Gain stages: How many in series?

[tca]

When thinking in coupling various gain stages, what number comes to mind? Big Muff has up to 4 stages. In a old topic the "right" number  seems to be 3?

Any thoughts?

[midwayfair]

Most of the stuff I like best out of what I've built is three when we're talking about using transistors to overdrive more transistors. Not including in/out buffers.

For diodes? One stage is often enough but not very sophisticated sounding.

For a combination? Basically, whatever sounds good.

A huge number of good things can be said about simple two transistor arrangements for fuzz, though.

Interesting thread, thanks for the link. :-)

As far as the big muff goes, it really doesn't sound the same if any of the stages are removed. It's kind of thin sounding without the last stage, has a weird decay is 2 or 3 is removed, and sounds a little gated without the input stage. So there must be some utility in four stages.

[gritz]

The Muff is an interesting (and enduring) example of multistage gain, but the first stage is a bit o'gain, rather than a deliberate clipping stage, while the last stage is mainly a "volume recovery" stage to boost the output of the lossy tone control. So ther are really only two distortion stages, each with some pretty heavy eq to limit the passband frequency of the signal.

[tca]

> ...talking about using transistors to overdrive more transistors.

...forgot to mention that. If we are talking about distortion the number 3 is also the upper level, for me I guess, feasible in a simulator. Past that number only breadboarding will clear your mind about what is happening to your signal.

[B Tremblay]

42

[WaveshapeIllusions]

3 does seem like a good number. I'd say one to boost the signal, one for a bit of distortion, and one to bring up levels after the tone controls. Perhaps some filtering after the first stage as well. Though, if we're looking for something smooth, perhaps we split that clipping stage into two, with a bit of attenuation between.

Looking at what has come before, 4 seems like a good number to me. The Fender Bassman goes: input gain, volume control, gain stage, tone control, gain stage (phase splitter), gain stage. The phase splitter part may be unnecessary for a distortion box (as would a push-pull output) so perhaps we can just look at those as a single gain stage. Toss in the right filtering and interstage attenuation, and it would probably sound pretty nice.

However, actually using some kind of phase splitter with a push-pull output might sound nice. Probably a totem pole output. If one makes the supply suitably soggy (series resistor) sag could even be introduced. Another thing to add to the list to try.

[psychedelicfish]

Over 9000!

[Thecomedian]

Tube amps distort at one of of their peaks, and do it successively in each tube stage as it passes it along. 3 transistors will do this and provide asymmetrical distortion via 3 clipping functions instead of 2 or 4. That may be why people feel 3 is a good number.

Regarding the buff muff, could they have solved the 4th stage issue by just having a current mirror to keep the stages running without needing a volume recovery?

3 does seem like a good number. I'd say one to boost the signal, one for a bit of distortion, and one to bring up levels after the tone controls. Perhaps some filtering after the first stage as well. Though, if we're looking for something smooth, perhaps we split that clipping stage into two, with a bit of attenuation between.

Looking at what has come before, 4 seems like a good number to me. The Fender Bassman goes: input gain, volume control, gain stage, tone control, gain stage (phase splitter), gain stage. The phase splitter part may be unnecessary for a distortion box (as would a push-pull output) so perhaps we can just look at those as a single gain stage. Toss in the right filtering and interstage attenuation, and it would probably sound pretty nice.

However, actually using some kind of phase splitter with a push-pull output might sound nice. Probably a totem pole output. If one makes the supply suitably soggy (series resistor) sag could even be introduced. Another thing to add to the list to try.

I've been tinkering with low gain input stages for allowing better fine tuning of distortion. The more functionality you add to it, the more "feature" it has.

[tca]

42

+1

[R.G.]

The problem with questions like this is that the question seems to imply that any number can be used. That's not the case.

How many can be used, or even should be used is a question of objectives. It's important to clearly state (even to yourself) what you're trying to do, and what side-effects are tolerable or intolerable.

One huge issue is noise. Every time a signal has a resistor connected, the resistor's thermal noise gets added to the signal in a manner that depends on the relative impedances of the resistor and the signal source and load. In terms of noise, the optimum number of gain stages is one; or at least one stage that gets you completely up out of the noise floor of resistances. More stages to get to the same gain will always add more noise, given the same kind of technology for gain stages.

Complexity and power are other issues. Complexity costs money and introduces difficulty with all phases of the product's development and testing. Powering multiple stages creates more ways to have power and grounding issues.

However, just getting up out of the noise floor with signal is not what pedals are about, like RF work is. We insist on particular kinds of amplification and distortion. Doing this with one stage may be impossible. So there is an inherent conflict between noise and other things.

Picking the right number of stages then requires knowing what you're trying to do clearly enough to state what "success" is, and often knowing what the limits you can stand on complexity, power, and other things, like perhaps parts in hand. It may even involve limits on what you can simulate, breadboard, or solder up successfully.

What I'm getting at is that a much better question, and I think what you may have meant, is "What are the problems, limitations, and considerations to be dealt with as  you increase the number of stages in series?"

[Thecomedian]

least one stage that gets you completely up out of the noise floor of resistances.

could you elaborate on how you can gain past resistance noise floor? Would lower current reduce thermal noise from resistors? Are transistors less noise polluting than resistors?

[R.G.]

could you elaborate on how you can gain past resistance noise floor? Would lower current reduce thermal noise from resistors? Are transistors less noise polluting than resistors?

Now that I read what I wrote (!) it's at least confusing. Let me try again.

There is a noise floor on both the signal source and whatever receives the signal. The signal source has some signal-to-noise ratio of its own. The receiver - the amplifier in this case - has some input noise no matter what you do. You are stuck with the signal to noise ratio in the signal itself, unless you have some means to average or interpolate the signal over time to bring up the signal while the noise is averaged out. The noise in the input of the amplifier is added to the noise in the signal in an RMS fashion.

So signal and its inherent noise is added to the input noise of the amplifier, then magnified by some gain. To make the most signal with the least noise, you want to get the least gain at the input to the amplifier, and the most gain possible. This produces the best signal-to-noise output for the output of the amplifier.

In consecutive amplifiers, each stage does this, so you get the input noise of each stage added. This matters most if the signal is kept small, so the (fixed) amount of noise at the input of each stage is added to a not-very-much-bigger signal. It matters least if the first stage brings the input signal up to a level where any added noise from the following amplifier stages is much smaller than the already-amplified original signal+noise and the input noise of the first amplifier stage.

In a word - get enough gain in the first amplifier stage so the input noise of later stages doesn't matter much.

[Gus]

42

Best answer

[tca]

Picking the right number of stages then requires knowing what you're trying to do clearly enough to state what "success" is, and often knowing what the limits you can stand on complexity, power, and other things, like perhaps parts in hand. It may even involve limits on what you can simulate, breadboard, or solder up successfully.

Knowing the limits on what one  can simulate and breadboard is in fact a *very* good advice. A "thing" with 7 BJTs, 7 pots is now on my breadboard (not counting Rs and Cs)  

"What are the problems, limitations, and considerations to be dealt with as  you increase the number of stages in series?"

That is also a *very* good question, you can study almost all those problems with 2 stages in series, ... but that was also not what I had in mind.

Probably what I should have asked: Can we make a list of distortion boxes with n gain stages in series for n>=3?

I'm now asking myself your questions in reverse order.

Thanks for your reply.

P.S.
BTW, just for the record, the 7 pots are not for controlling bias of the devices (it has nothing to do with the circuit of that old topic, it has 2 gain stages in series (3 if counting with the active tone control). They are vol, gain, mid cut and pos (passive), treble and bass (active), master vol.

[duck_arse]

I thought +1 was the best answer, but I'm down in the noise floor.

[nocentelli]

http://m.youtube.com/?reload=7&rdm=06vh#/watch?v=0irL1M15DH8

[GibsonGM]

Pretty complex (controversial? ha ha) question.   Don't forget that you can also use gain stages to *do things* involving tone shaping.   You can crank highs on one stage, distort them preferentially, then tame them back, amplify the whole thing again...on and on.   Maybe you pulled some low end out at the input, and got some glassy distortion....you might choose to put some low back IN as you get near the end of your stages....

R.G. -as always- nailed the most salient points here - keeping the SNR acceptable....getting up over the noise floor, making a signal that is strong and worth *doing things to*.   But don't forget; once that's taken care of, and you're into the 'meat and pototoes' of a design, you can easily bring the level DOWN again, if there is a good reason to, and then amplify back UP!    I do a fair amount of tube work - this is typical (universal, probably) in order to get any kind of usable, enjoyable end result that sounds better than a FF with the gain set to 10.

In short: You may not want to send a red-hot signal from one section to another, causing it to clip square (fuzz)...then to another, making that even worse with more odd harmonics.   You probably will want some attenuation in there in order to achieve your desired tonal results gradually and in a planned-out and well understood way...

[tca]

I was thinking something like this using SE topologies gain stages (GS), pretty standard I guess:

[clean channel]
Input GS-> passive tone control -> recover GS

[OD]
(from clean ch.) -> GS -> passive drive control (vol) -> GS -> passive tone control -> to power amp

4 gain stages (there is a lot missing, I know).

[Mark Hammer]

This discussion is bound to go nowhere unless we surgically separate "gain" from "distortion"

Because amplificaion is required to wring distortion out of a guitar signal, the two concepts have been equated in many people's minds.  I regularly see discussion where people think that somehow changing the clipping diodes used gets you a "more gain-ey" sound, withut ever altering how much gain/amplification any part of the circuit is set up to produce.

In that light, it would seem tca is asking one question, and RG is answering another one.

There is NO LIMIT to the number of gain stages one can have, if they are set for modest gain, and if one is willing to tolerate whatever cumulative noise is produced (which could always be largely eliminated by nesting all those stages within a companding framework).  So, if you have enough current to power them, there is no reason why one could not have a circuit with 100 op-amp stages, each set for a gain of 1.2x.  By definition, each is a gain stage, but the total gain produced is still quite modest.  For example, after 20 stages of 1.2x gain, our total is still only 38.3 (assuming I multiplied it 20 times and not more!).

I think, what tca is asking is really how many successive cliping stages one cold use.  And, if memory serves, on one of those rare occasions where RG and Jack Orman agreed peaceably, the conclusion was reached that after 3 such stages, there was really no point.  That is NOT to say that there couldn't be any preceding, intervening, or subsequent gain stages that were directed at producing clipping, but rather at doing something more utilitarian (e.g., tonestack).  But however it was arrived at, the maximum number of stages where useful clipping was produced would be 3.

As for the BMP, there are two clipping stages, one input gain stage to bring the signal up to level, and a gain recovery stage after the tone control to once again bring the signal up to level.

[mistahead]

Assuming perfect noise (zero, realistically impossible) and acceptable distortion (to taste/application) there isn't really a theory as to how many stages you repeat this step - Gain phases.

Distortion phases are horrible after around three cascaded as a rule of thumb I've observed, many settle for two. Stacking distortion phases... well are we looking at additive or subtractive distortions and where in the signal (wave) are we going to apply them?

Two identical diode clipping stages will not do much as stage one does all the work, stage two just passes it though pre-clipped, but make the two stages one diode and one clipped FET amp, or two different (decreasing voltage) diode stages and you are getting something that might become musical AND useful again, and if its too quiet after all that you can run it though some gain stages again... maybe at that stage the acceptable distortion is "some" so we can use that gain stage to generate some distortion on top of our X true distortion phases...

This novice came to this POV using LM386 chips, various diodes, some FETs and trannies, try cascading two LM386's together to created overdrive and them compare to EVERYTHING else that has been done to distort a guitar...