# Voltage proportional comparison (division?)

I'm looking for a circuit that produces an output voltage which represents the voltage between A-B compared to B-C here. IE if AB is 10V and BC is 1V, the output is 10V, and if AB is 10V and BC is 2V the output is 5V.

Essentially what I want is an output voltage that represents the resistance ratio between R1 and R2.

The absolute output values is not important, as long as I can derive the current value of R1 from the known values R1(cold) and R2.

The reason is that R1 will change value as it warms, and I want to track that with a microcontroller. V1 will vary too fast to sample A and B separately, but I can use a single channel differential ADC if required.

I don't think this is possible without a very complex circuit having gone through it this morning but I thought I would throw it out there in case I am missing something.

EDIT: Thanks for both answers (and thanks for the 3rd but I don't really understand your suggestions). Firstly I think I can see that the result for me is that 'no its not possible to do it the way I hoped'. IE bridge like resistor networks.

The op amp idea is nice and probably the closer to my aim as I wanted a mathematical approach, but the result is that high currents need to go through linear devices which will lose considerable power and produce considerable heat. Also during fault conditions (which I will encounter) I won't be able to clamp the 200Aish currents fast enough to protect the devices I think.

The multiplier approach is also nice as I didn't realise a multiplier could be configured to divide. This one is more practical I think - but I don't think I can use it as I suspect I need greater accuracy and stability than I can get from relatively standard components, and the cost as you say is high.

So the result seems to be that I need to find another way to do it. Its hard to know who to award this to because I think both answers are equally excellent. Any help 'choosing' the most stack exchange 'best' reply would be appreciated.

As for my problem, I guess its either a sample and hold (I was thinking a homebrew with a 4066), or I will search for the controller mentioned that does simultaneous conversion. None of the ADCs I have seen seem to sample and hold the Vref voltage at sample time which is a pity as it seems to me that if I could feed A into Vref, B into ADC in, and C to gnd, that would work perfectly. Any further comments on that would be great if anyone had them.

Edit2: Since no one has commented as to the 'best' answer I think I am going to choose the op amp one, because of the algebraic approach and principle behind it which is kind of what I wanted (even if I wanted a non active type). Thanks to both.

Thanks, Pete

• Are you trying to measure resistance changes in a 0.315Ω resistor? That will make it a bit trickier.
– W5VO
May 17, 2016 at 16:24
• Yup (0.315R) but my currents are high, 5 to 20A. So I'm getting 100 mV across BC. So for an accuracy of 1% I need < 1mV resolution which my ADC can do. But it just can't do it fast, hence wondering if I can do the comparison electronically.
– Pete
May 17, 2016 at 16:32
• Normally you would use a differential amplifier to measure the voltage across your resistor and amplify it to the range of your ADC. May 17, 2016 at 16:37
• I can use a differential amp - but the thing is I need both current and voltage at one instant. So Vab and Vbc at the same time. Even using 2 I2C ADCs, I can't trigger them both at the same time. Getting 2 ADC conversions at the same instant has turned out difficult. A dual sample and hold will be the only alternative but I hoped to avoid it.
– Pete
May 17, 2016 at 16:44
• How fast? How about a sample and hold circuit? They do make analog multipliers/ dividers. ~10 MHz (maybe some are faster now.) May 17, 2016 at 17:14

You are trying to calculate (A-B)/B, where A and B are the voltages at A and B respectively. For the voltage divider, B=A*R2/(R2+R1).

Let's do the algebra.
$$\frac{A-B}{B} = \frac{A - \frac{AR_2}{R_2+R_1}}{ \frac{AR_2}{R_2+R_1}}= \frac{A \left( R_2+R_1\right)}{AR_2}-1 = A=1+\frac{AR_1}{R_2}-1$$

simulate this circuit – Schematic created using CircuitLab

Of course, for your resistance and current values, you'll need a pretty special high current op amp for the first stage, maybe the MP38.

• +1 for out of box thinking. This may be useful for the OP with a bit of thought and adaptation. May 17, 2016 at 18:23
• Brilliant - although its not suitable for my use, this is kind of what I wanted. More comment put in edit to question.
– Pete
May 18, 2016 at 12:52

You can do this with an IC multiplier, however it will not be cheap. Also, note the bipolar supplies.

I suggest reducing the input resistor (to get gain on $E$) and using another op-amp (maybe half of a dual) to amplify $E_X$ so the input signals are reasonably high.

Alternatively, you could use an external ADC that has multiple simultaneously sampled channels. If memory serves, there are even a few microcontrollers that have that built in, for such applications as 3-$\phi$ energy metering.

• Also brilliant - probably the only practical way to achieve my aim I guess, but I am worried about stability of the resistors etc. More comment put in edit to question.
– Pete
May 18, 2016 at 12:54

Use subtractor circuit to get voltage across AB and use a micro-controller like pic with internal ADC to monitor the voltage internally, and since you can operate a pic at about 20MHz, you can keep close watch on the parameter.

Just an idea.

• Can you draw (or describe in detail) how? I can't see how.
– Pete
May 17, 2016 at 16:49