Transmogri-Notes Edition 1: Sallen-Key Filter Emulation of Classic Inductor Wah

First Rev: October 2015

Q: Why emulate the classic wah circuit with an active RC filter?
A.1: The original inductor wah sounds really good, but inductors are expensive!
A.2: Frequency and resonance can be set by resistors. Instead of rotary switches the
frequency sweep range can be set easily with a pot.

Schematic -- Classic Inductor Wah
Schematic -- Classic Inductor Wah
Schematic -- SKF Emulator
Schematic -- SKF Emulator

Notes on Salient Features of the Sound

The sound of the classic wah is in part due to the frequency response and in part due to the distortion characteristic
as the circuit overloads. First, here is the classic frequency response, assuming an inductor with series impedance of 50 ohms (this also varies between inductor wah models).

Notes about what the plot below represents:
1) Inductor parallel resistor is 47k, a popular mod.
2) Input capacitor is 0.022uF, another popular mod to increase low end content.
3) SKF emulator is tweaked to match the AS response. This includes a 1.75k resistor for R48
to bring the high end response to match classic wah.

Note trace "cbo" is "CryBaby Output" and "voutb" is the emulator circuit for comparison.

Classic Wah Frequency response
Classic Wah Frequency response

The main thing to note about the classic wah frequency response is,
1) That a resonant peak filter has a sweep range which passes through about 600 Hz to 1.5 kHz.
2) And, that Q decreases as the filter sweeps up.

I would suggest #2 is why the classic inductor wah produces the most vocal "ahhh" and the end of the "waahhh" compared to many
constant-Q active wahs. The constant-Q wahs only capture #1, which is the bare minimum to say "wah".

This observation is intuitively consistent with how the mouth forms a "wah" sound. Starting at the onset of the "W",
the mouth is closed, creating a more highly resonant cavity. As one progresses through the vowel "a" to "ah" range
the mouth begins to open and the cavity becomes less resonant.

It is my opinion this is why common complaints about Morley's Power Wah series often use descriptions such as
"Sterile", or "Active Filter Sound". They refer to the constant Q, or worse-yet, increasing Q response of these
bridged-T active filter networks creating a sort of a sheeee-oop, emphasizing more of a syllabance response
than an open-mouthed "ahhh". It's like saying "ah" with your teeth clenched while hissing.

The first thing that needs to be implemented in a proper emulation is the relationship of "Q" vs pot rotation.

In a prior attempt I did this with a state-variable filter and opamps with suitable results. The trick is to
modulate the frequency-setting resistor in the first integrator stage. Getting the correct filter response
in my experiment was by injection into two places in the state-variable filter loop. Ibanez did something similar
with the WD-7 (weeping demon) but instead summed the band pass and low pass outuputs with phase correction.
In either implementation a good deal of attenuation needs
to be applied before the filter, then recovery amplification afterward because the second integrator stage (low pass output)
has a lot of gain and readily clips.

In the end I found the state-variable op amp implementation to be a bit sterile compared with the discrete-component
Sallen-Key implementation presented here. Even though the AC simulation (frequency response) curves looked about the same,
there is something missing. This discrete component implementation of the Sallen-Key was a happy accident that produces
a distortion characteristic that decently emulates how a classic inductor wah distorts:

At the low resonant range there is less distortion because there is negative feedback feeding the LC tank. This creates
a certain amount of compression as the feedback loop goes nonlinear, reducing gain, reducing Q as devices go toward the rail.
Interestingly this creates less extreme distortion on the low range. As the wah sweeps up in frequency, it tends toward zero
feedback and relies entirely on the feed-forward signal, transitioning toward a bandpass response ~at the input~ of the
first transistor stage. This is then amplified to the rails and you see more of the square-wave clipping on the signal.

This emulator circuit by happy accident responds the same way, but for a different reason:

As resonant frequency increases, the impedance of C17 and C18 go down, and the impedance of R37 approaches resistance of
R44. This means more current is required to drive the resonant tank. The bias through Q1 & Q5 has a limit, and it is
therefore more readily exceeded at higher resonant frequencies. This behavior tracks that of the original inductor wah
at the "birds-eye" level. I can't claim this SKF emulator captures the full sound of the classic inductor wah, but
it definitely touches on some of the salient characteristics which make it sound much more "organic" than a cleanly implemented
active filter having the same frequency response emulated with an op amp state-variable circuit.

The state-variable filter implementation experiment not only sounds somewhat sterile in comparison, but it also sounds
bad when it's driven to distortion. Just the wrong kind of quack.

Now, this same Sallen-Key derived topology can be implemented also with an op amp. I found the op amp version also sounded
good to my ears, presumably for the same reason that R48 was more likely to drive the op amp to it's rails on the high range
than at the low range. The main deficiency is noise performance. This filter as implemented with discrete components
has noise performance equal to that of the classic inductor wah (100 Hz to 10 kHz has about 16 uVrms noise voltage). The
Op Amp implementation with an LT1058 (similar to TL072) in simulaiton integrates to about 56 uVrms noise voltage over the
same frequency band.

Emulator Implemented With an Op Amp

Notice the op amp implementation includes a 68 ohm in "R64" (compare to R50 in the discrete version).
The op amp provides all the gain needed, so the 68 ohm reduces the Q to where it needs to be. This is a hint
that if you want to make a more crazy adjustable wah, the op amp version is the best choice at the expense of
slightly more noise. Note that 56 uVrms noise is not bad, but it's audible when going into the high gain channel
of my amp. Still more quiet than an OD pedal like a TS-9, just for comparison.

I still think the sound produced by the discrete version is still more pleasing than the op amp version. Another advantage
is the discrete version can be biased to a current draw right on par with the classic inductor wah at the expense of
a bit more distortion. It can be biased a little hotter (like 1 mA draw) to decrease distortion.

Now to the ears the emulator circuit sounds far more brittle/piercing/strong on the toe position when played clean,
even though the simulation indicates the frequency response is the same. A hint for the reason is that it sounds fine
when the volume knob on the guitar is rolled back about 1/2 way (harmonic distortion on toe position is the reason
for the piercing sound).

It sounds really good going into the amp's dirty channel because the extra treble gives it some nice bite.

Changing R48 in the emulator circuit to 680 ohms rolls off the highs, but makes for a a sound that is much more
like an inductor wah modified per Classic Wah circuit (the reason will be explored further below).
Even better would be to construct this with a pot to adjust the "bite" to make it a more versatile effect.

Emulator Modified for More Balanced Sound

Final Circuit Frequency Response

Distortion -- Now We know why the ~7 dB attenuation on the highs sounds better

Here is a comparison of the distortion FFT responses when R48 = 1.75k.

420 Hz Sine wave with Resonance Set to about 423 Hz, 1 V peak-peak input:

2.1 kHz signal, 2.1 kHz resonance, 1 V peak-peak input:

Now change R48 = 680 ohms and watch this distortion drop down:

420 Hz Sine wave with Resonance Set to about 423 Hz, 1 V peak-peak input:

2.1 kHz signal, 2.1 kHz resonance, 1 V peak-peak input (Inductor Wah in forefront):

2.1 kHz signal, 2.1 kHz resonance, 1 V peak-peak input (SKF in forefront):

Comparing above plots it can be seen how both circuits have less distortion on the low end and more on the high end.
I would suppose this plays a big role in the overall "wakka-wakka" sound from the inductor wah circuit.

A final note about distortion:
With the component values shown, the bias current in the main filter stage is about 400 uA. With 250 mV input (500 mV peak-peak)
I added the harmonic components with both the classic wah and the emulator and came to the following:
THD, Classic = ~2.5%
THD, SK Wah = ~ 5.2%

Changing R47 also to 680 ohms brought it all into about the same ~2.5% THD range of the classic wah.
If a little less battery life is acceptable, or if using external power this is a highly recommended modification.
Also remember a typical status indicator LED burns more than 1 mA, so even this "high power" mod is not
very high power. Only it is double the original inductor wah power, which for me, was a design target
as I'm considering offering these boards as a modification to trick-out an inductor wah. Why? So pots can be
used to make it sweepable over a wide response range. I just thought keeping power consumption roughly the same
is a nice touch.

R47 could also be changed to a pot to make the amount of distortion tweakable on the fly -- another convenient
side-effect of this particular discrete-component implementation

Note the op-amp implementation is very low distortion if operated from 18V, or if you pre-attenuate and post-amplify
to maximize headroom. This also increases output noise.

The Ultimate Tweakable Version

The schematic below has been marked up with suggestion for resistors to replace with a pot for ultimate versatility in a
single enclosure (right-click, "View Image" for better resolution).

Emulator Modified for Versatility


All simulation plots

LTSpice simulation file

Hear It: Dirty (mp3)
Hear It: Low Gain Overdrive (mp3)
Hear It: Striking strings to hear full range (mp3)
Hear It: Funky Clean (mp3)
Hear It: Funky Clean, hard distorting the wah (mp3)
Hear It: High Gain Leads (mp3)
Hear It: Wakka Wakka (mp3)