Counteracting capacitance

[PBE6]

I was perusing some old threads, and came across this one that gave me an idea for a simple project for the weekend:
https://www.diystompboxes.com/smfforum/index.php?topic=114107.0

I like the idea of trying to get a different character out of a passive guitar by adjusting the resonance between the pickup, cable and controls, and I'm curious to see how flexible a control system like this could be.  Adding capacitance is easy to do, but the thread above makes it seem like taking it away might be almost as easy.  Wikipedia has an entry for it under "negative capacitance converter", so I assume it gets some use in the electronics world:
https://en.wikipedia.org/wiki/Negative_impedance_converter
https://en.wikipedia.org/wiki/Negative_impedance_converter#/media/File:Negative_capacitance_circuit.svg

I don't have Spice, but I do have a lot of scrap paper, and I was able to do some circuit analysis on a simplified guitar circuit with an attached negative capacitance converter to chart out some curves on Excel. It does seem to show that the negative capacitance converter counteracts the cable capacitance and moves the resonant peak higher with increasing opamp gain.  My question is, can it really be that simple?  Seems like a simple and cheap way to breathe some new life into a passive guitar, or even to brighten up dull pickups with excessive capacitance in the windings. If it really worked, and it was really that simple, wouldn't somebody have mass produced it by now?  Then again it might have been, I assume the Zerocap products use this idea:
http://zerocapcable.com/

[Rob Strand]

My question is, can it really be that simple?  Seems like a simple and cheap way to breathe some new life into a passive guitar, or even to brighten up dull pickups with excessive capacitance in the windings. If it really worked, and it was really that simple, wouldn't somebody have mass produced it by now?  Then again it might have been, I assume the Zerocap products use this idea:
http://zerocapcable.com/

I believe so.

IIRC, there was a magazine article about this method, perhaps in Wireless World.  It appeared in the "design ideas" section where readers send in stuff.  Maybe 1990's.  [I could be mistaken about this.  It might have been another method which drove the shield.]

[amptramp]

There were a number of circuits that used triaxial cable with a unity gain buffer driving the middle shield with the same signal on the inner (output) wire.  There were also similar designs using guard rings on a circuit board that were driven by buffers.  As long as the buffer can keep up with the signal, this is a good approach and in the audio frequencies, it should not be much of a problem.  We often used National Semiconductor LH0002CH and LH0033 buffers for this task.

[PBE6]

Welp, got sidetracked again this weekend but I still want to give it a try with a slight modification.

The whole idea for me is to be able to use this as a "natural" EQ of sorts, one that allows you to change the response curve by modifying the resonance of the passive guitar electronics as opposed to keeping that resonance static and using additional EQ on the back-end.  I got to thinking that it would be nice if I could use this system to add capacitance as well as to counteract it, so I could sweep a big range of mellow --> bright with a single control.  After dismissing a few convoluted ideas, I realized the simplest solution would be to - wait for it... - just add additional capacitance with an additional capacitor!   The math doesn't seem to care whether the cable capacitance comes from the cable itself or is being spoofed with another capacitor to ground connected at the input to this EQ box, so I figure adding one there would give me the mellow starting point I'm after.  Additional brightness can then be added by increasing the gain on the negative capacitance converter.  The whole circuit would look something like this:



L, Req and Cc are all part of the guitar electronics.  Cfake is the additional capacitor used to create the mellow starting point (I'll start with a 100nF cap, but might not end up needing more than 10nF).  Ccouple and Rref are there so I can use a single battery in the box (Rref will be 1M, Ccouple will be 100nF - have lots lying around!).  Cn, A and B are all part of the negative capacitance converter (Cn will likely be 100pF as it's the smallest cap I have, A will likely be anywhere from 1k-10k, B will be a 10k-100k potentiometer, depending on what I find lying around).

Does anyone see any obvious errors? Or any not-so-obvious errors?

EDIT: I found an error already. If I'm only adding 10x the Cn value, then I'm only going to end up counteracting the 100nF cap with 10x0.1nF = 1nF.  That ain't gonna work.  I guess I will start with Cfake = 10nF, and either increase Cn or change the ratio of A to B so that I get an appropriate sweep.

[j_flanders]

To get an idea what the effect is on the frequency response of the pickup, you could plot it in real time with something simple as this:
https://guitmod.wordpress.com/2016/09/26/diy-simple-measuring-of-a-pickups-frequency-response/
Or with something slighty more complicated like this:
http://guitarnuts2.proboards.com/thread/7723/measuring-electrical-properties-guitar-pickups

I used the excitation coil from the first link and it worked very well when I tested various ways of changing the frequency response of my pickups.
I used this free plugin in Reaper: https://www.voxengo.com/product/span/ as Audacity does not do real time frequency response plots.

[merlinb]

There was a recent EDN design idea related to this topic:
https://www.edn.com/design/integrated-circuit-design/4461568/Synthesize-variable-in-circuit-Rs--Ls--and-Cs-

[ashcat_lt]

If the gain is greater than 1, the cap starts to look like a "negative" capacitance.  When it's less than 1, it goes from "no cap" toward bigger and bigger "positive" capacitance.  If you had a circuit that could produce gains that go through 0, you could just use that one cap to go darker and brighter.  I know there are such things out there, but I'm not the one to tell you how to do it.

[PBE6]

This post got me thinking about different configurations for the opamp driving the cap.

As noted, the non-inverting opamp gives a minimum gain of 1 so it will never add capacitance back as required to simulate a regular tone control. The inverting opamp has a minimum gain of 0, but because it inverts the signal it always adds capacitance back and does not counteract capacitance as required to simulate a shorter cable (at least that's what the math says, I may be missing something there...).

If the above is correct, then a circuit that lets me transition between the non-inverting and inverting configurations would likely fit the bill. I think PRR posted something like this once a few years ago, but I can't remember when/where/why or how he did it. However, I think it might be possible to adapt the polarity inverting section from RunoffGroove's Splitter-Blend:

http://www.runoffgroove.com/splitter-blend.html

Their version has a switch, but if you replace that switch with a pot then the transfer function for that circuit snippet boils down to:

(Vout/Vin) = (P - B)/(P + A)

Where A is the value of both the input resistors (220k on the schematic), B is the value of the feedback resistor (220k here) and P is the value of the pot. Setting B equal to A gives the signal a range from -1 to 1, while setting B larger will increase the negative side of the sweep to -B/A and keep the positive side capped at 1.  No idea if this will annoy the opamp, or do what I expect, but I should breadboard it and find out.