# How to calculate "effective source impedance" in this audio mixing circuit?

I am new to electronics and have recently been trying to get my head around audio mixing. I stumbled across a helpful introduction by Rod Elliot on passive and active mixers, but I am stuck on a small part of one diagram. The annotation describes it as a "Passive Mixer With Channel Level Controls", in this case using variable resistors (faders) to control the levels of the input channels. It is used to explain the issues with passive mixing, but my question only concerns the following statement:

In Figure 3 you can see that the faders change the impedance seen by the mixing resistors. The effective source impedance is maximum when the fader is (electrically) centred, and will have a value of one quarter of the fader's total resistance.

Only one quarter of the the fader's total resistance? I would have thought that to maximize impedance, one would maximize the resistance on the variable resistor, resulting in 20k ohms of impedance.

I think it would be helpful if the terms "source impedance" and "electrically centered" were explained? I couldn't find any helpful search results for these.

How did he arrive at the conclusion that the "effective source impedance... will have a value of one quarter of the fader's total resistance"?

• "Electrically centered" as opposed to simply "centered." Potentiometers used in audio often have a logarithmic taper rather than a linear taper. For a linear taper potentiometer, "centered" and "electrically centered" would be about the same - rotate the potentiometer to the middle of its rotation range and you will have about the same resistance from each end terminal to the wiper. With a logarithmic taper potentiometer, if you make it so the resistance is equal in the two halves then it will be mechanically off center.
– JRE
Sep 16 '19 at 5:29

Remember that the effective impedance of the signal sources is approximately zero. Modern audio devices will often have a 47R or 100R resistor connected in series with the output (internal to the device) which (usually) makes the output impedance of that device equal to that resistor value.

Now look at the wiper of one pot. The bottom end of the pot is grounded. The top of the pot has an AC impedance of approximately zero. The highest resistance point is therefore when the wiper of the pot is midway between the top and bottom of the resistor element. That means that the approximate resistance from either the top or the bottom of the post is half of the pot value.

If you draw the pot as two resistors of about equal value, and if you model the ends of the resistors as having a source impedance of about zero ohms, you will see that the wiper connection has an impedance value of (about) the top resistor portion of the resistor track in parallel with the bottom resistor portion. The net impedance as seen at the wiper is therefore about 1/4 of the total pot value.

This impedance is maximum when the wiper is in (about) the middle position and becomes smaller towards zero ohms as you rotate the pot towards ground or towards the hi-side (the input signal).

Note that the above is accurate only if the input to the pot is actually connected to an audio source. If the input is disconnected, the impedance at the wiper is maximum when the pot is turned all the way towards the input signal. That impedance is, obviously, the pot value.

• That has cleared a lot up, I now understand why halfway is maximum given that we're calculating the total impedance as the top resistor portion in parallel with the bottom resistor portion. What I don't understand is why the impedance of the wiper connection can be calculated this way. If the input signal was connected to ground, so that both resistor portions were connected to ground, I would see why they are in parallel. I was hoping you could explain what I am missing? Sep 16 '19 at 12:48
• The top end of the pot IS at AC ground. Recall that a voltage source has a near-zero output impedance. Sep 17 '19 at 0:41

If you take a 10k pot and adjust it to center, you have 5k from center to each end. Having two 5k resistances in parallel is 2.5k of resistance. So the explained quarter is true. Electrically centered just means it is set to the middle position where resistances are equal. Source impedance means if you have an ideal audio signal output with zero output impedance, using a 10k pot to adjust audio amplitude to half would result the audio signal output impedance from the pot to be 2.5k.