A „Vox-Wah“ project, some circuit analysis and measuring results.

[Helmholtz]

Changing component values:

R1 (68k) is the series part of the input voltage divider and provides the major part of the pedal's input impedance.
Lower resistance increases overall gain without changing the sweep range. Some wahs (e.g. Maestro Boomerang) use a 47k here.
But lower input impedance increases PU loading and too low values may give rise to undesirable distortion.

Frequency response measurements and simulations are typically done using a low impedance signal generator. But when connected to a guitar, the PU impedance adds to R1.
PU impedance increases with frequency and can be as high as 20k to 50k @1kHz. So the real frequency response will be different with a guitar. I especially expect a lowered high frequency peak.


R2 (1k5) is wired in series with the PRC and defines the minimum value of the input voltage divider shunt impedance at the base of Q1.
Its effect is to add some floor level of unfiltered/full spectrum signal.
Higher values will reduce the peak to valley ratio by increasing dry signal content.


R4 is the emitter resistor of Q1. Old originals use 470R. The Vox V847 uses 510R, probably to compensate for the high current gain of the MPSA18.
Lower values increase the gain within the NFB loop (as well as the output) and thus increase the sweep range by shifting the "bass" peak to a somewhat lower frequency.


R7 (33k), sometimes called the "Q-resistor", is wired across the inductor. It has a damping effect on the Q factor of the resonance.
The Q factor is defined as the (relative) bandwidth or sharpness of the resonance peak.
But the main effect of R7 is setting an upper limit to the PRC impedance, which defines the height of the peak.
Increasing R7 will increase peak sharpness as well as peak height.


C2 (10nF), the feedback cap, together with the inductance defines the highest resonant frequency of the sweep (pot at zero = zero loop gain).
10nF and 500mH result in 2250Hz. The resonant freuency calculates as fres = 1/ (2pi sqrt(LC)).
For fixed loop gain and inductance, C2 also defines the lowest resonant frequency.
E.g. with 500mH and a loop gain of 24, the effective resonant capacitance is 250nF, resulting in 450Hz.
Higher cap values shift the total sweep range to lower frequencies.


The Wah pot.......sorry need a break. Also intend to do some simulations.

[vintagekiki]

Wah is basically a variable bandpass filter. The heart of the filter is the (ferrite) inductor, everything else is the periphery. All wahs schematic are similar, wahs be different from each other only by the type of inductor.
The inductance of a ferrite inductor depends on the AL factor of the ferrite used. The AL factor is relationship between the inductance, for a given ferrite core, and the number of turns..

From the number of turns used inductor depends its ohmic resistance and Q factor.
The lower the resistance of the inductor, the Q factor is higher and the filter will be narrow "sharp"
In contrast, when the inductor has a higher resistance, the Q factor is smaller and the filter will be wider.
In the datasheet for inductors can be find some basic data for inductance, resistance, ferrite type ...


https://sciencing.com/how-8293803-calculate-inductance-ferrite-inductor.html
https://dextermag.eu/al-inductance-calculator/

https://www.electronics-notes.com/articles/basic_concepts/q-quality-factor/inductor-q-factor.php
https://www.electronics-notes.com/articles/basic_concepts/q-quality-factor/basics-tutorial-formula.php

http://www.pocomagnetic.com/html/2014/03/06/2014030605592122540691.html
The calculation of inductance and core

[nickb]

Wah is basically a variable bandpass filter. The heart of the filter is the (ferrite) inductor, everything else is the periphery. All wahs schematic are similar, wahs be different from each other only by the type of inductor.

There are many ways to implement a Wah that do not need an LC tuned circuit. For example, state variable filter, parallel T RC filter and Sallen-Key are three that spring to mind.



Sallen Key 2P Filters.pdf

[vintagekiki]

There are many ways to implement a Wah that do not need an LC tuned circuit. For example, state variable filter, parallel T RC filter and Sallen-Key are three that spring to mind.

Wah with no inductor (RC wah), is a specific story. There are well-known solutions Morley, Mutron, EHX ...

[Helmholtz]

Ok, the Wah pot:

Early Vox wahs were typically equipped with a 100k (ICAR) pot. Doubling pot resistance from 100k to 200k reduces the loading of Q1. This increases loop gain.
I found that the "bass" peak increased by around 1dB and its frequency was shifted down from 433Hz to 410Hz.

Pot taper:

The original ICAR pots I saw were all stamped as 100k lin. But often they measure higher (up to at least 300k) and show a more or less pronounced S taper.
My theory is that they all started out as 100k linear taper pots and that increased resistance as well as the S taper is a result of wear.
There is hardly any application that wears out pots faster than in a wah pedal.
The result of the wear is increased track resistance in the sector of most usage. And that produces a more or less symmetrical S taper.

I have a useable ICAR pot measuring 186k, that has an almost perfect linear taper. Another one measuring 307k (still scratchy after thorough cleaning) shows a pronounced but soft S taper.
I assume that pots having increased resistance as high or higher than that all had to be replaced.

[nickb]

You theory is ingenious for sure, but just that, a theory. We need more data and there seems to be a real lack of that....

I found this plot here https://www.musikding.de/Blacktop-Deluxe-100k-ICAR_1



This is saying the ICAR pots have a 100K 'S' curve when new.

But then I also found this https://www.thegearpage.net/board/in...h-pots.801532/

He found the ICAR to be linear.

[Helmholtz]

You theory is ingenious for sure, but just that, a theory. We need more data and there seems to be a real lack of that....

I found this plot here https://www.musikding.de/Blacktop-Deluxe-100k-ICAR_1

This is saying the ICAR pots have a 100K 'S' curve when new.

No original ICAR pot among them.
It's a clever idea to market pots with an S taper as ICAR or ICAR taper, while there was nothing like that. There is no specific ICAR taper.
Especially there was no original black top ICAR pot. (I have a few "Black Top" replacement pots, though.)
Believe me, I did my homework and researched all that internet stuff. And I started decades ago.
Also measured the tapers of many wah pots.
The S shape not only developed with ICAR pots, e.g. happened with old Centralab wah pots as well.

BTW, Roger Mayer. Hendrix's "tech", sold his wah kits with a 100k linear pot. I think he knew why.

He found the ICAR to be linear.

As said above, I have an original ICAR pot with a linear taper as well. Seems to confirm my theory. But others have an S taper and higher resistance.
I actually own an old worn ICAR wah pot stamped 100k, whose resistance has increased to 740k!

And I don't think an S taper would by manufactured by accident or sloppiness.
Generally ICAR pots look rather rugged and well made. More so than CTS or Alpha pots. Never saw a worn out axle-bearing.


From a pragmatic POV it's not really that important to me, as I have a collection of wah pots with different tapers and can choose the taper that suits me best.

[Helmholtz]

Effects of different pot tapers:

While a linear pot evenly shifts the peak frequency with the rotational angle/travel, an S taper concentrates the "active" region to the middle part of the travel.
Consequently a linear taper gives more control, as the peak frequency shifts slower, but may require some gear adjustment for preferred range.
An S taper makes sure that the whole sweep range is accessible and allows faster "wahing" with little movement.

So the choice of taper is a matter of personal preference.

The wah pots used by Dunlop, HotPotz I and II (both 100k), show an extreme S taper, which essentially restricts the active sector to around 60°
or 20% of the full pot travel.
The taper of Fulltone pots (100k) is similar, having even sharper edges.

The pots used by Geoffrey Teese in his RMC 4 wahs (RocPot, ProPot, 200k) have a rather slight and soft S taper, resembling a slightly worn ICAR pot.

[nickb]

Based on what your research, I think that makes a pretty good case for them being linear originally. It also shows how myths get going.

This got me thinking. Musical notes are essentially exponential so I would expect the a linear movement of the pot if translated to an exponential change in frequency might feel better. With a linear pot the relationship between rotation and is not linear, but the square root of a reciprocal.

A graph of frequency vs pedal position follows and should make this clearer, I hope.

True linear rotation to frequency is "F lin" yellow , linear pot "F Vox" blue and what I have in mind " F log" in red follows.



So, maybe a log pot might feel better? I don't have a pedal to try but I know someone who does

[Helmholtz]

So, maybe a log pot might feel better? I don't have a pedal to try but I know someone who does

Thanks for your thoughts.

In fact there are no ready-to-use log taper wah replacement pots (with the rack-wheel attached).
But I plan to do dedicated pot comparisons at a later point.
Right now I'm not even sure if I prefer lin or S taper. Seems the player (me) and his foot adapt to different tapers.
What I don't like is pots having high mechanical friction.
In my project wah I am using the 100k linear pot (blue cube, Bourns?) that came with the Roger Mayer kit.


Next chapter will be about the wah inductor, maybe the most interesting component (at least to a physicist ).

[Helmholtz]

Wah inductors came/ come in different shapes and sizes - and unfortunately often different footprints.

All inductors in 60s Vox wahs I've seen were either the "Halo" type or the rarer "Film Can" type. From around '72 also other types like Italian made Fasel inductors
( http://www.egosonoro.com/history.php?m=2 ) or the "Stack of Dimes" and TDK inductors can be found.

It is essential for wah inductors to have high inductance but low leakage and thus good self-shielding against magnetic noise. This is best accomplished by using either a pot core or a toroidal core.

Halo, Film Can and Stack-of-Dimes inductors all use a pot core. Not sure of original Fasel types, but red Dunlop Fasels use a toroidal core while the yellow one has a pot core.

I wound some pot core inductors. It's essential that all inductor parts are securely fixed to avoid microphony. Particularly the coil should be glued to the core.
It is essential that the joining faces of the core halves are perfectly clean, as any dust particles or glue residue between them will noticeably lower inductance.
By disassembling and cleaning the core faces of a yellow Fasel inductor I could increase its inductance from 450mH to (more desirable) 510mH.


Also cured the microphony of my Vox Film Can inductor by potting it in paraffin like a guitar PU.

[Helmholtz]

Inductance values:

I found that I like the upper peak frequency to be around 2.2kHz. Below 2kHz it sounds too muffled to me.

My 2 old Vox wahs (Halo and Film Can) both measure 2.22kHz calculating to an inductance of 510mH (feedback cap C2 = 10nF).
Higher inductance results in a lower peak frequency. If the frequency is too low, a lower C2 value can be used.
E.g. 600mH and 8.2nF result in 2.27kHz.

I was somewhat surprized to find that the inductance of wah inductors varies with frequency (as well as with temperature and most likely also with current).
So some caution is advisable when comparing measurements and published data.

In fact, inductance drops with increasing frequency to varying degrees (and increases with temperature).
Consequently 2 inductors measuring the same at 1kHz may produce somewhat different high and low peak frequencies.
Generally toroidal cores show the strongest f-dependency.

Some examples:

Dunlop Fasel red (average of 3 samples), toroidal core: 650mH @ 1kHz, 840mH @ 100Hz,
Dunlop Fasel yellow (after repair), small pot core : 510mH @ 1kHz, 560mH @ 100Hz,
Roger Mayer RM9090A, big pot core : 441mH @ 1kHz, 443mH @ 100Hz.

[Helmholtz]

WARNING
The following may contain indigestive theory and even formulas, likely to cause allergic reaction with some.


Nevertheless it required a little theory of parallel resonant circuits (PRC) to find the answer to my main question: What causes the different frequency responses of the wahs shown in post #11?
Particularly, what makes the the lower peak of my project wah so weak and that of the Film Can wah so strong?

Component differences are/were:

C3: 2.2µ RM board, 4.7µ originals - no change with original value.
C4/C5: RM board 0.1µ, 0.22µ originals - no change with original value.
L1: 440mH @1kHz RM board, 500mH @ 1kHz originals.
C2: To get an upper peak frequency around 2kHz I used a C2 value of 15nF (later 12nF) with the 440mH inductor instead of 10nF with the originals.

While there are ways to increase gain, that won't change the ratio of upper to lower peak height.

Then I found that the Film Can inductor has the lowest DCR (15R) and the 440mH RM inductor has the highest DCR (57R) of the three wah inductors.

It was clear to me that the DCR of the inductor impacts the resonant Q. And I initially assumed that the resonant Q would correlate with peak height(s).
But that's wrong. The "bass" peaks all have higher Q (around 10) than the treble peaks (around 2.5).

I remembered that the peak height directly correlates with the impedance of the PRC.
So I looked up the formula for the impedance of a PRC at resonance....

[pdf64]

How about the asymmetric saturation of the inductor mentioned by RG?

[Helmholtz]

How about the asymmetric saturation of the inductor mentioned by RG?

That's not likely with a pot core inductor.
As signal current is higher than DC current any normal DC remanence will get erased.
It might be different with toroidal cores. But remanence will not show with linear frequency response.
I know from experience that potting toroidal cores may have some magnetostrictive effect, meaning that compression forces reduce inductivity.
Designed some toroidal saturation current transformers for SMPSs in the 80s as a novice electronics designer.
I hadn't heard of a "frozen remanence" effect before, though.

I would expect toroidal inductors to show more non-linearity than pot cores, but I'm not sure that's desirable with a wah.