Variable resistors to ground: Can we cheat?

[Taylor]

It's common that we want to have multiple resistances to ground, being varied for some effect. This is the basis for JFET and optical phasers, and a variety of filter types. But these varying resistances are kind of a pain. Expensive/need matching/need sorting/physically impractical (5-gang pots). It would be great if we could minimize our dependence on these elements. Looking at Top Top's Mouthmeistor, it occurred to me that he has in effect shorted the 2 filters together within their feedback loops via a 10k resistor (the pot).

So I wondered to what extent we can get away with something like this:



I simulated this and it actually does kind of work. We get a much steeper rolloff than we'd see with a single HPF, but the action becomes somewhat shelf-like instead of the curve continuing to silence.

Please note: this question isn't about the above filter in itself: three RC filters in series would be a dumb filter. My question is simply about the idea of connecting the R's together to a point, then varying the resistance from that point to ground, in order to fake the effect of 3 separate resistances to ground.

Does this kind of work in real life? What are its limitations? Obviously it can't work all that well, or you would see people doing it all the time. So how does this fail?

[Earthscum]

I screwed around with this idea a bit before. What I think I observed was that as the variable resistance increases, you get feedback between the other resistors. I can't remember the setups I used, but with a phaser-ish design I got feedback and oscillation. With what you proposed, I didn't get anywhere near what I thought I would.

Try it out, but I kinda remember R.G. giving a long speech in a phaser thread about this and why you need multiple resistances.

Maybe cheat by changing the reference voltage to those resistors with some kind of source (op amp output).

[Taylor]

Yeah, oscillation seems likely, since we're basically connecting points of a circuit that aren't supposed to connect. I think it might actually work in some cases, though, so perhaps I'll try some things and get back with results.

[R.G.]

Yeah, oscillation seems likely, since we're basically connecting points of a circuit that aren't supposed to connect. I think it might actually work in some cases, though, so perhaps I'll try some things and get back with results.

In normal, linear operations of a circuit like this, the circuit *is* the same as the math. The equations for a variable impedance ground are very different from separate resistors.

However, there is a simple way to get linked-value variable resistors to ground. Use the lowest value resistors you'd ever need and PWM a switch between the resistor and ground, or use a switched-capacitor variable resistor setup. Both can be done with CMOS switches. A CD4066 will do you up to four PWM'd resistors to ground, and a CD4053 will do up to three switched capacitor versions of the resistors. The switched resistors need PWM, the switched capacitors only need a variable frequency, not variable duty cycle. Then you need a suitable high frequency clock drive for the switches.

This seems complicated, probably. However, it does some things that can't be done any other way. At least not well. Since the variation is digital, the resistors track as they vary, and you can concoct any possible scheme of different value tracking variable resistors, something that is impractical with pots. You can also concoct any number of tracking resistors this way. I've only once seen a quad-section pot, and tracking is always suspect for this. A quad-section variable resistor can be done with one CD4066 and a PWM clock.

Note that you can do variable tracking capacitors too, by PWMing switches in series with capacitors. And tracking resistors AND capacitors if you're so inclined. That last is impractically difficult with pure analog techniques.
Switched resistor and switched-capacitor techniques are how many programmable filter chips are done internally.

[Taylor]

Right, I've seen the PWM'ed resistor approach in your ASMOP article (when you say "read Geofex, all of it" I really have! Although of course I've forgotten some of it, and some was over my head when I read it, so I continue to go back to it) and it's a good one. I guess I'm just thinking about this as a means for discovering a new tool for our toolboxes.

Playing around with the idea some, I made 2 twin-t bandpass filters in Falstad, then connected them via 1k resistors where their individual variable resistors should be, then put a single pot there to ground.

Schematic:



simulation code (the analog filter app doesn't support direct linking simulations). File>import.

Code Select Expand

$ 1 5.0E-6 5 50 5.0 50
% 0 28853.998118144256
a 272 384 384 384 0 15.0 -15.0 1000000.0
r 384 288 304 288 0 220000.0
r 304 288 224 288 0 220000.0
w 224 288 224 368 0
w 224 368 272 368 0
w 384 384 384 288 0
c 224 224 304 224 0 1.0E-8 0.0
c 304 224 384 224 0 1.0E-8 0.0
c 176 400 272 400 0 1.0E-5 0.0
w 224 224 224 288 0
w 384 224 384 288 0
c 304 288 304 320 0 1.0E-9 0.0
g 304 320 304 336 0
170 176 400 176 336 2 20.0 4000.0 5.0 0.1
g 656 320 656 336 0
c 656 288 656 320 0 1.0E-9 0.0
w 736 224 736 288 0
w 576 224 576 288 0
c 528 400 624 400 0 1.0E-5 0.0
c 656 224 736 224 0 1.0E-9 0.0
c 576 224 656 224 0 1.0E-9 0.0
w 736 384 736 288 0
w 576 368 624 368 0
w 576 288 576 368 0
r 656 288 576 288 0 220000.0
r 736 288 656 288 0 220000.0
a 624 384 736 384 0 15.0 -15.0 1000000.0
O 736 384 848 384 0
r 304 224 304 128 0 1000.0
r 656 224 656 128 0 1000.0
w 656 128 496 128 0
w 496 128 304 128 0
174 496 128 496 224 0 50000.0 0.9950000000000001 Resistance
w 512 176 528 176 0
w 528 176 528 224 0
w 528 224 496 224 0
g 496 224 496 256 0
w 528 400 480 400 0
w 384 384 384 400 0
w 384 400 480 400 0


So, according to the filter app, it actually works ok. We do get 2 resonant peaks whose frequency varies with the pot to ground. The tracking is far from perfect, but they both vary across different ranges (due to different caps in the feedback loop).

So, am I wrong in thinking that this does kind of work? Again, my aim here is not to create a perfect weapon, but just a tool which is cheap, simple, and works to some extent.


Here's the freq response at max and min resistance. The lower filter tracks across a wider frequency range - 2.5 octaves vs less than one octave.