What size fixed resistor to use in voltage divider with variable resistor

[amateurasu]

I've done a bit of googling on this, and it is always suggested to match the fixed resistor to the variable one. Say, a 10k fixed resistor for a 10k photoresistor/thermistor/whatever. I'm just wondering why it's necessary for it to be so high. Say your voltage divider is jooked up like so:

(+5V)---<variable resistor>---[analog in]---<fixed resistor>---(ground)

If the variable resistor is 0-10k and the fixed one is also 10k, that limits you to only half the possible range of voltages for your analog input to read, from 2.5V to 5V. Since the resolution of the ADC is fixed, that gives you less sensitivity, and half of the ADC is wasted. Wouldn't it be better if the fixed resistor was set to a smaller value, like 1k, allowing your variable resistor to cover 91% (0.45V to 5V) of your analog input's range? The fixed resistor just needs to be big enough that a low value on your variable resistor doesn't result in excessive current, right? 5V/1kOhm gives 5mA as a worst case even if the variable resistor ends up a dead short somehow (unlikely). Am I missing something?

...Before posting this, I thought of plotting the curves of voltage at the analog input over the range of the variable resistor for both 10k and 1k fixed, 0-10k variable. The curve for the 1k fixed resistor has a pretty sharp curve up as the variable resistor approaches 0. The 10k fixed resistor curve is less curved, though still not really linear. But is that the reason for suggesting matching k values? A compromise between the linearity of the curve and the sensitivity of measurements you are able to make?

[adafruit_support_bill]

It depends somewhat on what type of variable resistance you are have and what you are trying to get from it. Here's an app-note describing a bunch of different circuit designs for thermistors: http://ww1.microchip.com/downloads/en/a ... 00685b.pdf

[amateurasu]

Interesting read. Thanks for the link.

[adafruit_support_mike]

As a general answer, you're looking at a tradeoff between range and precision.

If you put a 10k pot in series with a 100R fixed resistor, you'll be able to tune it across 99% of the voltage range. Thing is, you'll do well to get within 2% of any specific voltage, assuming you have a single-turn pot with a zero-to-full range of 270 degrees.. a 1% adjustment in voltage requires a 2.7 degree turn.. and given the mechanics of an actual pot wiper, there will be some sticking, slipping, and sticking as you move the wiper.

If you flip the values around and put a 100R pot in series with a 10k fixed resistor, turning the wiper 27 degrees changes the output by about a tenth of a percent.. much higher precision, much smaller range.

The general idea is to decide how finely you want to adjust the voltage, use fixed resistors to get close to the target value, then use the pot to tweak the details.

If you want wide range and fine adjustment, try building a divider from two 10k pots with a 1k pot between the wipers. The idea is to set the general voltage with the 10k pots, then do the fine adjustment with the 1k pot. The trick is to keep the resistance across the whole thing close to 10k at all times.. if you want to adjust around 90%, set the top 10k to about 500 ohms and the bottom one near 8.5k, then take values between 85% and 95% from the wiper of the 1k.

[amateurasu]

Well, my specific application only gives me access to the wiper and one end terminal of the pot, and I am trying to choose a fixed resistor to use in a voltage divider to read the position of the pot. It's a setpoint dial on a thermostat. The pot itself can spin 360 (it just rolls back to the beginning after a small dead zone), but the dial is blocked in such a way that the pot is effectively limited to a range of 2.4k at the 85 degree end to 9.1k at the 55 degree end. In this case, neither precision nor linearity are particularly important, because nobody will be able to distinguish a difference of even a couple degrees, certainly not tenths or hundredths of degrees. It's just a wishy-washy, vague indication of "make it warmer" or "make it colder", really. I suppose since even 1 degree resolution is fine enough for my purposes, I should build a resistor network that gives as flat a curve as possible along that range, as long as I can detect at least 30 different levels in it. I'm probably overthinking it anyway, but I was just curious, in general, what factors would go into choosing the resistors, and why the blanket recommendation seems to be to match the maximum value of the pot.

[Zener]

You are overthinking it and I am surprised no one has said so. Just hook one end of the pot to 5V and the other to ground. if the pot is 10K then you will have half a mA through the pot, basically nothing. You will have no current through the wiper if it is attached to an A/D pin. Done.

[amateurasu]

Like I said, I don't have access to both ends of the pot. I have access to one end and the wiper. Otherwise, yes, this would be an incredibly easy problem.

[Zener]

I thought you said one end was connectewd to 5V. What is it connected to?

[amateurasu]

5V. I sketched out the general shape my circuit will take in my first post.