Effect of multiple gain stages on harmonics created

[swamphorn]

Cascaded gain stages offer access to the intermediate inputs and outputs. Consider a cascade of non-inverting clipping stages with common gains, but rather than taking the last amplifier's output, mix the outputs of each stage. When a stage is in clipping it contributes all the signal it can to the sum. As the signal amplitude increases, the stages will progressively clip last-to-first; so the outputs of the earlier, cleaner stages are more prominent in the output. As well, phase shift and frequency response variations from stage to stage ought to produce tonal shifts that follow the signal dynamics.

For a single stage this is equivalent to a so-called clean-blend circuit; and so adding further stages in series with the intermediate outputs mixed in is one way to generalize this concept. But since it is the case that cascaded hard-clipping stages be replaced by a single hard-clipper (inter-stage phase shifts notwithstanding), we can just as well generalize the clean-blend overdrive by adding additional parallel stages! Not multi-band clipping - but multi-gain clipping.

[Steben]

Clean "component". It is not that hard to construct a TS like signal by adding a hard clipped signal to the clean original ... That's what is ment.

I understand. My point was that when you add additional harmonics to fundamental frequency or frequencies, the "clean" signal, the outcome is fundamental plus harmonics, which is effectively synonymous to, and very definiton of, distortion. You can't have a clean AND distorted signal at the same time, they are mutually exclusive. Either signal has extraneous harmonics in it or not, but both conditions can't exist at the same time.
Without this principle we could throw the concepts of waveform arithmetics and harmonic theory to thrashbin.

Our "clean component" is that fundamental frequency or frequencies, but it's a misleading concept because we have those even in a square wave with about 74% THD and we don't actually speak about that signal being a "mix" of clean and distorted, we simply say it's distorted. To extract the "clean" we get rid of the extraneous harmonics and if we do that then we no longer have a distorted signal.

Concepts like "clean blend" or "mix" of clean and distorted are fallacies, though I realize they are a handy shortcuts to talk about specific circuit ideas, similarly as separating "overdrive" and "distortion" to refer to specific tones instead of certain phenomena that they actually are. The problem with such stretching of concepts is that it confuses folks who are just learning the principles and they actually learn the false concepts instead of real effects behind them. Then they keep spreading the false information and the effect accumulates.

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To get on topic, I believe different transfer functions of distortion simply combine and superimpose each other (e.g. several soft knees superimpose and become a harder knee etc.) and we could effectively treat such several transfer functions as one single function...
UNLESS
..The signal is subjected to changes of phase, amplitude or time in between applying those transfer functions. Which is exactly what the aforementioned capacitive coupling between stages will usually do. The resulting dynamic, non-static, effects are usually the reason why "cascaded" distortion stages are employed in the first place.

Every distorted signal is in a way reproducable by the sum of a clean signal + an additional waveform. So yes, it is all in extend the same but different. The thing is talking about the "clean portion" in such soft clippers emphasises the rather large portion of clean in them compared to others. It makes them soft.

A non-inverting opamp with back to back diodes in the loop and no resistor will come pretty damn close to the sum of a square wave with the diode treshold as amplitude and the original signal.
No wonder circuits like a Klon and TS can sound pretty alike.
If the ideal diode were to be used in the non-resistor circuit (Vf = 0), it would be a simple buffer.... If used in a TS, a linear gain stage. Clean = 100%.
The larger the forward voltage, the more distortion can be achieved because the ratio of max signal beyond the treshold (unity gain) and signal to treshold becomes smaller and smaller.
An infinite gain and headroom with higher and higher forward voltage in the circuit would converge to a square wave (but never reach it).

It is not a secret germanium diodes usually are not advised in a non-inverting feedback clippers. While arrays of silicons and LEDs are onmipresent. It makes the clipping tighter than a TS, but softer than a hard clipper. Stacking TS's and using high outputs guitars might give your rock on sounds.... because the opamp starts clipping.

And yes, the other reason is that aforementioned effect of "softer" transfer functions cumulating to harder ones. However in those cases the design generally wishes to avoid the said phase shifts and all. Couple of examples of these I can think of are, say, a late 1990's Yamaha DSP patent that outlines how a single "soft" distortion waveshaping function can be employed to generate a wide array of different waveshaping effects ranging from soft to hard. In latter case just repeat the waveshaping function until the preferred "hardness" is achieved. And in the very same vein the famous early 1970's CMOS linear amp app note that advises to connect several stages in series to achieve a harder knee of clipping and simultaneously more linear output with aid of higher loop gain. The latter idea I have seen often employed in CMOS linear amp distortion circuits of which the common complaint is that they are a little bit too "soft" and non-linear as is.

Speaking of CMOS the app note also addresses the likes of TLC2262 if you read between the lines. A CMOS output in an opamp does not load its input stage, which means it can achieve very high voltage swings whereas CMOS output as is can swing within millivolts of its rails. So a perfect combination for "rail-to-rail" duty. It will naturally clip as hard as any closed loop opamp but at least more symmetrically and gracefully.   

Indeed. Just as a high NFB tube power amp.