Square Law Potentiometer Circuit

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.

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

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

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

Figure 5: Empirical Results.

About mathscinotes

I am an engineer who encounters interesting math and science problems almost every day. I am not talking about BIG math here. These are everyday problems where a little bit of math really goes a long way. I thought I would write some of them down and see if others also found them interesting.

View all posts by mathscinotes →

This entry was posted in Electronics. Bookmark the permalink.