BMP clipping stage frequencies

[Scribe]

Hi all,
My name is Matt, and I'm new to the DIYstompbox community. I've been prowling the forums for a while, but I figured it was about time to make myself known!

Forgive me if this question has been asked before, but I had a question regarding the clipping section of the Big Muff Pi circuit. I've attached a schematic
of the Civil War BMP  and NYC BMP clipping stages to the bottom of this post for reference.

I'm working on using a similar clipping stage for a bass distortion pedal. The goal is to have the circuit clip high frequencies more aggressively, but allow low frequencies to pass with less clipping in order to retain definition. I want to ensure that my logic in tinkering with this system is sound.

My main question is: how does one calculate the cutoff frequency at which the clipping cap allows frequencies to be clipped by the clipping diodes?

Below is my (probably flawed) logic:

My thinking is this:
I assumed (please correct me if I'm wrong!) that an RC filter is created via the feedback capacitor (470pF) and feedback resistor (470K). In this case, it creates a feedback path that essentially functions as a low pass filter, rolling of frequencies above ~720 Hz.

Thus, I guessed that the clipping capacitor (0.047uF) operated on a similar principle, creating an RC filter system along with the feedback resistor (470K). However, the result is that frequencies ABOVE the filter cutoff would be affected by the clipping diodes. In the Civil War BMP example, this would mean that frequencies above 7.2 Hz would clip. Decreasing the cap thus increases the low frequencies unaffected by the clipping diodes.

The issue with my assumption is this:

It seems like the Civil War BMP allows more lows to pass the clipping stage than the calculation assumes! It becomes apparent when comparing the Civil War BMP to other BMPs clipping stages such as the NYC version (which uses a 1uF clipping cap).

The calculations would be as follows:

Civil War BMP:
clipping cap: 0.047uF
feedback cap: 470K
corner frequency: 7.2 Hz

NYC BMP:
clipping cap: 1uF
feedback cap: 470K
corner frequency: 0.3 Hz

If it is true that these filter networks are allowing diodes to clip anything above the cutoff frequency, then it would be assumed that both of these clipping networks would basically clip all the same frequencies (both cutoffs are well below the range of human hearing). However, the Civil War BMP seems to allow MUCH more low end to pass under the diode clipping than the NYC BMP.

The only significant difference between the two clipping stages seems to be the size of the clipping cap.

I assume there is something wrong with my assumptions as to how the circuit works.



My Questions:

1) Are my assumptions regarding the RC feedback networks correct? If they are, is there some interaction between the two RC networks which affects the frequencies passed through the clipping diodes?

2) If they are incorrect, how does one calculate the cutoff of the frequencies allowed to pass through the clipping diodes?

I appreciate the help and look forward to further expanding my knowledge on this forum!

~Scribe

Edit: Grammar, corrections to schematic

[PRR]

> Hi all, My name is Matt

Welcome, Matt!

I'm tempted to tell you to buy a cap-kit and try all values.

Clippers are hard to analyze (and formulas are not "sound"). Worse with caps in them.

The part you may be missing: those diodes are impedances also, falling with current, and could go as low as 300 Ohms when grossly over-driven. So the corner predicted by the 470K could shift all the way to the other end of the audio band. The mind boggles. Or my mind does.

[antonis]

As Paul said, semiconductors aren't linear devices and it's hard to analyse their behavior..
(they exibit wide parameter spread even among "identical" items..)

As Paul also said, I would experiment with different cap values but mainly for feedback caps (470pF)..
(to form a frequency selective gain rather than a frequency clipping one..)

P.S.
Wellcome...!!

[ElectricDruid]

Awww, c'mon guys! You're bottling out!

It might be difficult to give an accurate result, but it's far from impossible to provide some kind of *idea*. For example, there's a pretty good analysis over on Electrosmash, complete with a frequency response graph:

https://www.electrosmash.com/big-muff-pi-analysis

Probably the definitive reference for all the versions is here:

http://www.bigmuffpage.com/Big_Muff_Pi_versions_schematics_part1.html

Presumably the Electrosmash graph is generated by a Spice simulation of some sort, so certain limitations still apply, but it gives you some "ballpark" ideas of why sort values you need to be looking at, and then you can adjust by ear. If you go in with no idea at all, my experience is that you waste a lot of time just trying to get the thing working with realistic values and don't really know why what you've done has the result that it has.

The other significant part of the BMP frequency response is the tone control, which is certainly well-understood and studied. The way that its response adds onto the the response of the previous stage is what is going to determine the overall sound of the whole pedal. You can play with the values of that part of the circuit here:

http://www.guitarscience.net/tsc/bigmuff.htm

Tom

[Scribe]

Thanks you all for the responses! I've spent a good amount of time switching around the caps to play with clipping various frequencies, however I was hoping to better understand the nature of the clipping cap value, which seems to causes a much greater difference in clipping frequencies than I initially expected.

As Electric Druid stated, this is to help with ballparking similar designs in the future, as this method of selective diode clipping can yield some interesting results.

The part you may be missing: those diodes are impedances also, falling with current, and could go as low as 300 Ohms when grossly over-driven. So the corner predicted by the 470K could shift all the way to the other end of the audio band. The mind boggles. Or my mind does.

Even if it just ends up being a thought experiment, I'm tempted to further explore how the clipping diode impedance interacts with the RC network. The clipping cap blocks DC current, so thus the impedance of the diodes are dictated primarily by amplified AC current feeding back from the collector of the transistor.

Increasing the AC current running through the diodes will decrease their impedance. This impedance is added in parallel with the clipping capacitor, which I'd imagine would have a significant effect on the corner frequency

The greater impedance can theoretically have a swing from infinity (with inputs below the forward voltage) to ~300 Ohms. However, in practice I'd imagine that the relevant swing is a much smaller range than this. Is there a way to determine the input impedance of a 1n4148 based on the current being fed across it?

I did some poking around in LTspice, but am fairly new to the program and can't seem to find a way to model this.

Any thoughts or ideas? Other avenues to consider?

Matt

[PRR]

> input impedance of a 1n4148 based on the current being fed across it?

Shockley's Law.

[antonis]

<Shockley's Law.>

Which deviates enough from linearity, exibiting also a huge amount of uncertainity due to diode ideal factor (n) variation between 1 and 2..

Maybe Scribe wants to use explicit solution using the Lambert W-function or an interative solution using continously differentiation by a computer program or a graphic solution using transcendental equations or even piecewise linear solution using PWL modeling...

@Tom: Bottling out is sometimes much more preferable than possible brain damage..

[ElectricDruid]

I don't know how well LTSpice handles this sort of thing. I have to say that I generally *avoid* doing simulations for things where I know I'm pushing typically linear components into a non-linear region or just going outside the usual specification. It might be that the LTSpice component model is really good and models all that weird stuff, but more likely it doesn't. So I wouldn't expect to see op-amp latch-up or distortion characteristics in LTSpice, for example. And I wouldn't expect it to give me a particularly realistic result for diode clipping either, although it may do, I dunno.
However, even with that caveat in place, I do use it for this sort of thing. Instead of modelling the circuit with the diodes in and expecting the model to behave right, I'd just make an assumption about diodes: They're either "on" and conducting, or they're "off" and they're not conducting. So you can model the circuit without the diodes and any parts that would be out of circuit if they were "off", and then you can model it with the parts in place as if the diodes were "on" and see what the differences are and assume that the response of the circuit goes roughly from one to the other. Essentially, I'm just treating the diodes as "ideal" diodes - a switch with infinite resistance when off and zero resistance when on.
This is a simplification, clearly, but this is a distortion pedal we're talking about, not a space shuttle, so I don't care too much. If it gets us close enough, that's fine for me.

It avoids brain damage, anyway!

T.

[PRR]

Oh, golly. It is NOT as messy as you want to make it.

Diodes in this music-driven plan are NOT "on/off". Not "linear". Nor is any Lambert-W(??) needed.

R ~~= 26r/I(mA)

Semiconductor diode is 26 Ohms at 1mA, and scales directly inversely (for our purposes) with current over many decades. (I like "30" as a better number for thumb-counts.)

100nA  - 300K
1uA  - 30K
10uA  - 3K
100uA - 300r
1mA   - 30r
10mA - 3r

[reddesert]

My two cents here are that:

- for AC/audio signals, it's useful to think in terms of impedance, and you can think of a capacitor's reactance, which is effectively a frequency-dependent resistance: reactance = 1/(2pi * f * C).

- the feedback cap and the cap + clipping diodes are in parallel with the feedback resistor, not forming a divider with it. Forming a divider is how a typical RC low or high pass filter works.

Here, you have in parallel in the feedback loop: a 470K resistor, an 0.47 nf cap, and a (47nf cap + diodes).  So we can use the reactance formula to calculate their impedances at a few representative frequencies (in ohms):

100 Hz:  470K, 3.4M, (34K + diodes)
1000 Hz: 470K, 340K, (3.4K + diodes)
10,000 Hz: 470K, 34K, (340 ohms + diodes)

This makes it clearer what the 0.47 nf feedback cap is doing. It reduces the impedance in the feedback loop at high frequencies, which reduces the gain at those frequencies.

The 47 nf cap in series with the diodes does something similar, at 100x lower frequencies, but it only affects signals that are large enough to get over the diodes' voltage drop.  Or you can think of PRR's more sophisticated way of considering this: the 47nf cap will let some AC current through depending on frequency, and then the diode equivalent resistance will help determine the gain at those frequencies.

[ElectricDruid]

That's a nice summary, Reddesert.

[Scribe]

Wow, thanks for all the diverse approaches to the situation! I'll definitely keep them in mind for the future