input and output impedance of volume pot

[rbruss82]

It seems like I once read that the output impedance of a volume pot is 1/4 the value of the pot.  (Hence, a 100K pot would have an output impedance of 25k).  Can anyone verify that this is correct?  Also, does anyone know anything about the input impedance of a volume pot?

[Sir H C]

It is a maximum at 1/4 the value if the rest of the circuit is relatively low impedance.

Worst case is when the wiper is 1/2 way, so you have the same as two resistors of 1/2 the value in parallel, therefore 1/4 the resistance.  Wiper at ground, output impedance is zero.  At the max, it is whatever the output impedance is of the circuit with the pot in parallel.

[R.G.]

Simple question, but moderately complicated to answer.

In general, the input impedance of a volume pot is not constant, nor is its output impedance.

You have to include the load that the wiper is driving to figure the input impedance.

If you draw up a general volume pot with its wiper connected to a resistor to ground, you get a general circuit for what a volume control looks like.

At full up, 100% rotation, the impedance is the pot value in parallel with the resistance of the wiper to ground. At full down (0% rotation), the impedance is just the pot resistance because the resistance from wiper to ground is at ground on both sides. In between...

Let's call the total pot resistance Rp. Let the resistance of the upper part of the pot resistance be R1. Let's call the resistance of the lower part of the pot R2, then immediately note that R2 is equal to Rp*%rotation, or just Rp*%. We can then call R1 Rp-%Rp or Rp*(1-%). Let the wiper loading be RL
Then the input impedance Zin is

Zin = R1+R2||RL or Rp*(1-%)+Rp*%||RL

Which is equal to Rp*(1-%) + (Rp*%*RL)/(Rp*%+RL)

(by now, the math averse readers are screaming and fleeing)

But let's play what if. What if RL is much bigger than Rp? If it is, the term Rp% +RL becomes almost exactly RL, and then Rp*%*RL/(Rp% +RL) becomes just Rp*% as RL/RL is one, and the whole thing simplifies to Zin = Rp.

If RL is almost zero compared to Rp, then the whole thing simplifies to Zin = Rp*(1-%), and the input impedance is anywhere between Rp and zero, depending on the rotation. In between, the impedance depends on the parallel value of Rp*% in parallel with the wiper load, and it varies from a lot to a little.

The output impedance is easier. It's zero at both 100% rotation and 0% rotation. Well, at 100% rotation it's whatever the source impedance is, at least. The pot contributes little to it. As you rotate the pot away from 100% and 0%, the impedance rises, and it hits a maximum at 50% resistance rotation of the top and bottom resistances in parallel. That is, the top resistor and bottom resistance are both Rp/2, and in parallel, that's Rp/4. And that's where the 1/4 of the pot resistance you heard comes from. That's actually a maximum.

[rbruss82]

Okay, thanks!  Now, does anybody know anything about input impedance of a volume pot?

[rbruss82]

Sorry R.G.  Disregard my last reply.  I had not seen your post when I made it.  Thanks!