subtractor (diff amp) will work - eventually. The problem is that thermistors are notoriously non-linear. More importantly, non-exponential. Their response curve looks exponential, but it actually is far more complex than that. So getting an analog subtractor to work with the two thermistors as inputs and produce a linear, scaled output probably is impossible. Still, within a specified temperature range it is possible to "linearize" the thermistors and do the subtracting after that. Note that a comparator chip will not work if you want a linear output voltage, as in so many volts or millivolts per degree difference.

What is the temperature range over which you need the best accuracy?

ak

#### weekendguy

##### New Member
AnalogKid alec_t Thank you both for your comments. This is not a precision device --non linearity is not an issue. The output could even be in (10) steps - it's adjusting a hydronic circulator based on the supply and return temps.

The temperature range of interest is:

Low- 40C (100F) ~ 5.3K ohms
High- 100C (200F) ~ 750 ohms

It may be determined that the actual speed changes will occur only within a range of 50F and will fall off beyond that. That's the reason for the trimmer requirement - to tweak this in vivo.

While T1 is always > T2 for control purposes, it is possible that T2 could drop below although that could be treated as a zero difference - no negative difference is required.

#### alec_t

##### Well-Known Member
Simulation shows that simply measuring the difference between the two thermistor resistances over a range of 40C-100C could lead to ambiguity.
Here's the sim, where one thermistor temp varies (over an arbitrary 1 sec simulation interval) from 40C-80C while the other varies from 40C-100C. The difference is represented by the white curve, which has a point of inflection at around 65C (represented as 0.65 sec on the horizontal scale). Before that point the two thermistor curves diverge with increasing temperature difference: beyond that point they converge.

#### weekendguy

##### New Member
alec_t Thank you for your help. But... I don't understand what you are suggesting. To me, all I want to do is provide an output roughly linear to the (positive) difference. I know the difference will vary, therefore the control output will vary as well. There is no actual feedback from the control variable. Maybe because I'm a software engineer - I don't understand the implication for ambiguity in my simplified case. Do you think an opamp circuit can be used?

#### MikeMl

##### Well-Known Member
I dont understand why you want the motor speed to be proportional to the difference between two temperatures? What are the two thermistors measuring?

#### weekendguy

##### New Member
@mikemi Thank you for your comment. This is a fairly common approach used in hydronics - as the Delta T (difference between the 2 temps) increases, there is a requirement for the motor to speed up to theoretically reduce the DeltaT. Conversely, a lower DeltaT indicates a need to slow down the motor which should theoretically raise the DeltaT. The idea is that as the corrections are made, subject to some amount of hysteresis, the DeltaT will converge on a known good level for heating efficiency.

#### Ari

##### New Member Use R2 and Rx as your 2 thermistors and experiment with values for R1 = R3.
Vg will be 0V if the thermistors have equal resistance and increase/decrease with differing thermistor resistance.

#### AnalogKid

##### Well-Known Member
The problem, and it is the same whether the thermistors are driven constant current, constant voltage, or constant resistance, is that dV/dT is not a constant. That is, the voltage difference between two sensors at 80 and 100 degrees is much larger than the difference between 180 and 200 degrees. Same 20 degree delta T, but a much smaller delta V. Of course you can flatten out just about anything in a uC lookup table, but that is not trivial code. I have a thermistor linearizing circuit that is pretty good over a 30 degree range, but the requirements of posts #1 and #4 are tough for a bunch of opamps.

ak

#### Ari

##### New Member
Yes, you're right about non-linearity with thermistors. I understood from his requirements a range of 40...100C to drive a motor the error (non-linearity) would be insignificant. Sorry to have misled anyone.
Another possible solution is LM35 instead of thermistors which is pretty good and linear. Then a simple op-amp (e.g. LM358) to differentiate the 2 values, set the gain, etc.

#### alec_t

##### Well-Known Member
I don't understand what you are suggesting.
I'm saying that below about 65C an increasing measured difference means the temperature difference is also increasing, so you'd need to increase the motor speed (as you'd expect), whereas above 65C an increasing measured difference would mean the temperature difference is actually decreasing, so you'd need to reduce the motor speed (contrary to what you'd expect).

#### spec

##### Well-Known Member
Hi WEG,

I hope I understand your requirement, but it seems to me that you simply need an output voltage proportional to two temperatures. Based on this, the solution is to use two linear voltage output temperature sensors connected to the two inputs of an instrumentation amplifier, either off-the-shelf, or constructed. The output from the instrumentation amplifier would then be the difference between the voltages of the two temperature sensors.

If you would like to peruse this approach, please let us know and I will post a circuit for your consideration.

spec

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#### AnalogKid

##### Well-Known Member
Now that everyone else has asked, I'll pile on. Are you restricted to using thermistors, or are other types of temperature sensor allowed?

ak

#### weekendguy

##### New Member
alec_t Aha! Thank you for the explanation. I did not consider that possibility - was assuming that the difference would be consistent (if not linear). That pretty well rules out a straight resistance difference approach. AnalogKid I have written code for linearizing raw inputs but I am trying to avoid another Arduino at this point (I already have several looking at temps with DS18B20 sensors). I should have mentioned that the goal here is to characterize the dynamics rather than necessarily provide an end-solution. It may well be that I end up with a micro ultimately. spec It seems that your suggested approach would be one to pursue. I assume the LM35 that Ari proposed is a candidate? A circuit would be much appreciated. I believe I have some 8-pin DIP Inst. Amp ICs - I'm pretty sure they are ADxxxx.

Thank you all.

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#### spec

##### Well-Known Member
spec It seems that your suggested approach would be one to pursue. I assume the LM35 that Ari proposed is a candidate? A circuit would be much appreciated. I believe I have some 8-pin DIP Inst. Amp ICs - I'm pretty sure they are ADxxxx.
OK WEG,

Can you let us know the exact part number of the Analog Devices instrumentation amplifier chips that you have?

Also, would plus and minus 15V power lines be suitable?

spec

#### AnalogKid

##### Well-Known Member
Analog Devices, Maxim, Dallas (now a separate part of Maxim) Linear Tech, and National (now TI) all make solid state temperature sensors that have a linear response. Lots to choose from. Note - pay attention to the max/min specs. The "typical" accuracies are great, but for some parts the total unadjusted error budget is large.

ak

#### weekendguy

##### New Member
spec AnalogKid I have AD620 ICs. +/- 12v would be easier but no doubt I can find a PS for +/- 15vdc... Thank you.

#### spec

##### Well-Known Member
POST Issue 4 of 2016_12_06

Hi WEG,

Below is the schematic for the circuit I had in mind.

spec

CIRCUIT DESCRIPTION
(1) The differential gain of N1 is set by R5, according to the formula R5 (in K Ohms) = 49.4/(G-1), where G is the differential voltage gain of N1.
(2) The differential voltage gain of N1 is 10 with the R5 value shown.
(3) The voltage output from the LM35s is 10mV/Deg/C, which means that if the temperature of N3 is 100 Deg C higher than the temperature of N2, the output voltage of N1 will be 10V.
(4) If the temperature difference of N3 and N2 is reversed, the output of N1 will be -10V.
(5) If both N3 and N2 are at the same temperature the output from N1 will be 0V.
(6) C1, C7, C4, and C5 are decoupling capacitors
(7) R2/C3 and R3/C2 are low pass filters to minimize noise effects.
(8) R4 is an isolating resistor to keep N1 happy.

COMPONENTS
(1) All capacitors are ceramic X7R dielectric, +-10% or tighter.
(2) All resistors are 1/4 watt or higher, metal film, +- 5% or tighter, except R5 which is +-0.1% or tighter

DATASHEETS 