Knowing what you can and cannot change about a circuit can make projects much easier There have been several times in the past, in which I've found a circuit I liked, but been annoyed because it had bizarre potentiometer values, and I've wondered, "can I just use whatever pots I want?"
For example, the yu synth oscillator has 22kΩ potentiometers as well as some other, what I would consider harder to find trimpot values. When I breadboarded the circuit, I decided to just use more common values for the pots (I used 100k) and trim pots and it all seemed to work just fine.
Then, this last term in my circuits class, I made the blanket statement that for pretty much any voltage divider, the pot values don't really matter because of the voltage division rule...
We show that Vout is really just a ratio of Vin based on the position of the pot. Unfortunately this is not always true as I found out when I started considering the voltage divider as part of the various circuits it is usually implemented in.
Consider the case when a voltage divider pot is used to scale the voltage of an incoming signal to a simple op amp inverting amplifier/mixer....
This equation right above tells the whole story. RB (and therefor RP) must be considered with respect to Rin. To understand the equation, lets consider a few cases...
The simplest case is when RB << Rin (note: << reads as "much less than" and allows us to do some mathematical magic to simplify our equation; basically we are going to say that Rin = ∞ with respect to RB).
We can say that RB << Rin when Rin is at least twice as large as RP(the pot value). This math is hardly a "proof" as I skip steps like taking limits. It is only meant to give a feel for what is going on.
From the above, we can say that when Rin is at least twice as large as RP, the circuit works as a classic linear voltage divider (we're gonna show that with a graph in a minute).
Now lets consider another case when Rin = RB. When Rin is larger that Rp, like in the above example, this can never be true. So, now we must assume that RP is larger than Rin
I decided to graph a few different values in wolfram alpha to express this idea. I choose to evaluate this with Vin=5, Rin = 1000, x represents RB,
This first graph is the case when RP is 10 times smaller than Rin. as you can see, the output is very linear.
How about Rp being just half the size of Rin (as we defined in some of the math above). As RB approaches 500, you can see the transition becomes less linear and more exponential (I guess we were a bit liberal with our assumptions.)
Now lets look at a graph where Rin = RP. This exponential response kicks in sooner.
Finally, lets look at the case when Rp is 10 times greater than Rin
In summation. If you are looking for a linear response, Potentiometer voltage divider values should be chosen such that their value is at least the same if not less than the value of the Rin resistor. So for the Potentiometers in the yu synth oscillator, replacing a 22k pots, it would be better to use 20k or even 10k rather than 50k.
One last thing to consider is the amount of current you are allowing through your pot. replacing a 100k pot with a 100Ω will probably mean much higher power consumption and should probably be avoided. Replacing a 22k pot with a 10k pot should be fine.