Unit Processes in Amps / Pedals

[Vivek]

I am a Chemical Engineer.

About 100 years ago, Chemical Engineers studied each industry separately.

It was considered that a Sulfuric Acid production factory was very different than a Cement production unit.

Then, some wise people invented the concept of "Unit Process"



Heating, filtration, reaction, distillation etc were identified as "unit processes"

This concept had many advantages.

Each production process was now seen as a string of unit processes. Instead of books on "Production of Sulphuric Acid", one began to see more books titled "Heat Exchange" or "Distillation Technology"

For example, we could say "Production of Unobtanium Oxide follows the unit processes of filtration, reaction, filtration, distillation"

and another engineer would understand that new industry to a very large extent.

If an engineer studied filtration, he could understand its use in each and every industry.

Then an engineer could decide to improve/modify the production capacity by deciding to change the reaction unit process. As long as the pipes between the unit processes were compatible and no limits of other processes were violated, the process would still run, and the modification/improvement would show up in the final product while other unit processes remained untouched.


It appears to me that Amps and Pedals are made up of unit processes. These could include

Buffers
Filters
Non-linear stages
Time effects


So it could be possible to state something like

My "Dumble sound" is :
Buffer
High pass(200)
Distortion (cube, 4.2V)
Low Pass (6000)
Distortion (Square, 3.8V )
Low Pass (5000)
Filter (Dumble tone control)
Buffer

and my "Fender Sound" is :

Buffer
High pass(300)
Distortion (square, 3.5V)
Filter (Tweed tone control)
Low Pass (6500)
Distortion (Square, 3.8V )
Low Pass (5000)
Buffer

Or graphs for those unit processes that cannot be reduced to a few numerical parameters.

Then the truth of Line6 and Fractal statements that each of their Amp models is only a set of parameters in a SuperAmp model is more readily understood.

I began to feel that "AC Transfer Function" and "Frequency response" of each unit process (Stage of the Amp or pedal) are some of the signatures of that unit process and provide a lot of information. There can be other dynamic, time bound signatures as well, like sag, swell, bloom etc.

For example, while studying the Clipping unit process in the Big Muff (repeated 2 times)


The traditional way was to plot out a transient analysis like this:

The above shows a plot of output at one fixed input voltage.


A better way would be to describe a AC Transfer function or plot out the AC Transfer function of that unit process.

Indeed, new software waveshapper addons do allow you to define the desired transfer function graphically.

Here is a cumulative AC transfer function at points inside the BMP:


An AC Transfer function is really one of the important "signatures" of the unit process of clipping. The posted example can be used to predict the output for any voltage swing from 0 to 2Volts. It can be seen that the earlier Transient Analysis is just one snapshot of one level of input signal being passed through this AC Transfer function graph.

New types of Amps/effects can be modeled by changing the parameters / orders of the unit processes that make up that Amp / pedal.

We can now see that the excellent idea to add a BMP type tone control after an AMZ Booster 2.5 was an addition of a well known unit process after an existing process chain.

The AMZ Booster 2.5 itself was also a string of well known unit processes (Mu Amp, Mu Amp, Buffer)

As long as the pipes are compatible (Impedances and Voltages), the new unit process will fit right in and start delivering its results.

[ElectricDruid]

Yes. I completely agree.

There will be people who will want to argue that something magical happens at some point (although they don't tend to hang out here, to be honest - there are audiophile forums for that!) but the truth is that audio engineering is engineering, and you put a signal in at the front, do stuff to it, and get a signal out at the other end. *How* that processing is done in-between makes absolutely no difference if the the processing is the same.

Of course, there are practical debates to be had over things like digital versus analog - at exactly what level of processing power / sample rate / bit depth / sophistication does digital processing become indistinguishable from analogue? That's a valid question. I don't think many people these days still think the answer is "never", although that wasn't an uncommon view twenty years ago.

I think your "unit process" framework is a useful way to think about audio effects. I mostly design with "black boxes" - these are circuit elements that I know the behaviour of, but I don't know what is inside the box. The standard op-amp is the classic example. I don't know how to design an op-amp, and I don't need to. All I need to know is how the black box works and what to do to get it to behave the way I need. Meeting the specifications given after that is the job of the chip designer, not me.

So we take "unit process" elements like buffers, filters, mixers, allpass stages, delays, etc etc and we add them together to get an overall effect. Many of these processes could be implemented many ways (FET buffers, BJT buffers, op-amp buffers, for example) but those are differences of quality in the process, and not fundamental differences in the process itself.

Of course, in the effects world, sometimes the *quality*of the process *is* the effect, or at least a significant part of it. Making a univibe "clone" done with modern parts, using modern circuits in a topologically equivalent way isn't likely to sound the same - sometimes the limitations of a particular process are a big part of the sound.

I like the fact you're thinking about effects designing at this "meta" level as well as at the "nuts and bolts" level of how to actually do it. Push us, Vivek. Let's take this thing somewhere new if we can!

[aron]

That's the way I think except I don't have the level of understanding. Very nice!

[Rob Strand]

In electronics the equivalent way a concept is generalized is with a block diagram.   There are common processes that appear on a block diagram.

There are some differences between "signal processing" and *implementing* signal processing using electronics.   For example the concept of a buffer (impedance, not software) is not required when we are talking signal processing.

Complex non-linear circuits like diodes interacting with capacitors it isn't so easy to segregate clipping and filtering.   The same goes for bias shifting.

Putting the interactions aside, you can pretty much write a lot of DSP algorithms the way you have written it down.    When you have feedback, like with a reverb, the process needs to be done on a sample by sample basis (you can buffer chunks but the processing is effectively done on a sample basis).
 

[jatalahd]

At least in the field of Control Engineering the block diagram is a general way of describing any process (mechanical, thermodynamical, electrical, etc...) mathematically, using branches of transfer function operations, usually consisting of a feedback loop to make the process stable. For example, here is a block diagram for a 3 op-amp state variable filter in low-pass form:



it consists of several integrators (1/s) and an inverter (-1).

Another very similar approach would be the signal flow graph, here are some examples:



The signal flow graph uses the same idea, that a signal from a node is multiplied by an operator (transfer function) and combined to following node. Again it is very commonly used in feedback analysis, where the general single-feedback loop signal flow is described as (according to Bode, Blackman and as later described by Jacob Millman):



I have never though about how to deal with non-linear transfer functions, especially in the case where clipping occurs. In that case is the interest in the frequency response (the s-plane) or in the time domain? As for linear transfer function you put in a sine of frequency F1 and get the same F1 out, but with different magnitude and possible phase shift. In non-linear system you put in a frequency F1 and get a Fourier series representation of F1 out (several frequencies). Then in the end you need to evaluate the transfer function for all input frequencies Fx and for output you need to sum up all frequency components of each input frequency to get the "complete" transfer function of the system, which I guess would be different for all input signal amplitudes .... That is a discrete process (making non-linear function "linear" again using series expansions of functions), my brain cannot handle this a a continuous "analog" process.

But OK, now I forgot what was the actual topic, so better stop writing now

[Vivek]

Dear Jarmo,

Thank you for publishing your web site http://www.guitarscience.net/

It has some very pertinent information !!!


In particular, the article at http://www.guitarscience.net/papers/bigmuff.pdf was very useful to me when I was trying to understand the Big Muff recently.


Thanks also for accepting my suggestions to add Baxandall, James and Blackstar ISF tone controls to the "TSC in the Web"


Thanks again, sir !!!

[jatalahd]

Thanks also for accepting my suggestions to add Baxandall, James and Blackstar ISF tone controls to the "TSC in the Web"

With these I had a lot of help from user TheseGoTo11, who also posted to the thread about the tsc in the web. As I had much other things to do lately, he did so much improvements on the TSC project. The credit for all the Baxandall and James additions goes to him. Otherwise I take in all suggestions, but can't fulfill them all by myself.

Also unfortunately I have not posted other new stuff to my website in quite a while. I started a new book project three years ago, but currently it is on hold, I need to wait for new motivation and energy to continue with it.

[Eb7+9]

Then in the end you need to evaluate the transfer function for all input frequencies Fx and for output you need to sum up all frequency components of each input frequency to get the "complete" transfer function of the system, which I guess would be different for all input signal amplitudes .... That is a discrete process (making non-linear function "linear" again using series expansions of functions), my brain cannot handle this a a continuous "analog" process.

You'd be spending an infinite number of lifetimes getting nowhere ... why? because there are un uncountably infinite number of NL transfer functions per gain stage that have the exact same H(s) response ... reminds me of the guy who tried doing a hardware emulation of an AC30 using op amps and diodes

Btw, there is no such thing as an AC transfer profile per se in engineering ... the closest anybody can get is by averaging multiple transient responses (sim'd or measured) as was done in this landmark paper:

https://www.dafx.de/papers/DAFX02_Moeller_Gromowski_Zoelzer_measurement_nonlinear.pdf

[ElectricDruid]

Then in the end you need to evaluate the transfer function for all input frequencies Fx and for output you need to sum up all frequency components of each input frequency to get the "complete" transfer function of the system, which I guess would be different for all input signal amplitudes .... That is a discrete process (making non-linear function "linear" again using series expansions of functions), my brain cannot handle this a a continuous "analog" process.

You'd be spending an infinite number of lifetimes getting nowhere ... why? because there are un uncountably infinite number of NL transfer functions per gain stage that have the exact same H(s) response ... reminds me of the guy who tried doing a hardware emulation of an AC30 using op amps and diodes

Btw, there is no such thing as an AC transfer profile per se in engineering ... the closest anybody can get is by averaging multiple transient responses (sim'd or measured) as was done in this landmark paper:

https://www.dafx.de/papers/DAFX02_Moeller_Gromowski_Zoelzer_measurement_nonlinear.pdf

Seems to me that thee are just more dimensions than a typical "transfer function" allows for. The transfer function gives a non-linear response of one variable to another - so an input voltage and an output voltage. But as jatalahd says, that curve is possibly different at every frequency, and again for every amplitude. So it's not a curve, but a 3D surface, and not a 3D surface, but 4D solid, or perhaps even some higher-dimensioned shape. Clearly at this point this stuff is getting hard to visualise, but there's no problem from a computational point of view. Processors don't care, so long as you've got enough memory and enough cycles.

[Rob Strand]

But as jatalahd says, that curve is possibly different at every frequency, and again for every amplitude.

It's worse than that because each input frequency has multiple output frequencies due to the distortion.
When you input two signals of different frequencies you get intermodulation that means new frequencies with different levels.

If you have one clipper and look at the output spectra then take a different clipper which has a different output
spectra.  EQ'ing the output doesn't end up with the same result.  In particular the strength of the intermodulation
terms.

You can go a long way by *separating* the features.   For example a fixed EQ and a fixed non-linearity.    You can even incorporate a crude approximation of bias shift by combining an estimate for the DC shift with the input signal so the input to the non-linear curve is Vin = Vac + Vshift_estimate.    If you look at the Crate sag circuit it's more or less doing that.

In order to go beyond that you need to start digging into the small print.   That  means modelling more of the non-linearity.   A general way to handle this type of thing is with non-linear state-space models.   In its full form you would expect the result to follow a spice sim.  However you can do things like simplify the model and "fit" parameters to emulate the behavior of a more complex system.   IIRC, there's a thesis on-line somewhere where a guy models a whole heap of pedals using that idea.

The general tools for handing non-linearity are:
- Describing function.   More useful to analyse oscillators.  It's a way of modelling non-linear gain.   For example a Wien-Bridge oscillator needs an amplifier gain of 3 for clean oscillation but if you set the gain to 3.3 you will get oscillation but it will be distorted.  And if you set the gain to 4 it will be more distorted.   The describing function models harder clipping as a lower gain:  the output of the clipper is fixed and as the input increases the effective gain output/input looks smaller.   The amount of clipping adjusts the gain to make the overall non-linear gain 3.   

You can extend this idea to frequency dependent gain by separating the frequency dependent behaviour and the non-linear behaviour.

- Volterra Series.  This is a way of modelling non-linearity together with LTI behaviour (like circuits with caps and inductors).  It uses a series and in order for the series to converge the non-linearity needs to be weak.

- Non-linear State space.   Basically non-linear differential equations.  OK for computer calculations and modelling but doesn't give much in terms of intuitive understanding.

[Eb7+9]

Seems to me that thee are just more dimensions than a typical "transfer function" allows for. The transfer function gives a non-linear response of one variable to another - so an input voltage and an output voltage. But as jatalahd says, that curve is possibly different at every frequency, and again for every amplitude ...

Um, no ... you guys simply fail to understand what frequency response (one half side of Bode response) is or what it represents in the greater scheme of things // a grandiose silliness that we see in hobby circles ... this forum's recent threads on the false concept of "AC transfer" indicate implying f-response as a black-and-white concept that can somehow simplistically (magically) side step a NL circuit's real-time response, which is typically too complex to put into forum chit-chat (hence that paper I referenced above) ... in the same sense you also don't understand what to do with DC-transfer analysis inside a SPICE package ... these are powerful tools meant to be used in specific instances, the same way a stethoscope is - outside of having fun listening to a heart beat

as a result there's this strong tendency to extrapolate basic wrongness into a type of meta-wrongness that leads to nothing of great merit ... proof lies squarely in the fact that it has yet to net any real design work (here I'm excluding the cobbling of luck-based distortion circuits) and also in the many futile attempts to do real-world debugging work ...

the four or five years that are spent learning circuit design in an EE program has much to do with learning the correct methodology so this confusion hopefully doesn't end up happening - which is why the whole thing starts with learning network theory first, way before anything about active devices is even considered ...

btw, there is no such thing as a typical transfer function, rather the concept needs to be properly defined and treated in a general sense ... why a competent engineer can go from designing a signal processing circuit, to a power generating circuit, to whatever ... generally by starting from top level block thinking and then going down to device level to make things HAPPEN

[R.G.]

Um, no ... you guys simply fail to understand what frequency response (one half side of Bode response) is or what it represents in the greater scheme of things // a grandiose silliness that we see in hobby circles ... this forum's recent threads on the false concept of "AC transfer" indicate implying f-response as a black-and-white concept that can somehow simplistically (magically) side step a NL circuit's real-time response, which is typically too complex to put into forum chit-chat

Hmmm. Sometimes I'm amazed that even if you get something right, you put it in a way that insults and hacks off any readers. From "you guys simply fail to understand" through "forum chit-chat" all the way to the end, you're insulting the folks who are trying to learn. Was it really necessary to put all the participants down?

These guys are trying to put together a mental model that helps them understand. Being dismissively pedantic about their efforts is a disservice to them and the forum. Most of them freely admit that they do not have EE backgrounds. Why put them down for that?

Indeed, time response and frequency response are two different things, and it's best to learn both. A fundamental concept on frequency response measurements is the assumption that any nonlinearities are small enough to be ignored, and that there is no particular beginning or end of the waveform being profiled, or that time changes in the waveform are so far away (in time) that they can be ignored with small errors.

Anything you do know would be better received if you could dial down the attitude. Perhaps you could edit your post to be more helpful and less holier-than-thou. It would surely help the readers learn.

[Vivek]

Very well put, RG !!!

My father used to say "People get hired for their technical skills and fired for their personal skills"

Most Engineering Universities don't teach Emotional Quotient classes, but that is one of the greatest skills that will take you places.

I sometimes wonder what percentage of Steve Jobs success was based on pure technical knowledge and what percentage was based on knowing how to make a team feel respected, committed to working together for a common goal.

I would feel he would have been an unknown if the only skills he had were technical.

[Electron Tornado]

It appears to me that Amps and Pedals are made up of unit processes. These could include

Buffers
Filters
Non-linear stages
Time effects

Kind of the way I think of distortion pedals. They do three things (unit processes) to the signal - amplify, clip, filter. In what order, to what degree, and how many times is where you can get creative.

Regarding amps, this book might be of interest: https://www.ampbooks.com/mobile/books/system/