Input capacitor blend math

[RandomGlitch]

I'm about to attempt to a capacitor input blend to a pedal I'm building.

It's similar to the one seen here for the "Deluxe Bazz Fuss" (mentioned on this forum today, coincidentally!) http://www.home-wrecker.com/bazz.html

I'm looking to replace a switched 4.7nF / 100nF input.  My idea is so that I can get all variations between 4.7nF and 100nF, or thereabouts.

Now, I can just experiment with values, but what I'd really like to know is, is there any math that determines the effecting capacitance for large capacitor in series with resistor, in parallel with small capacitor.

(a) Full on tone (ie pot to zero resistance) - easy actually , just the sum of the small and large cap

(b) Full off tone (it must be larger than the small value capacitor, but by how much?

(c) The sweep between (a) and (b) - linear, logarithmic or something else? (assuming linear pot)

Thanks!

[R.G.]

Yeah, there's some math that describes it. 

A switch alternates between a very small resistance when closed and a very large resistance when open. So much so that you can usually ignore the resistances that do exist there because they're trivially bigger or smaller than would make a difference.

When you go putting blend pots in there, the resistances in the non-full-on positions are no longer negligible.  They cause frequency rolloff and shelving effects that may or may not sound like a variable cap like you've described. This may be good or bad, but it's not all variations between two caps. Also, the non-negligible nature of the resistances mean that they interact with the source impedance driving the input and the input impedance loading it. Again, this may not be bad, but it is not all variations between two caps.

The math comes down to describing the driving signal impedance, the two caps and two resistances the pot makes depending on how you hook it up, and the input impedance loading it; the description is best done with complex (i.e. real+imaginary numbers) or s-transforms, and once you describe the impedance of the network, you can do some algebra to get the transfer of voltage and/or current as a function of frequency and plot that as either complex numbers or magnitude and phase.

Yes, there are simpler approximations. If the small and large caps are quite different, you can ignore the small one at low frequencies because it may be much higher impedance than either the resistor and large cap. At high frequencies, the big cap is long since much smaller than the resistor, so you only need to take into account the small one. Between the two points, or if the caps are near one another in size, or the resistor changes a lot, it gets messy. At least messy to quick and dirty approximations.

Your caps are about 20:1 different. That's awfully close for being able to ignore one or the other. You're right - if you have the pot set up as a variable resistor, the resistor set to zero (and not all pots actually go to zero; there's some end resistance in many of them) and the caps are paralleled effectively. With the resistor at max, the resistor plus large cap form a high pass which depends on the following driven impedance. This gets "shorted" at some frequency above the RC turnover point of the resistor and the small cap, but the driven impedance still determines the overall rolloff. The sweep between the two amounts to the changing turnover points of R*C1 and R*C2. It's linear in frequency with each of the caps. But the ear "wants" to hear exponential frequency changes as linear, so you may need to go either log or reverse log, depending on how you want it to act.

[nocentelli]

As RG shows, you can do the math(s), but it's complex. I find a 100kB pot works well and I tend to use caps that are 1:100; For the bazzfuss, for example, I think I used a 10n for the small one, and a 1uF for the biggy.

[RandomGlitch]

Thanks RG, what a honour to have such a detailed reply from you.  I've built quite a few of your circuits.

  I thought it might be "non trivial" as my science teachers used to say.  It's been a while since I did any imaginary number maths so I recon i'll just get the top cap value I want, then fiddle with the small one till i'm happy. nocentelli, The 1:100 sounds like a good starting point.

Many thanks

[effection]

If you have a multimeter that measures capacitance, hook up that network and and play around with the pot until you find something that you like.

The smallest possible value is definitely the best route to go, in my opinion. You'll get the most action out of the knob that way. This is what I do: If you want the "full-off" to be simply the value of the small capacitor and you want the most action out of the pot, try something like a 50k and see if that's enough to block the large cap fully. If not, add a 5k or 10k or whatever pot and work it until you get the full-off value that you want, measure the resistance you have that pot set to and swap it out with the fixed resistor closest to that value. Keep in mind that when you do this, you won't get the sum of the two when maxed, so again, go to "full-on" and do the same thing until you reach what you feel is the best compromise and you get the sweep that you want from it.

There's probably a more math-y way to do this, but, in all honesty, I just like to play.