Another Stab at Explaining the Wah -- And an interesting inductorless wah

[thomasha]

it's not a clear plate, I just put the rubber feet so it wouln't slide during the video. It happened on my first attempt.

I made the plate later using an aluminum sheet and some black paint so it won't reflect the light.
So far I had no problem with a little of light leaking throuth the sides. I think the resistance is much higher and is more affected by the direct light.

[Transmogrifox]

It's rewarding to see somebody getting some joy out of this circuit.  Thanks for posting the build report.

Really cool mechanical job.  That's always the challenge with DIY wahs

How does it feel with a mini like that?  Does the travel feel natural or does the lack of mass mess with your sense of balance?

[thomasha]

like I said in the beginning it's like fighting with the pedal until you find a good position that works for you.
It's better to play with the middle part of the foot. I tried with the toe and heel but it kept sliding off. It's also much easier to play without shoes.

[EBK]

Have you posted any info on the mechanical aspects of this pedal?

[Eb7+9]

continuing my investigation of alternative wah topologies floating around the net ...
and one of the more interesting design threads on this forum IMO

esp. for the approach taken ... to try to fix what nature can't provide
... and doing fairly well in the end

---

basically ...

first, you're going up the ass-end of a gyrator based SK filter,
in itself somewhat unusual relative common audio practice, but rule breaking is almost mandatory in FX design

-> to produce a peaky low-pass Biquad (2nd order) filter response ...

and then chopping off the low-pass part with a fixed 1st order HP with a roll-off at about 100hz

so, producing a 3rd order (factorize-able) response overall

kinda breaking the usual SK "input/output" rule and applying a fixed low-end truncation that doesn't respond to WAH pot ...
then later, another tweak to fix the Q variation against said resistance

the only thing I would critique otherwise is taking the output in the "wrong" place relative to the usual SK transfer function
and also, where the circuit little to no drive because of the variable (high) resistance in the (your) emitter leg
and a very high (theoretically infinite) Zin before the buffer part ...

that's not super crucial here as far as producing a basic response purely speaking
(but as a practical implementation, yes - probably ... with buffering adding more noise)

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some background ...

the std. SK equations show a peak response that doesn't stay constant with variable resistance

https://en.wikipedia.org/wiki/Sallen%E2%80%93Key_topology

with Q varying as inverse of SQRT(Rwah)

these SK equations hold for a gain of exactly unity (how it is commonly studied)

the ideal (math only) response, replacing any device by a "pure" controlled source looks like this:



what happens when the gain is dropped by a mere 0.5% looks like this:



equations no longer hold and starts looking like the response of your circuit
(circuit sensitivity of the SK topology is one of its main criticisms)

gain from unity to 0.995 being akin to going from op-amp follower to emitter follower, as you discovered ...
worth making note of anyway, ... and, as far as I can see, the crucial reason why your route "works"

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the part I found interesting was with your approach to later tweaking the follower section via signal bootstrapping

in fact, producing and extended Gyrator response
(sorry, I don't buy your op-amp argument since the feedback is positive and return impedance not low enough to being with)

A, B, C curves shows yours, with cap-bypassed signal injection, with un-bypassed signal injection, and then with basic current source (allowing for varying gain factor ...) ...

your approach "C" produces an extended range of inductance simulation ... (well done!)



combining the two you get something that is in the ball-park, and is stable at toe end ...
(unlike couple of other op-amp based attempts as I pointed in another thread)



tho, compared to classic WAH reponse, there are a few differences in the profile shape
and how the tow-end response is arrived at versus pot resistance sweep

important as a practical comparison, but as far as circuit analysis secondary

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a few comments about the math here:

the DSP research guys have been tackling the emulation problem for a few years now
several decide to cut corners and, for sake of simplicity, leave out elements that provide full modeling ...

for example,

Zolzer in his DK Nodal paper:

"We exemplify the method with the Dunlop Crybaby wah-wah
effect pedal, as the continuous change of the potentiometer position
is an extremely important aspect of the wah-wah effect. Whether
a full-featured non-linear physical model of the wah-wah is really
necessary or simpler approaches (e.g. as described in [3] Smith's biquad modeling above) suffice
is anyone's choice; but the circuit is well suited to explain the
technique presented in this paper which is why it is used here."

note: implied here: large-signal response includes small-signal response as well (!)

Smith shows off the discrepencies exhibited by his response here :
(a little similar to yours I might add)

https://ccrma.stanford.edu/realsimple/faust_strings/Digitizing_CryBaby.html

while Zolzer's bang-on response are shown in his paper:

https://www.researchgate.net/publication/242020949_Physical_Modelling_of_a_Wah-wah_Effect_Pedal_as_a_Case_Study_for_Application_of_the_Nodal_DK_Method_to_Circuits_with_Variable_Parts

reading between the lines and looking at the assumptions made in a couple of the other papers
reveals THE key element removed to make the analysis easier, and which would otherwise provide "bang-on" emulation ...

turns out, for example, the the circuit that Smith is working with produces and unfactorizable 3rd order function
while the full version - which Zolzer is alluding to - is really an unfactorizable 4th order function ...

in either case, this shows (or proves) that a factorizable 3rd order function (ie., yours)
must exhibit deviation from a non-factorizable 3rd order function (one level removed of approximation)
and certainly somewhat more deviation from a non-factorizable 4th order function (zero level of approximation)

and explains why your circuit performs a swept bandpass response that is not totally (classic) wah-like but rather biquad like
(so, more than one-level removed of approximation)

from this I had to check out whether or not this subtle distinction
was perceivable to the ear ... even tho visually the difference might seem rather subtle to some

an op-amp wah was devised to include and exclude the key ingredient that turns the response
from 3rd order to 4th - both non-factorizable - at the flick of a switch :



and yes, the ear can tell the difference between these two very-close responses ...

thanks for posting your work Transmo, this encouraged me to take a second look at what was missing in my previous attempts ...
it finally answered what constitutes THE classic Kushner-Plunkett WAH filter response
(mathematically speaking)

it also showed me how KP arrived at their circuit and where exactly they must have started from ...
but that's another topic altogether