Square Law Potentiometer Circuit

Posted on 25-May-2012 by mathscinotes

Quote of the Day

The question isn't who is going to let me; it's who is going to stop me.

— Ayn Rand

I do not have an immediate need for a circuit that generates an output voltage proportional to the square of the potentiometer setting, but this circuit was interesting enough that I thought I would document it here. I found it while looking for a logarithmic potentiometer circuit.

Figure 1 shows the original article describing the circuit.

Figure 1: Circuit that Generates a Square Law Voltage Output Based on a Potentiometer Setting.

Figure 1: Circuit that Generates a Square Law Voltage Output Based on a Potentiometer Setting.

This circuit generates an output voltage given by V_{OUT} = {{k}^{2}} \cdot V_{CC}, where k is the potentiometer setting as a percentage of full scale and VCC is the supply voltage.

To explain how this circuit works, let's redraw the circuit using idealized components (Figure 2).

Figure 2: Idealized Representation of the Circuit of Figure 1

Figure 2: Idealized Representation of the Circuit of Figure 1

For {{V}_{CC}}=I\cdot {{R}_{P}}, this circuit generates a voltage output of {{v}_{OUT}}={{k}^{2}}\cdot {{V}_{CC}}. Figure 3 shows my derivation.

Figure 3: Derivation of Square Law Characteristic.

Figure 3: Derivation of Square Law Characteristic.

There are lots of ways to build a current source that are well documented on the web, so I won't go into detail here. I will attach a Maxim reference that I think is excellent.
AN3869

Empirical Results

Figure 4 shows a version of this circuit that I simulated using LT Spice (free simulator).

Figure 4: Square Law Circuit From Simulator.

Figure 4: Square Law Circuit From Simulator.

Figure 5 shows my empirical data. I did no resistor tuning. Just threw it together and it seemed to work well.

Figure 5: Empirical Results.

Figure 5: Empirical Results.

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5 Responses to Square Law Potentiometer Circuit

  1. Pingback: Some Empirical Potentiometer Results | Math Encounters Blog

  2. Oscar Pacheco says:
    5-March-2015 at 1:43 pm

    Fantastic!....nice results and ingenious treatment of Circuit Laws. Did you find some applications for?....

    Opacheco.

    • mathscinotes says:
      5-March-2015 at 2:00 pm

      I thought the circuit was very interesting. I have not used this circuit for any designs. I stored it on my blog so I would not lose it, which has been my main use for the blog.

      • Oscar Pacheco says:
        5-March-2015 at 3:10 pm

        I think I can use it in order to replace a potentiometer in order to get this transfer function (Vout/I), like a transimpedance circuit maybe for get a specific function of rotation very similar to loudness potentiometer compensation(here is different no linear transfer function more complicated I think!).....but similar!

        Thanks
        Opacheco

    • mathscinotes says:
      2-May-2016 at 1:20 pm

      I found an interesting application using a related square law circuit for compensating a pneumatic system (paintball gun) at this link.

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