However, qualitative analysis is pretty straight forward and, if you look hard enough, you'll find that there is indeed some sort of R-component (or L component) whenever a capacitor is used as a filter. For low-pass RC filters, the cap IS the load. For high-pass, there is a resistive load somewhere.
Lets break the schematic apart. The volume control is a volume control. It's the same way it was done for a long time in guitars. The tone controls are just tacked onto that. You can remove the tone controls and the volume works the same, and vice versa.
You are assuming they designed a standard tone control as an RC filter, but they did not. It just looks and possibly works that way. These are just building block passive circuits stuck together.
If they REALLY wanted to implement true tone controls or RC filter they could have, but then would have had insertion loss to make up for. RC filters generally have a series resistance. These circuits do not. These kinds of tone controls were quick and dirty "hacks" that had minimal impact on the output of the passive guitars. So while these may form a certain filter circuit, that wasn't the intention.
Note that the parts chosen are just commonly used pot and cap values. I can guarantee you that no calculations where done!
In the case of the Rick circuit you sent, the treble volume control (330k) forms the high-pass filter with the .0047uF cap; that load is there when the volume is turned up. When it's rolled back, the filter value changes. In the Carvin circuits, the "bass tone control" circuits are all low-pass with the cap to ground. By the very nature of the configuration, they could not sink low-frequencies to ground - the cap would block those low frequencies from sinking to ground and allow them to pass through the circuit.
Once again the bass blocking cap and the treble tone control are separate entities. You can remove one or the other and they still work. They were never designed as part of a filter that required the other part. it was just a way to contrast to the tone of the two pickups. My Ric used 500K pots. It still worked the same. I also removed the treble pickup tone circuit and bridges the cap with a 1sM pot, as in the G&L circuit. Then I had an additional stereo master volume control. None of those things drastically altered the tone of the bass.
This is something to remember about treble cut tone controls. When on 10, the cap is doing nothing. You do have some load from the pot however. As you turn down the tone control pot from ten, the major effect is changing the resistive loading on the resonant circuit. This is because the impedance of the capacitor in the range of the resonance is a lot less than the pot value. As the pot gets closer to zero, the capacitor becomes important, but the initial effect is just resistive loading.
As far as Craig Anderton's Mighty-Might preamp, the circuit had an input impedance. He may not have used a resistor, but if he buffered in any way, using any sort of active transistor, the circuit had an input impedance. That's is exactly what transistors do: they provide current gain. Current gain is what happens when you turn a high impedance (low current) into a low impedance (high current).
First, it was an op amp circuit. Most audio circuits with op amps have an input impedance setting resistor. Without that they run at very high input impedance. That buffers the pickup, but can produce noise. I don't have the circuit in front of me to look at, but it was pretty novel and allowed the input impedance to be set by the pickup.
I'm sure you know as well as anyone that sometimes in electronics and circuitry things are hidden and less than obvious. Heck, I work with a Sr. EE (my boss) who doesn't understand most of this stuff. He's a computer guy and totally lost when it comes to circuit analysis (seriously). I won't go much further than that... And, just for the record, I don't actually simulate much of anything. I was trained and mentored by several retired analog engineers who could intuitively analyze a circuit so well that they didn't need to simulate anything. I hope to someday be like them...
By the way, I also have a background in the electronics industry, and used to work for a large corporation that did defense communications contracts back in the late 70s.
Back to the G&L circuit at hand, I would bet *something* that if I take my old G&L bass/treble controls and put them on the bench with a function generator and scope, that I will be able to accurately predict the effects of that 250k volume pot arranged like it is, as well as changes in the value of that resistance. I won't be at work tomorrow, so I don't have access to the function generator, but I'll try to remember next week.
The function generator is not going to work the same way a pickup does. With a passive system like this, you are forming a tuned resonance circuit. You can use a driver coil over the pickup, but even then it's very difficult to get accurate graphs of what's going on. The pickup has a lot of different things going on.
If you are interested in discussions on this kind of thing, you should hop on over to the Pickup Makers section of the Music Electronics forum. A few of the guys there are scientist and one works for a major semiconductor firm. At least one is a PhD. You will also find people like Jason Lollar and Rick Turner. We have had long discussions on modeling passive guitar circuits and using function generators and scopes to plot frequency response, etc. Trust me, it ain't that simple, and hasn't really ever been 100% successfully done.
Pickup Makers
Heres some good recent threads:
Why does ^ reluctance ^ RAC?
Making good measuremnets with imperfect driver coils
measuring resonant peak
Just try this, try wiring up the various parts and using your ear to listen to them. Then you will see. I did that back when I was 16 after I opened up various guitars and my Ric bass and saw when they were doing there.
