Wheatstone bridge?


I am looking for some calculations about the precision of a wheatstone bridge. Actually I have a thermistor 1kOhm with a 0.1°c precision and I would like not to loose that with wrong resistors in the bridge. I try to find something on google but no results...

Have you got a link? Do you think I need special resistors?

Thank you

A good link is:-

However you don’t gain or loose precision with a wheatstone bridge. All it is, is a potential divider with an active element in one arm. The other side is just a regular potential divider to provide a reference. Generally the resistor to choose is the same as the active element at mid range.

Have you got a link? Do you think I need special resistors?

Well the bridge resistors would have to have a accuracy tolerance better (X10?) then the thermistor if you want the sensor to be the limiting factor in overall measurement accuracy. And then there will be the needed bridge op-amp and it's resistors to deal with. And you will have to see what the arduinos only 10 bit precision factors into the whole system.


Another link:


There is also the problem of calibration, A Wheatstone Bridge's output is bi polar in nature and depending on the actual values on either half... Extremely sensitive, Typically used for making matched pairs of resistors... to .001% or more. A Wheatstone Bridge isn't a really great idea unless you are after 10th's of a degree accuracy over a narrow range of temperatures Use a current source fed from a constant voltage source... Independent of the Arduino's Vcc. I usually use a pot and a TIL431 reference diode (read Variable Zener Diode) fed from a clean 9 to 12V source. I use a 10K 1% MF or better, use a stable one with a low tempco (10PPM/deg C.). There is a "Table" of values for calibration by PH Anderson and a formula for doing the same thing "On the Fly" available freely on the Internet for final calibration. Don't forget 2 really important things... Bypass the regulated voltage source well and really important use a star grounding layout... 5 or 10 mV of combined ground drop voltage can destroy any real accuracy however if you pay attention to detail you can easily make a nearly "Traceable" and very accurate thermometer... for a few dollars extra... IMO



Thank you all for you answers, I can now begin to work well on that thermistor. Docedison, it seems that I don't have all the electronic skills needed for the understanding of you answer, have you got a schematic? I really would like to understand, would you not use a wheatstone bridge at all? What is the goal of the current source? What is the "calibration" that you told me?

I'm just in first year of electronic engineer school.

Well get out your books and reference the devices… a constant current diode is a jfet operated at it’s “pinchoff voltage”… they are available in 2 lead diode like packages… a constant voltage power supply feeding the diode will produce a constant set of conditions that the thermistor can react to.
The Wheatstone Bridge is a fine tool but because of it’s bi-polar nature is much more difficult to directly interface to the A/D inputs on the Arduino.
Reference the “Star” method of power supply distribution in your texts and see what I was talking about as far as noise both distributed from the power supply and created by individual elements…
Getting back to the thermistor issue, a constant current through the thermistor will produce a variable voltage, temperature dependent and that will give you the information you need from a stable source.
I hope this helps a little. Unfortunately I need to go and do some “Honey Doo’s” now and I will be busy for the next 3 or 4 hours… I think.


Okay I begin to understand. So with a really stable current in the thermistor (with the advices you gave to me), the voltage around the thermistor will just have to be measured to have a good accuracy. And it will be maybe more stable than with a wheatstone bridge, without all the resistors problems. Is that right?

Last thing, you told me about calibration but I didn't find anything about PH Anderson and the tables on google, have you got another keyword please?

Thank you very much. Sebastien L.

Docedison: The Wheatstone Bridge is a fine tool but because of it's bi-polar nature is much more difficult to directly interface to the A/D inputs on the Arduino.

I dispute that

  int val = analogRead (1) - analogRead (0) ;

is "much more difficult" than

  int val = analogRead (0) ;


My Comment was based on the fact that a Wheatstone Bridge can swing negative and is equally likely to do so as to swing positive and on top of that... If you are after ~1% accuracy it still requires a Very Clean, Stable and known Reference Bias for the sensor... Then there is the issue of the accuracy of the Vref, nominally 5V or the chip Vcc. This forces a ratiometric measurement because the Vcc line might not be very stable or accurate. There are similar issues with the internal 1.1?V reference... it seems that it can vary somewhat. So I made these assumptions about the use of the thermistor because there are many ways to achieve that level of accuracy but the temperatures are lower, the thermistor can be limited only (reasonably) by the melting point of the solder... Not all or many but possible. So those thoughts first I thought to recommend a voltage source stable enough that it could through the proper voltage divider be the Vref for the measurements as well as the Thermistor Reference bias... that was to come after he gave me some indication that he understood my thoughts and was interested.



I think I understand the pros and cons of the weathstone bridge. I will look for some information about the jfet as a current source, it seems to be quite useful. But indeed with a stable voltage source and if I use 1% resistors maybe I can have a quite good accuracy for the temperature measurement. I will make all the calculation needed with this page :


And I will come back to tell you what accuracy I can have. Thanks

The Jfet… device is available as a calibrated (measured) diode package from several sources the use of a stable voltage to drive it makes for a VERY stable reference that can supply current to your thermistor voltage divider. You then measure the voltage and apply the correction factor to it and then use it. For an Arduino there is little use for the accuracy attainable with an Wheatstone Bridge as the bridge configuration can easily measure milliohms in 10’s of hundreds of ohms… .01 (10 mOhm) ohms/100 ohms = .0001%… From a an accuracy standpoint you will get more information than you can use. The Principal reason I suggested an accurate reference/divider was to simplify your task. If it is necessary that you learn about Wheatstone, Hay or other forms of the same type of network for your education (Instructors recommended project) there are better ways of dealing with it. However if you must deal with a bridge instead of a simpler divider network then use the lowest temperature and add 10 deg to it and use that Resistance as the beginning point (Make the other resistor in the thermistor side equal to that value and the bridge can never swing negative. It will be a rising potential equal to the difference in value of the two resistors in the “variable” half of the bridge. It in effect becomes a voltage divider again… with two un needed parts whose temperature stability can be a major factor in the total accuracy of the measurement method. I have included a data sheet from one manufacturer of CC diodes. The Jfet idea I mentioned is the beginning of that technology. Basically it is a low pinchoff Jfet and a resistor in series with the source (as I remember…) and the gate is tied to the other end of the resistor when the voltage across the resistor (dropped by the diode load connected to the source, drain to V+) the Jfet cuts off limiting the current to that level.When a precise current is placed across a known value of resistance a precise voltage is developed. I discussed this on line in this thread with another person and there I explained my thoughts… Did you read my response? and my thinking?. A Wheatstone Bridge is a great tool for certain things and a VERY interesting thing to investigate, I’ve used them for many different things in many different ways… Used one to make an AM modulator for a transmitter I built 30 years ago. I used one to make an FM modulator several years later… these are a few uses I have Bent from the original work I did with bridges when I was in school. In short unless there is some outstanding reason why you NEED to use a bridge remember the total stability/accuracy is dependent on a good reference bias source and 3 other parts besides the measurement variable, a lot of bother for questionable returns. IMO


CCL0035_V2.pdf (75.8 KB)

Ok I think I have understood the advantages of the two solutions. Indeed the jfet device seems to be quite easier than the wheatstone bridge, but you are right, i'm still in my studies and it will be very recommended for me to be able to use fastly a bridge network. However thank you very much Docedison for all this information that you gave me and all the time you took to answer me.

->This forum is just perfect. Let go!

Well, Young man the knowledge was given to me for free... and the only way I can repay the patience of the people who took the time to explain things to me is to do the same for as many others as I can reasonably. You Are quite welcome and thank you for the opportunity to explain it to you...


A 1K 0.1C thermistor seems like a bad use-case for a wheatstone bridge. With a typical Beta of 3800, a 1K NTC thermistor at 25C will vary about 42 ohms (~4%) per degree of temperature change. In a 5V Wheatstone bridge config with 1K resistors, the +/- 4% change in resistance per degree will make the voltage difference across the terminals of the Wheatstone about +/- 4V. With a 10 bit ADCs on the terminals of the wheatstone, you might sense 0.1% differences, which would correspond to temperature differences in the +/-0.025C range.

But, with a 1K thermistor at 2.5V, you could be heating the thermistor significantly: 2.5V/1000ohm=2.5mA, P=2.5ma*2.5V=6.25mW With one particular 1K thermistor's dissipation constant of 1.7mW/C, it could self-heat by 3.67C, introducing a systematic error 147 times larger than the sensitivity of the wheatstone.

If you need to do this with an arduino, use a larger resistance thermistor and a very small reference voltage to minimize the self heating. And figure out your operating range and what that would mean at the terminals.

The other problem is how you are going to to the +/- differential voltage measurement on the arduino. If you hook the AREF to your wheatstone bridge's reference voltage, half of the wheatstone bridge is essentially useless-- you can do the inactive branch of the wheatstone bridge in math rather than measuring the terminals with ADCs.

Some AVRs can do differential +/- voltage measurements with some ADMUX magic: http://arduino.cc/forum/index.php?topic=147830.0

One of the nice things about using a simple resistive divider network with a thermistor is that the accuracy of the excitation voltage doesn’t matter because it drops out of the equation and you are solving simply for the resistance of the thermistor as a function of the resistor you place in series with it. Therefore, the accuracy is just dependent on the precision of the series resistor, the thermistor, and the ADC. A little easier to characterize over ambient temperature.

RT = RS / (1024/ADC - 1) where RT is the resistance of the thermistor and RS is the resistance of the series resistor.

If you are using the ADC from the Arduino, it is probably the least accurate link in the chain, so you can ignore the rest.

Indeed I ‘plugged’ no numbers into the thread knowing that until there were more than generalizations the data would get in the way…
@DaveX an interesting scenario… The worst you could dream up?.. The data sheet I referenced has CC diodes from 35uA to 5.7 mA… I posted it for this diode… Not for the part itself because it’s unlikely that the part is available but the basic theory is still around and the methods with it. No, for the data to point out something of passing concern

CCL0750 0.600 0.760 0.920 1.0 0.2 1.4 0.0 TO -0.32

and it’s effects both on the resistors as well as the accuracy of the excitation or bias supply for the thermistor. Finally to do a thermometer of even 1/2% accuracy would be a challenge because the Arduino’s Vref sources are somewhat less than ‘stellar’ I’d make my own first, thus the initial comment about the TIL431… It’s temperature stability is fair to good and with good design can be better, certainly better than either the ‘normal’ ratiometric A/D measurement or using the largely uncalibrated internal reference. All of this discussion is rather pointless because of the basic limitation of 10 bits and with oversampling, a little noise and some decimation can produce 12 bits of equivalent accuracy… But why when really cheap devices are available that essentially ‘bolt’ on to the Arduino with uVolt accuracy where the Uno for example is capable of a millivolt/bit resolution but at what temp and under what conditions? of noise or supply voltage and noise flowing in the grounds… One, or two grounds for Everything off board was the reason for my seemingly off the wall comment about star grounding methods.
Even after all is said there is no device that can be all to everyone and before this discussion is put to bed… where it sorely needs to be…
Is that the Arduino was intended as a teaching machine. That it does as much as it does is testimony to a good design… To do as much as it does as well as it does and for as little as it cost’s to get one working… I make Rolls Royce breadboards… I buy the little '328 stickers from Adafruit… They look “Cute”… and I can never remember what pin does what and my uno’s are lost somewhere.
I’m also happily retired, this is my plan to keep sane and active as I grow daily more senile and I hang out here and once in a while make a fool of myself as well.