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Updated: Sep 8, 2020

Finding the right resistor combination to create a specific voltage range can be cumbersome. This short article aims to show you how to calculate the resistors needed for a precision voltage sweep.

On the left you can see what we have to work with. A potentiometer with a resistor above and below. This gives an output voltage(Vo) between Vl and Vh. The tricky part is determining the values of R1 and R2 when Rp is known. By using the voltage divider principle and a little algebra, we can easily find the two values.

First we need the formulas for Vl and Vh. They are shown below.

Now with some algebra, we can rearrange both formulas for R1, combine, and solve for R2. The resulting formula for R2 is below.

Finally, we take the formula for R2 from above, and plug it into one of our formulas for R1 that was originally found from Vl or Vh and solve. The resulting formula for R1 is below.

With our two formulas in hand for R1 and R2, we can now try an example.

For this design we will use the following parameters:





Starting with R2, the value is:

R2 = (10,000 * 0.8)/(3.56 - 0.8) = 2898 ohms

and R1 is:

R1 = 2898 * (5 - 3.56)/0.8 = 5217 ohms

Now using the original formulas for Vh and Vl, we can check that the two resistor values are correct.

Vl = 5 * 2898/(5217 + 10000 + 2898) = 0.8v

Vh = 5 * (2898 + 10000)/(5217 + 10000 + 2898) = 3.56v

Exactly as calculated. If you are looking for a little brain workout, give the algebra a go and see if you come up with the same as I have here.

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