Deciding on the gain of each stage of a multi-stage Amp / Distortion pedal

[Vivek]

After reading a lot of posts here, I now feel I began to slightly understand that the reasons for multiple stages in an Amp or distortion pedal include

A) Less intermodulation if the distortion is built up gradually in multiple stages rather than all in one stage

B) Dynamic changes in harmonic content since different stages start to clip at different signal levels, leading to "movement of harmonic content" and feeling that you are playing with a live thing rather than an algorithm

C) The chance to have bias shifts in between the stages, leading to even more "movement" of harmonic content.

For reason B, I guess that it would make more sense to space the "start of clipping" point of each stage somewhat logically between 0mvp and let's say 800mvp guitar input signals

Let's  have a look at the Uberschall pedal over at https://pcbguitarmania.com/wp-content/uploads/2019/08/Uberknall-1.1v-Building-Docs.pdf

It's basically a FET buffer
Gain stage 1a
Gain control set up like an inter-stage volume control
Some more gain stages 1b, 1c, 1d
Hard clip diodes to ground
FET Buffer

When we set the gain pot to 5% we get a graph like this



Immediately we can see from the shape of the transfer curves that they are set for a high gain type of sound. They are not smooth tube shaped sigmoid curves with smooth corners.

Using arbitrary eyeball method for "starts to distort",

we see stage 1 (Green curve 1a) starts to distort at roughly 1.1Vp input

Then stage 2 is after the gain control. When gain is 5%, this stage acts linearly (Blue curve 1b)

Stage 3 (Teal curve 1c) starts to distort at 0.85Vp input

Stage 4 (Pink curve 1d) starts to distort at 0.25Vp input

(Then comes a hard clipping stage with diodes to ground, not shown in this plot)

So the critical points for "starts to distort" are fairly logically spread across the normal range of guitar signals, for a medium type of distortion.

The circuit behaves like 2 gain stages that dont clip (Only shape the freq response), 2 clipping stages and one hard clip stage.


When we set the gain to max, we get :




We now see that the critical points for "starts to distort" are at

1.1Vp (This stage is before the gain control, so nothing changed)
0.36Vp (The blue curve now shows that this stage will distort)
0.1Vp
0.03Vp
(Then comes a hard clipping stage with diodes to ground, not shown in this plot)

Again, this appears to be fairly evenly spread across the expected range of guitar signals. These data points are quite typical for high gain pedals

Almost all stages are now clipping the guitar signal !

We can expect that at different input frequency responses, the gain stages are at different parts of their curve (Linear, breakup, clipped), hence as the signal builds up or decays, the harmonic content changes, and the player can coax different sounds based in his pick technique.


After having analysed a few pedals, they all seem to be loosely following somewhat similar logic of

If you want a mid gain pedal with multiple stages, the stages should "start to distort" somewhat evenly across the expected signal range, very roughly as follows:

1 stage : lets say about 20 mVvP

2 stage : Maybe about 20 mVp for first stage and 150 - 350 mvP for the second stage

3 stage : maybe 20 mvP, 250 mvp, 500 mvp

4 stage : maybe 20mvp, 100mVp, 300 mvp, 600mvp


If you want a high gain pedal, the "starts to distort" numbers could very roughly be

1 stage : 2 to 5mVp

2 stage : 2mVp, maybe 50mvp for the second stage

3 stage : 2 mVp, 50mvp, 200mvp

4 stage : 2mVp, xxx, yyy, 500mVp


Looking at the suggestion of "1 stage : start of distortion 2 to 5mVp input" more closely.
Suppose we have diodes in the feedback loop that clip at 0.65V
Getting a 2mvP guitar signal to start to clip at 0.65V means a gain of 325. Indeed many one-stage high gain pedals will have gain of around 250- 500 at max gain


Of course, each stage could have slightly different frequency response too, which all adds up to harmonic movement of output based on level of input signal.



Ref :
Peavey patents
https://patents.google.com/patent/EP0662752B1/en
https://patents.google.com/patent/US5647004A/en
https://patents.google.com/patent/US5619578A/en

some docs on Carvin Quad X Amp schematics
and other papers



Please help me to fine tune my error-filled beginner's impression of whats really going on with multiple gain stages.

Please be kind to post gain curves of multi-stage Amps/distortion pedals that you have calculated / measured / simulated. Thanks

[mdcmdcmdc]

The way I think about it (and this may well be very incorrect) is in terms of compression in an audio chain.

If I want to achieve the maximum amount of signal compression with the minimum amount of compression artefacts, then one way of achieving that in an analog signal path is to string together a series of compressors with different characteristics, each set to do something a little bit different. I might use three in a row - the first with fast attack and release, a high threshold, and a high ratio to catch the peaks; the second with less severe settings to average out the content once those spikes are removed; and maybe a third to add some subjective "grit/character/sparkle/glue." AKA the time honoured 1176—>LA2A—>670/660 setup.

Each marginal step gives you an opportunity to address the signal and fine tune what's going on. For high-gain/multi-stage pedals, being able to shape the EQ a bit or attenuate the signal between stages is suer useful.

[PRR]

Don't write absolute levels. The user has fingers and knobs, nothing is absolute. You want ratios. (Gain in the engineering sense is the same thing.)

Study a strange object: RF signal log amps. The intended purpose is to get a value of signal level over a wide range. More accurate and less cost than an ideal detector and a logarithmic amplifier. Successive approximation in a chain of clipping stages. Instead of adding the levels of all the stages, we want to tap the last amp where I note "mush".
https://datasheets.maximintegrated.com/en/ds/MAX4003.pdf

[Steben]

Note how Mark's WattBreaker and my mods on the BluesBreaker function. It features the minimum of multi-staging: 2. But it makes a huge difference. And all with soft clippers. The result is a combination of transparency and slight compression. You can never get that with a single diode clipper.

[J0K3RX]

@Vivek,

I knew that schematic for the Uberknall at pcbguitarmania looked familiar...

Maybe the link below will help you figure out the "what, how and why" of this design.
https://www.free stomp boxes.org/viewtopic.php?f=13&t=28844&hilit=baja+ubs+overdrive

In the link above just take the spaces out of "free stomp boxes" 

Bajaman is Brilliant!

~ Jim

[Vivek]

@Vivek,

Maybe the link below will help you figure out the "what, how and why" of this design.

~ Jim

Thanks for that link !!

I feel that there is a difference between

A) Design an Amp in a Box that sounds good

and

B) Design an Amp in a Box that faithfully replicates the response of a real amp at every stage


This thread here has lots of info on "what" this circuit does at each stage, "how" it does it, and makes a guess on "why"

The other thread that you point to has absolutely no information on the stage by stage analysis of the actual Tube Amp that the circuit purportedly simulates, or the stage by stage analysis of the proposed circuit.

There are no schematics of the tube amp, and no graphs of transient response and frequency response of both the target Tube Amp and the simulation, on the same graph.

There in no evidence given on why this circuit should be called "Uberschall" rather than "My Interesting High Gain Amp"


For comparison, some other folk publish this  :




Back to the "how" that was dissected in this thread but there are no details on the other thread: It is a very simple idea which I wish more experimenters played around with:

A) Decide on how many gain stages you wish to try in your Amp in a Box

B) Decide upon the points where "distortion starts" for each stage. Distribute them somewhat uniformly between roughly 2mvp and 800mvp

C1) Cut bass before first stage, and maybe before other stages as well

C2) Cut treble after each stage

C3) try to make the cut off frequencies slightly different in each stage

and Voila, you have just got yourself an Amp in a Box !!!

This design ideology will surely sound acceptable

But can you boast/prove that it emulates XXX Tube Amp ?

Maybe not unless many more details are revealed and peer reviewed and listening tests done....



PS : I reserve the name MIGHA and "My interesting High Gain Amp" for a future project.

PS : I had sent you a Private message about a week ago

[FiveseveN]

But have you considered why there needs to be an amp in a box at all, and a specific one at that?
To continue the Uberschall example: the amp is still in production, Reinhold even makes his own "pedals based on Amplifier Channels". Where is this great need in the guitar world for an elusive Ubersound that warrants yet another emulator?
Of all the things one can do with electronics, making a box sound like another guy's product from 2001 seems like one of the least interesting endeavors.

[teemuk]

But can you boast/prove that it emulates XXX Tube Amp ?

It's largely a question of accuracy. How much detail one needs and how much detail one can omit without sacrificing certain key ingredients of "trademark tone" (in lack of better term)?

Most high gain preamp designs, regardless of their seeming conplexity, still follow certain design practice, which can be simplified to very easy recipe in this order:
1. Boost mid-range frequencies
2. Distort signal by clipping
3. Attenuate harshest high order harmonics
4: Optional: bass and/or high frequency boost / mid-range notch

You will not find many examples breaking the norm.

Now to that accuracy...
1. Does the design boost the right frequency? Is a single filter stage adequate or do we need to distribute the filtering to several stages? How much of these design choices are audible in practice?
2. Does the design distort in adequate magnitude (remember option to fine tune with gain control)? Is timbre (harmonics) of the distortion similar? Are dynamics similar? How much of this is sudible in practice (i.e. timbre, dynamics)?
3. Does the design low-pass in similar fashion? How small difference in low-pass response is actually audible?
4. Does the design share similar response (remember that it's usually tweakable with associated tone controls)? Can one do this in single stage or do we need distributing? How much audible difference these design choices make?

Usually there is at least some importance to these finer details, otherwise i.e. Uberschall would sound like any other modified Marshall 2203; Soldano SLO, Peavey VTM, Lee Jackson, Laney AOR, you name it... Yet, how different from each other those amps actually do sound like? I would argue they all still have that specific "modified Marshall" tone.

[Steben]

Do not forget gain in a tube amp with its huge voltage supply is to be seen in scale to low voltage design.
Imitating each gain without scaling is not a correct imitation.

[teemuk]

Indeed.

I also like to review much of emulation with "black box" - approach. For example: Say, we try to emulate the typical "hot rodded Marshall", a 2203 with additional gain stage in input. The first two gain stages don't contribute anything significant in harmonics, they merely provide a gain control and mid-range emphasis. So, we don't need two unneccessarily complex triode gain stage emulators with distributed filtering to replicate those contents of that "black box", we can likely simplify all that to a single gain stage realixed with a generic opamp. Maybe not 100% realistic emulation of those two stages but accurate enough for its simple task.

And how much is REALLY audible or perceivable? Say, a single clipping stage is lacking in dynamics. We can cascade eleven gain stages to emphasize harmonic shifting, like Carvin Quad X distortion module, but do we really hear a striking difference vs. cascading just three or two? If we have an amp where three stages distort - first asymmetrically, second and third mostly in symmetric fashion, do we need to replicate that exactly in an emulation or will we have nearly identical outcome with just two stages, first asymmetric, second symmetric.

And realistically, how tiny nuances we can hear or perceive? Because I'm not convinced we can sense the smallest details. For example, if primary clipping mechanism of a preamp is just a single CC+CF stage we can go on and write a long study about compression in CC plate due to variance in loading of the CF and about unique clipping of the CF under capacitive loading, and how all this results to slight differences in how positive and negative lobes clip... and... and... And in the end it's still just moderately symmetrical clipping cell, which one can probably approximate convincingly enough with a generic pair of shunt clipping antiparallel diodes, or with just any other stage that distorts in about same magnitude.

...at least that will do as good job as mimicking very complex clipping of tube power amp by simply overdriving the phase inverter. No pentode tubevclipping, compression, crossover distortion, sag or any other dynamics. Just somewhat similar symmetric clipping to what push-pull amp produces. Yet, if you don't point out what's missing most people are willing to testify how the [insert a varying trademark] is the best invention ever in the realm of guitar amplification and replicates the tone of a roaring Marshall at whisper levels.

So how accurate emulation again? Can we hear or sense that in a double blind test repeatedly?

[Vivek]

Thanks Teemu,

I understand the design ideology a bit better after reading your posts.

You had made a wonderful analysis of the SansAmp GT-2 in your ebook, where you wrote that its not radically novel a design, its just clever and artistic use of clipping and filtering, using ideas that are well known.




As you mention here, 2 of the settings on the GT-2 used your idea 1 Boost mid-range frequencies, but with slightly different frequencies. The Tweed setting uses a Midrange Notch (Idea 4).



It is easy to think about inventing many more Amp settings by changing the F, G, Q characteristics of these response curves.

But as you say, all variants might sound somewhat similar to each other, and the added complexity might not produce tangible audible differences.


Question 1 : Is a bass cut needed after each clipping stage ? Why ?

Question 2 : What can we do different besides

-- Different gain levels per stage
-- Band pass with different F and slopes,
-- Notches of different F and Q

How can a new Amp be substantially or radically different than what came before ?

or has everything under the sun already been discovered ?

[Vivek]

how much is REALLY audible or perceivable? Say, a single clipping stage is lacking in dynamics. We can cascade eleven gain stages to emphasize harmonic shifting, like Carvin Quad X distortion module, but do we really hear a striking difference vs. cascading just three or two? If we have an amp where three stages distort - first asymmetrically, second and third mostly in symmetric fashion, do we need to replicate that exactly in an emulation or will we have nearly identical outcome with just two stages, first asymmetric, second symmetric.

And realistically, how tiny nuances we can hear or perceive?

So how accurate emulation again? Can we hear or sense that in a double blind test repeatedly?

I'm totally with you, Teemu

We need to decide on the complexity of the emulation versus cost in terms of components/development time/weight versus rewards of refinement in sound.


I would feel that Amps will be designed and heard in software before they are built in hardware. It will be easier on the Software to check the effect of yet another gain stage, or change in the clipping characteristics/ frequency response/signal levels of each stage. When a designer is happy with the sound of his Software emulation of an Amp, he can transfer the parameters into a hardware design.



I was in touch with Mr. Michel Buffa about a year and a half ago. He did research on real time emulation of Guitar Amps on a PC.

He has published some interesting papers in this field.

But interestingly, he wrote web based S/W where one can play around with Amp parameters like gain/frequency response of each stage, number of stages etc, and hear it in real time

https://mainline.i3s.unice.fr/AmpSim5/index.html

[teemuk]

As you mention here, 2 of the settings on the GT-2 used your idea 1 Boost mid-range frequencies, but with slightly different frequencies. The Tweed setting uses a Midrange Notch

It's not MY idea.

Design of anything but fuzz-sounding distortion effects (whether amps or offboard) has been evolving towards this arrangement (boosting mids) practically since the mid or late 1960's. Common trend of amp designs was to make them brighter. Bright is louder and cuts through the mix better. (Important when arena PA was still just a 50W amp and a pair of column speakers). If the amp didn't do this as is then it was common to use a treble booster.

There are simple reasons why: Intermodulation of low frequencies sounds muddy. Intermodulation of high frequencies adds too much harsh high order distortion. Imagine you need to crank your amp to distort to even be heard.

So, not my idea but a common design trend especially for those "british" sounding amps developed by e.g. Marshall and Sound City engineers. Their tone was tweaked and tweaked in interaction with many trendsetting artists. Because they largely played certain type of music this is where the design eventually evolved.

There were other alternatives too: Take for example early Sunn, Orange or Fender amps (and what was derived later from those). These commonly have less mid-range oriented response and they produce much "thicker" overdrive tone, which also breaks into bassy flubbyness when one strums power chords or picks quick lead melodies. I heard Jimi Hendrix was never much a fan of that and that Clapton and Townshend got overall better support from Marshall (which at the time was just a boutique company that made Fender clones more inexpensively, and took serious hint of modifying THEIR versions brighter so they would fit better for this new music style that was emerging).

Each category of tones has its fans (this is a matter of taste and application) but generally a treble boosted 2203 lends itself to early archetypal high gain tones of blues, rock, hard rock and metal better than an early Orange or Sunn amp that might in hand excel better in archetypal high gain tones of stoner, garage and doom.

Fender? Yeah, some of their classic tube amps traditionally have that exaggerated mid-range notch in the preamp response (which - ironically - e.g. tweed -era Fender amps do not feature because they have just a crude hi-cut tone control). It works great for clean tones these amps were originally designed for. BTW, many roll the bass control down if they ever crank such Fender amp, to avoir excessive flub and to make the tone tighter. Yep, common tip for early Mark series Mesa amps too (which basically just cascaded the channels of a Fender preamp effectively resulting to clipping of the preamp instead of the power amp).
...and when you roll down the bass knob of a Fender tonestack the response you get is ....drumroll.... the same boosted mids and highs that early stages of classic Marshall amp (i.e. 2203) introduces.

How can a new Amp be substantially or radically different than what came before ?

"How" is the easy part. I think the right question to ask is would a substantially or radically different amp ever be successful commercially? Are majority of guitarists - the potential market - looking for to turn their guitar to sound like substantially or radically different instrument or to sound like AC DC, Hendrix, Page or Van Halen?
By an accident deliberate distortion was radically new invention that actual did become an incredibly popular effect. Can you invent the new radically different effect that revolutionizes the concept of guitar tone in similar fashion? If not, then your radically different approach has an extremely limited interest.