AVOID DISTORTION/INCREASE HEADROOM, in CRYBABY WAH?

[matt239]

Is wah filter gain highest at heel-down, (bass) end of the sweep?

[Transmogrifox]

The answer is "it depends".

If you have an inductor with a higher series resistance (or do like Morley did and ADD more resistance in series with the inductor), then the heel-down gain will be lower than the toe-down gain.  If you have an almost ideal inductor in there, then the heel-down gain will be very high compared to toe-down gain.

Adding a resistor in series with the inductor to increase this value will lower the heel-down gain.  It works by increasing the amount of pass-band negative feedback.  Increasing negative feedback decreases closed-loop gain of a system.

My LTSpice simulation indicates the inductor series resistance of 47 ohms gives a nearly constant-gain response between toe and heel.  This would be the total resistance in series with the inductor -- for example if you added an extra 27 ohms to a 20 ohm inductor, you would have the magic 47 ohms.

Now, increasing inductor resistor decreases Q, so you can compensate that by using a larger "Q" resistor (normally 33k parallel to inductor).
So...the parallel equivalent (series to parallel transformation) is this:
Qp = Rp*sqrt(C/L)
Qs = sqrt(L/C)/Rs
We want to maintain this relationship:
Qp = Qs
Therefore
Rp = L/(C*Rs)

So...  if you measure 20 ohms series resistance in your inductor, the Q will be equivalent to replacing the inductor with an ideal (0-ohm) inductor with a parallel resistor of the following:
Rp_l = 500mH/(10nF*20) = 2.5M
if Rp = 33k, then the equivalent Rp with an ideal inductor, but maintaining the same Q is this:
Rp_new = 33k||2.5M = 32.57k

Then, if you add 47R to that, you now have this:
Rp = 500mH/(10nF*(20+47)) = 746k
and,
Rp_new = 33k||746k = 31.6k

So to get back to the equivalent Q, you need to increase Rq such that Rq||746k = 32.57k
Rq = 34k gets pretty close
As you can see for small changes in Rp you probably don't even need to care about Rq because 33k to 34k is pretty small, and likely inaudible change.  However, you can see the process for compensating the Q in case you add a significant amount of resistance in series with the inductor (like >100 ohms).



The next topic is overall circuit gain adjustment:
For overall circuit gain adjustment, you can scale Rin, Rmix, and Rq:

To maintain the same Q, you want the parallel combination of Rin  and (Rq+Rmix) to remain constant.

For example, with
Rq = 33k
Rmix = 1.5k
Rin = 68k
Rineq = Rin + Rmix = 68k + 1.5k = 69.5k
Rp = Rineq||Rq = 22.4k

If you change
Rin = 250k

And Rmix (1.5k) has to scale in proportion to Rin to keep the same wet/dry mix ratio:
Rmix = 1.5k*250k/68k = 5.5k

Then, you have to change Rq such that
255.5k || Rq = 22.4k
Rq = 24.6k

So you would then change the 33k Rq to 24.6k (or nearest standard value).

The end result is lower total gain but nearly the same frequency response and sweep range (equivalent input resistance seen at the BJT base with have some effect on this assumption, but it will be subtle).

[matt239]

Wow! Thanks!
A lot to digest there.

How does all that affect the DC voltages / bias?

Would adding resistance between the wah pot and ground liked I mentioned, reduce gain at heel-down also? (more negative feedback..)
Of course it also affects the sweep..

I wasn't too concerned with maintaining exact ratios, and the exact same Q and sweep..
Along with a bit lower gain, I actually wanted a little lower Q, and lower sweep.

I was also trying to maintain near - half - voltage bias..

I've got 90%of what I wanted.
I'm just trying to eliminate the last little hint of distortion at the heel down position..

- I may lower the sweep range just a bit more too..

[R.G.]

This is probably not going to be of any real help to you, given what I think you're doing, but it deserves to be said, just for completeness.

The crybaby wah circuit has some built-in limitations. They are accidental, as back when that circuit was designed, what, 50 years ago, no one could foresee what we don with guitars today. But they're there. Headroom is one of those issue.

A modest redesign of the circuit to use a higher power supply voltage would do it; this is one of the few places where a higher power supply woul be of real use, not just something to do because modz are kewl. That could be done with just a rethinking of the circuit for a 12V or 18V power supply. Just glomming on more volts may or may even work. Another way is to preserve the design intent, but not the transistor application. The wah circuit as it sits can be done with a dual opamp and not two transistors. This may well produce more headroom. It would need the rethinking I mentioned as well.

But you're on the right track - get the first transistor to having the biggest possible range without distortion, then check the voltage on the emitter of the second transistor for it being near the middle of the available voltage as well.

[Transmogrifox]

How does all that affect the DC voltages / bias?

The beauty of this tactic (adjusting input resistance and inductor series resistance) is that it has very little effect on DC bias.
Changing inductor series resistance will have almost nil effect on DC bias.
Changing what I call "Rmix" (nominally 1.5k) may have a small effect on DC bias, but the 470k/82k bias resistors are still dominate.

Would adding resistance between the wah pot and ground liked I mentioned, reduce gain at heel-down also? (more negative feedback..)
Of course it also affects the sweep..

This is actually less negative feedback.  Yes, it reduces gain overall, but not only at the heel position.  To adjust the heel-toe balance you need to play with a resistor in series with the inductor.

The con:
The equivalent resistor divider network formed by adding AC-coupled loading is like the fuzz-face output -- it reduces output level, but it's divided down from a larger signal.  The clipping is then dominated by base-emitter cut-off voltage.   

The Pro:
It may reduce gain enough that it fits your signal into the headroom that is there, so it may be enough.  If so, then you don't have to re-adjust the bias.  .

I would lean toward messing with the collector resistor (22k) -- change to a smaller value and re-bias.  This effectively increases the bias current and requires a larger negative-going voltage on the first-stage BJT base to cut-off.  This also reduces sensitivity to external loading.

I wasn't too concerned with maintaining exact ratios, and the exact same Q and sweep..
Along with a bit lower gain, I actually wanted a little lower Q, and lower sweep.

Anyway, the main point is if you mess with the inductor series resistance and it reduces Q more than you like, you can easily compensate it without reversing the desired effect of reducing heel-down gain.

I've got 90%of what I wanted.
I'm just trying to eliminate the last little hint of distortion at the heel down position..

So maybe all you need is resistor in series with the inductor.  You can make a 6 to 10 dB difference on the heel-position gain with this component alone.

If this lowers Q more than you want you can easily compensate it by making the nominal 33k larger, as explained in my prior post.

Headroom is one of those issue.

I'm one of those who considers it a desirable side-effect.  I really like the gravelly growl at the heel position when the circuit is licking the rails.  I have in the past played around with substituting JFETs and MOSFETs in this first gain stage just to see how it changes the character of the heel-position growl.  The differences were all subtle, but was fun to experiment.

[matt239]

Thanks again R.G. and Transmogrifox!

Yes, I get what you're saying.
I think that one resistor will probably do it.

It's so close.
It's really working quite well. - I've got the bias right for the 2n5088s, there isn't much perceived volume drop, there is very little distortion remaining, the thing is DEAD QUIET, (low noise) and sounds good!

So; much success, with lots of help from you guys.

I'll report back, but it may take a while, because I'm working all the time, and not spending much time at the bench..