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Advanced Distortion Questions

1/9/1999 12:44 PM
Ed Rembold
Advanced Distortion Questions
OK-When considering "Multiple stages of very soft distortion,and careful frequency shaping"  
Which of the following is the "ideal"  
concerning transistor,(or OP amp ),in series, gain stages-  
Are we talking about selected transistors  
with "ramping" gains- lowest to highest?  
Are we talking about ramping the clipping elements- LEDS then Si diodes then Ge diodes?  
What about ramping the Caps feeding the clippers- Large caps to progressivly smaller?  
How about ramping the High freq. filtering caps- smaller to larger?  
Which, if any, of these things is desireable in theory or practice? ANY thoughts, changes, corrections, additions would be MOST welcome.  
Thanks to all, Ed R.
And now, a word from our sponsors:

1/10/1999 11:38 AM

Actually, none of the above.  
John, Jack, Gus, GWR, and a few others will be off (re)designing distortion pedals when they read this.  
If you'll read Russell O. Hamm's paper on "Tubes Vs. Transistors - Is there a difference?" you'll pick up up a bit of it.  
The biggest differences in distortion devices happens when they just begin to distort - that is, the abruptness or softness of the "knee" of the input/output transfer characteristic, how abruptly the gain changes from whatever the unclipped gain is to the gain when fully clipped or limited.  
If that is a nice sharp corner, then you will get high order harmonics in profusion in the output. If it's a soft, rounded knee, then only lower order (and more musically pleasing) harmonics are generated. If the knee is different or at a different level for the (+) side clipping and the (-) side clipping, you get different spectrums, primarily by the inclusion of even harmonics which are sweet sounding below the tenth.  
The apparent sharpness of the knee as translated to a signal depends on the degree of overdrive - that is, the peak level the signal would have gone to at the unclipped gain had the clipping not occurred. If the unclipped gain is huge and there is no particular limiting of the degree of overdrive, then it's just about impossible to get soft clipping. If you feed a square wave to ANY clipper, it still comes out looking like a square wave. The sides are vertical, so a soft knee doesn't do much good. Hugely amplified signals of any kind have substantially vertical sides when the clipping level is greatly below the signal peak, so you get almost the same response as you would with a true square wave - square waves out and sharp sounding corners, high harmonics and harshness, that have to be smoothed out with post clipping filtering.  
If, however you limit the amount of overdrive per stage to between 3 and 12db, you get to take advantage of the softness of a rounded clipping knee and get to have soft, musical, touch sensitive, and sweet, creamy distortion.  
Unfortunately, the amount of overdrive is also the amount of apparent compression and sustain. For long sustained notes with no big change in tone and only one clipping stage, you're forced to huge gains in the one stage, many db of overdrive to get essentially a square wave out, and then post filtering to tame the harmonics. There is some advantage to pre and post clipping EQ and you can diddle the response a bit, but you're trapped by having only one clipping stage.  
For long sustain/ high compression with inherently soft clipping, you still need the many db of overdrive, but if you distribute the overdrive over multiple stages, you can take advantage of a soft clipping knee if you can get it. The string of soft clippers each runs with an output very close to the output of the one before it because the soft parts of the preceeding stage lie in the soft portions of the current stage's transfer function. All you accumulate is overdrive db, not harsh harmonics. This is the sound you hear in Santana's self-titled album - the note is distorted, but not harsh, and does not change much in character from initial pick attack to final decay.  
You can replicate this somewhat with a real compressor before a single clipping stage, but level adjustment is crucial to this setup.  
A multistage soft clipping setup will self regulate as to clipping levels because the overdrive db accumulate so that the initially loud note clipps every stage, but as the note decays away, the earliest stages come out of clipping but still contribute gain so the later stages are still clipped. Since the clipped output of all stages is remarkably similar, there is no big tonal/spectrum change until the note decays down under the (soft) clipping level of the final stage and you've used up all the db of overdrive.  
Since the multistage clipper is inherently a soft clipper, harsh intermodulation products do not accumulate in any stage the way they do in a single stage clipper with equal overdrive/compression.  
Getting to your notes, I'd make every stage identical to have the best control of signal level and hence clipping threshold and db of overdrive, but you are of course free to diddle with frequency response and clipping characteristic of each of the stages.  
There are some other practical considerations about actually designing a real multistage soft clipper that I'll leave as an exercise for you guys ;-)  
Have fun...
1/10/1999 3:14 PM
Joe Fuzz

R.G. If I can just jump in here:  
If the knee is different or at a different level for the (+) side clipping and the (-) side clipping, you get different spectrums, primarily by the inclusion of even harmonics which are sweet sounding below the tenth.  
Could you elaborate a little bit on this? I've noticed several schematics with a mixture of Si and Ge clipping diodes, for example two Ge for the - peak to one Si for the + peak (though this is by no means the only combo I've seen).  
Are you saying that the different clipping voltages allow a different range of harmonic frequencies to pass? I assumed that in the example above the Si was added in there for its hard knee i.e. to add an edge to the Ge sound. How will different +/- clipping voltages give you different spectrums?
1/10/1999 4:04 PM

"Are you saying that the different clipping voltages allow a different range of harmonic frequencies to pass?"
Not quite. A clipper is not a filter, allowing different frequencies to pass. The output waveform is what it is depending on the nonlinear waveshaping that the clippers do. However, if you do a fourier analysis of the resulting waveform, you'll find that the clipping has introduced harmonics and cross modulation products that were never present in the original waveform.  
If the original signal was a pure sine, to oversimplify, at 1kHz, the output of a perfectly symmetrical clipping stage would be 1kHz, 3kHz, 5kHz, etc, in amplitudes that go down with the harmonic number. If you unbalance it slightly, say by moving the clipping point of the positive clipper up a bit, a spectrum analyzer would now notice some 2kHz, 4kHz, 6kHz, etc. The more unbalanced the waveform from (+) side versus (-), the higher the magnitude of the even harmonics.  
The change in spectrum is a result of the frequency decomposition of the clipped, shaped waveform. The more different the top and bottom of any waveform, the more it contains even order harmonics. The human ear does it own spectrum analysis to separate out different frequencies and allow you to hear different tone qualities in the same note.  
You can introduce asymmetry either by changing the clipping voltage (subbing two Ge's at 0.2V each for a 0.6V silicon) or by changing the sharpness of the conduction knee by using a razor sharp signal diode and a soft, early conducting, large junction power rectifier, a technique used by a Prominent Boutique Maker.
1/10/1999 9:26 PM
Mark Hammer

Perhaps it's good at this point to clarify what "distortion" is. In terms of reproduction of recorded music, we talk about the sound being "distorted" when it doesn't resemble the original. There are a number of ways in which it might not resemble the original, but the classic manner concerns the timbre of the reproduced version vs the original. If the relative balance of harmonics tends not to reflect the original very well, we describe the sound as distorted. What we call "harmonic distortion" is essentially additional harmonics of the original sound source, produced by the circuitry (or microphone, speaker, vinyl, etc.), added to the original so that the timbre is not like the original. As it turns out, there are a number of circumstances when harmonic imbalance ("low fidelity") has a pleasing quality, which is what brings us to fuzz boxes and tube amps, etc.  
Why am I telling your this? Simply because the object of designing devices which deliberately distort is that they add harmonics to the signal which weren't there originally. The clipping mechanisms, and thresholds, and quirks of the various designs dictate what harmonics are being added, their relative proportion to the original and each other, and the degree to which harmonics are added for one fundamental frequency, relative to another. You shouldn't forget that all of these roads are intended to lead to a certain harmonic balance (and to some extent amplitude envelope).  
Okay. When you have cascaded stages that all introduce distortion, you need to realize that stage two is not only adding harmonics to the original, it is also adding harmonics to whatever harmonics were deliberately or inadvertently added in the preceding stages. So, adding the 4th or 5th harmonic of a 3rd harmonic coming out of a preceding stage gets you into that range of undesirable harmonics that yield fizzy tone rather than soulfully vocal tone. The bottom line is that whenever a device has several potential harmonic generating stages, or several devices are lined up in cascaded fashion, you have to ask yourself "How much, and what kind of, harmonic content is added at each stage?". If the net effect of the combination of filtering, gain, and clipping at each stage is to goose the level of lower order harmonics in an appropriate balance without letting the higher ones go nuts, then the outcome seems to be pleasant. If the higher harmonics are allowed to snowball, then it starts to become an industrial sound rather than something a little more lyrical or vocal.  
What rules of thumb can we draw from this?  
1) When several gain stages are cascaded so as to produce an output high enough to clip, it's a good thing to rein in the high end at each stage with frequency-limiting caps, wherever they happen to work.  
2) For any single stage, higher gain usually implies a lower cutoff frequency for hi-filtering (assuming the rolloff is the industry standard 3-6db/octave).  
3) Each stage contributes harmonic content, based on the content of what it receives, and its ability to handle that signal level without clipping (i.e., the combination of actual signal level, power supply, gain demands, and deliberate clipping elements).  
When I built Craig Anderton's Tube Sound Fuzz from the original late 70's schematic in Guitar Player, I liked it. When I built the revamped one from the book, I hated it. I looked closely at the differences and realized that the magazine version had an extra stage, and distributed gain across three stages, rather than two. When I added more treble filtering at each stage, and trimmed back on the gain, I found I REALLY liked it, because the distortion never got away from me.
1/10/1999 10:01 PM

Yep. It goes without saying that you have to pay attention to what you're doing at each clipping stage, and make sure that each stage does not give you a dose of the "insect-attracting harmonics" (quoting a wise old man who taught me a trick or two). This can be done either by carefully rounding the clipping knee relative to the signal level and paying strict attention to the amount of overdrive or by deliberately canning the gain at higher frequencies within the clipping stage, or filtering in/after each clipping stage.  
In all these cases, the point is to not ever generate harmonics much above the fifth, or to kill them before you do harmonics of harmonics.  
"When you have cascaded stages that all introduce distortion, you need to realize that stage two is not only adding harmonics to the original, it is also adding harmonics to whatever harmonics were deliberately or inadvertently added in the preceding stages. So, adding the 4th or 5th harmonic of a 3rd harmonic coming out of a preceding stage gets you into that range of undesirable harmonics that yield fizzy tone rather than soulfully vocal tone."
This is one of the things that I thought about for a long time.  
If we are careful about where the clipping points of a given stage are with relation to the clipping input levels of the next stage, we can set the thing up so that harmonics don't accumulate much on simple signals at least. I hacked together a test setup with six series distortion stages that will softly round either a sine or triangle into a round-topped thing that is more squashed than a sine and which does not get markedly more or less clipped at the output of the last stage for over 36db of input range at the input to the first stage.  
When the input signal is high enough to give the roundtop at the output of the first stage, that's also what you get at the output of the last stage, very nearly. Of course there are some other gotchas to this setup that keep it from being a God-pedal - like hiss, and hideous complexity.  
Things are not that simple with a real guitar signal, of course, but for single note melodies, the tone is very even for a huge range. It's creamy and compressed, probably too much so for good touch sensitivity. If I were going to mess with a commercial pedal like this, I'd probably add more variation in clipping back in by running the stage gain higher on the last stage or two.
1/11/1999 12:19 AM
Joe Fuzz

Let me just make sure I understand you:  
For purposes of this discussion, I am imagining a distortion circuit with a single clipping stage. Specifically, I'll refer to the Rat Distortion: FET input feeding a FET op-amp feeding a pair of "squaring" diodes (the distortion stage) feeding another FET. I'm assuming that the FET op-amp doesn't clip nor do either of the FET input or output transistors.  
Supposition: A perfect square wave has only odd harmonics. Anything besides a perfect square wave will have both odd and even harmonics. For practical purposes, let's say that a perfect square wave can be achieved/approximated with fast-switching Si diodes, specifically 1N4148s.  
"Non-squareness" (if you will) can be introduced by either:  
a) changing one of the 1N4148s to a rectifier diode, say a 1N4001. The +/- peaks are still the same but the 1N4001 has introduced a little curvature into one of the peaks.  
b) changing one of the 1N4148s to 2 or 3 GE diodes in series, say 1N34s. Now, one of the peaks will have a little curvature and the +/- peaks will have different amplitudes.  
Am I on the right track? Which configuration will have more even harmonics?  
Another question: am I right to assume that odd harmonics are perceived as "crunch" and even harmonics give a more bell-like quality?

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