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How to measure the voltage across a potentiometer ratiometrically

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Rerouter:
Struggling with a concept, I am trying to convert a signal from a variable resistance sensor to a voltage with a way of compensating out the supply voltage, I am trying to keep everything analog,

The issue I face is, with most bridge differential amplifier methods, if you halve the supply voltage, you halve the difference between the 2 inputs, meaning half the output voltage,

Other methods require control of the ground node to compensate there, that node is where the sensor bolts into an engine, so left unable to change that,

So with all that in place, are there any op amp circuits that given a voltage divider like a potentiometer, to have a consistent output when the voltage across the potentiometer changes.

Linear would be ideal, but can work around it, and hoping for an output voltage in a 0-5V range, don't mind which direction, last point is, I only have a single supply available.

Anyone come across a circuit like this in the past?

SiliconWizard:
Of course one of the easiest approach would be to insert a voltage regulator/reference of some kind between the input voltage and the divider. Would that be a problem here? I see you're looking for an output voltage in the 0-5V range, and your min input voltage seems to be 5V. Should be workable with any decent LDO. What did I miss?

Rerouter:
There are a few edge cases where I don't control that, but I may just have to say tough luck. That is my fall back plan if nothing like this exists,

Picuino:
Search for wheatstone bridge.
Amplifiers and compensation.

mikerj:
The other possibility is driving the sensor with a constant current.

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