Using a digital potentiometer in a voltage divider

Question

I'm using an MCP3008 ADC and an MCP4131-103 (10k) digital potentiometer to try and create a sort of "adjustable voltage divider."

For the project, the resistance I'm measuring will vary, and I hoped to use the MCP4131 to adjust my reference resistor on the fly. Namely:

Vin
|
R1
|
|--Vout
R2
|
GND

I'm measuring and logging R1 (a material) over time, and it increases from maybe 500-20k Ohms over the duration of interest. If I use a fixed resistor for R2, I get poor resolution when the value is mismatched with the current value of R1. I hoped to have the digital pot adjust itself based on the running average so I also maintain my resolution.

I believe I have both the MCP3008 ADC and the MCP4131 working individually with my Raspberry Pi 3 using SPI, but they don't seem to work like I expect in a voltage divider setup.

Wiring up the MCP3008 like this Adafruit guide, I used a voltage divider with a 10k resistor as R2 and the following formula to find R1:

v_out = adc * 3.3/1024
R1 = R2*(3.3 - v_out)/v_out

| resistor used |  calculated |
|---------------+-------------|
|          1000 |        1010 |
|          4700 |        4628 |
|         47000 |       46574 |

That confirmed that my ADC appears to be functioning well.

In addition, I cycled through settings for the MCP4131 and manually read the value between the high (3.3V) and wiper with an multimeter. In each case I'm sending a value of target resistance * 128/10000. I plotted the results and get:

That looked good enough for me to believe the pot is also connected and functioning correctly.

Now, when I try to setup a voltage divider like the above to test both the digital pot and the ADC together, I get wonky results. I've tried two configurations to troubleshoot, substituting the 4131 as either R1 or R2, with a fixed resistor as the other one used:

wiper pin of 4131 --|-- resistor -- GND
                    |
                    |
                   ADC

3.3V -- resistor --|-- wiper pin of 4131
                   |
                   |
                  ADC

Using a 10k resistor in the first configuration and setting the digital pot to 5k, I get a raw ADC reading of 403, or 1.3V. I'd have expected:

3.3V * (10000 / (10000+5000)) = 2.2V

This results in a calculation of:

10000*(3.3 - v_out)/v_out = 15384 # should be 5000

Swapping things around and using the second configuration, I get an ADC reading of 624 or 2.01V. I'd expect a value of:

3.3V * (5000 / (10000+5000)) = 1.1V

This results in a calculation of:

5000*(3.3 - v_out)/v_out = 3209 # should be 10000

I'm wondering if because the potentiometer is really a voltage divider in and of itself, it's not behaving like I expect. Should I be, for example, changing my ADC Aref or GND to one of the R_a or R_b pins on the potentiometer? Or perhaps the error is in my code and I need to account for two voltage dividers in a row?

I haven't found any examples of using a potentiometer as one of the resistors in a voltage divider. Unfortunately, a potentiometer is one, searching "using a potentiometer in a voltage divider" gets a ton of hits that simply explain what pots are.

Thanks for any guidance, and I'm happy to post whatever other information would be helpful.

Answer 1

You need to configure your digital potentiometer as a rheostat. If you connect the wiper with one of the terminals A or B, you will get a variable resistor between the two terminals A and B.

According to the datasheet, the wiper is at B when the digital potentiometer is set to 0, and A at full scale. This means you can choose whether the resistor will be near 0\$\ \Omega\$ or 10 k\$ \Omega\$ when you set the min/max value in software depending if you connect A or B to the wiper. This may make your software routine more convenient.

Answer 2

The numbers you read nearly perfectly match the circuit you built (whose schematic sadly you have not posted yet, but can be reversed though)

^{simulate this circuit – Schematic created using CircuitLab}

On the first one:

$$V=3.3\,\text{V}\times\frac{3.33\,\text{k}\Omega}{3.33\,\text{k}\Omega+5\,\text{k}\Omega}\approx 1.32\,\text{V}$$

while on the second one

$$V=3.3\,\text{V}\times\frac{5\,\text{k}\Omega}{3.33\,\text{k}\Omega+5\,\text{k}\Omega}\approx 1.98\,\text{V}$$

However I don't think that's the best circuit for accurately measure resistances: wiper resistance, which is usually far from stable e repeatable in both electromechanical and electronical potentiometers, is probably going to drift and offset your measures.

Answer 3

I know this probably isn't great form, but I wanted to capture supplemental data/plots for others who run into this. I started putting it on the question, but that really made it long, so it's just going to sit here as an answer.

---

Huge thanks to awjlogan and carloc for their answers.

I'll start with carloc, who created a wonderful schematic of what I couldn't wrap my head around. Accepting this "double voltage divider" reality, I just had to change my calculations, however I found this is far from ideal due to the equivalent resistance formula. Take this scenario from the answer, which is what configuration I planned on using:

For the schematic on the left, I envision my pot setpoint, setpt as the sort of "upstream" resistor created by the wiper, and I'll get an R2 as my "downstream" resistor. R1, my measurement of interest and setpt end up forming an equivalent resistance, R_eq, which is what's shown as Rpar on the right. I simulated various ranges of my material from 1000-20k Ohms, and a range of pot setpoints. For any setpt:

R2 = 10000 - setpt
R_eq = 1/((1/R1) + (1/setpt))

Here's a plot of R_eq vs. R2, with R1 grouped/colored:

So, it works, but notice that the highest R2 I can achieve is much less than R1 as it gets bigger, which is exactly why I wanted to try this approach anyway.

That said, the illumination of the circuit was gold, and really hit the nail on the head with respect to the readings I thought were so strange.

---

On to awjlogan's suggestion, which was to short the wiper pin and one of P0A or P0B, usine one of those (vs. the wiper) as the input to my ADC. I imagine a circuit like this:

^{simulate this circuit – Schematic created using CircuitLab}

I've drawn the potentiometer as two resistors in this case, and the electrical flow is sort of "blind" to the top half due to the short. In this way, I get exactly what I was looking for, which is a simple voltage divider where one leg is adjustable.

carloc pointed out that this may be too noisy/inaccurate/non-repeatable, and that will take some checking. For my preliminary test, here's what I got with some resistors and various potentiometer setpoints:

Here is the corresponding raw data, with error as abs((adc-measured)/adc) in percent:

   setpt     adc  measured  error
1   2000  9441.3      9880   4.65
2   4000  9429.5      9880   4.78
3   6000  9515.2      9880   3.83
4   8000  9467.0      9880   4.36
5  10000  9504.8      9880   3.95
1   2000  4340.6      4610   6.21
2   4000  4376.3      4610   5.34
3   6000  4431.2      4610   4.03
4   8000  4431.0      4610   4.04
5  10000  4442.9      4610   3.76
1   2000   913.2       981   7.42
2   4000   934.9       981   4.93
3   6000   958.1       981   2.39
4   8000   914.0       981   7.33
5  10000   998.9       981   1.79

To wrap this up, we'll see if this works for my test case. ~5% isn't too bad,but it's not great either. Compare that a redo of my initial test of the ADC itself, adjusted for the measured value of my 10k R2 (9880):

     adc  measured  error
0    998       981   1.70
1   4635      4610   0.54
2  46640     46500   0.30

That makes 5% look pretty bad!

I'll start a new question on how I could measure resistance of a variable material, but this was a fun exercise and hopefully it helps someone down the road.

Answer 4

Your resistors are too big for this ADC, see Figure 4-2 of the datasheet. You can add a buffer just before the ADC, e.g. an op-amp–based unity gain buffer amplifier. I think an MCP6001 should suffice for your configuration.