Harmonic content created by multiple gain stages

[Rob Strand]

Results of the simulations on effect of multiple gain stages :

I really admire the fact you did the experiment (and didn't just take what I said and left it).

Don't let this fool you to stop whatever you want to search for.

Definitely the case.

The hard limiting case with no filter is clearly the simplest case.   Far too simple to take non-results to heart.

The fact there is a difference for softer clipping, which is much more realistic, means multiple stages do have something to offer.   And if we add filtering between stages then that will change the results even for the hard limited.    For multistage amps with transistors we need multiple stages to get enough gain.

Yet ... We all know addition of even and odd harmonics come from this and that.

It's not well known but when you have intermodulation it's possible to get even harmonics for a symmetrical soft limiter.

[Vivek]

Rob Bro (Anagram intended)

What should I try next ?

1Vp 1Khz signal clipped at 0.5v and then passed through a LPF at 3Khz
versus

1Vp 1Khz signal clipped at 0.85V
Passed through LPF at 3Khz
clipped at 0.5V
Passed through LPF at 3Khz

Both hard clipping and soft clipping ?

Somehow that does not seem to be an Apples to apples comparison with additive effect of 2 LPF in the multi-stage Amp. How to make it more equal ?




And for Intermodulation ?
How about a composite signal of 1VP 1Khz + 0.5Vp 3.14159 Khz with a phase shift

A ) Passed through clipper at 0.5V

B ) passed through clipper at 0.85V and then 0.5V

First Hard clipped and then Soft clipped
and see the intermodulation harmonics ?


or can you peer into your crystal ORB and predict the results in advance ?

[teemuk]

Red has 2 knees because of 2 stages of soft clipping.

As expected, the transfer function is composite of the two non-linear functions. Notice how that composite effect also turns the clipping "harder" as the non-linearities enforce each other. The composite effect is less obvious with "brickwall" clipping.

As a side note, had one of the functions been expanding-type the composite effect with compression would have linearized the transfer curve.

Red is different than green. For soft clipping, the output of multistage amp is different than a single stage amp

This composite effect is exploited often. e.g. Early Yamaha DSP tube emulation relied on a single (and rather "soft") non-linear transfer function, but they applied it several times in a row to generate preferred amount of harder clipping. CMOS linear amps are often driven in cascade inside a global NFB loop: Net result is greater linear range and harder clipping. Classic Big Muff circuit. Don't let anyone claim that the second clipping stage is a "hard clipper". It's just as soft as the first one but it displays the composite effect. Opamp driving shunt diodes: at the opamp overdrive threshold you get composite of shunt diode clipping and brickwall clipping, brickwall being dominant in the composite. Effects fade from softer clipping to very hard clipping depending on how hard they are driven. Diode linearization: diodes are employed to pre-distort the signal in expansive-style, in composite with compressive-style non-linearity of following BE junction the net result is increased linearity.
And so on.

And yes, in guitar effects things can get very lively and dynamic when DC bias points between these clipping stages shift.

[Vivek]

> As expected, the transfer function is composite of the two non-linear functions. Notice how that composite effect also turns the clipping "harder" as the non-linearities enforce each other. The composite effect is less obvious with "brickwall" clipping.

Yes sir !!!

Each subsequent stage makes the transfer curve go more horizontal.


> As a side note, had one of the functions been expanding-type the composite effect with compression would have linearized the transfer curve.

Yes sir !!!

If an earlier stage has expanded the signal, the next stage would not have gone so horizontal.


> This composite effect is exploited often. e.g. Early Yamaha DSP tube emulation relied on a single (and rather "soft") non-linear transfer function, but they applied it several times in a row to generate preferred amount of harder clipping.

Yes sir !!!

Early Yahama patents show their favorite curve




Using this same curve 2 or 3 times ( with different signal levels) can lead to a wide range of sounds, from clean to metal


FV-1 programming also suggest using the same stage of distortion many times in series if one wants more gain and harder clipping than what can be achieved with one stage


That is what I wish to try out in my concept of "Lego Block Amplifier design". Design a simple stage with easy to calculate gain, compliance, LPF , HPF;  and then users can use 2 of 3 or 4 of these stages in series to get their custom sound.

> Classic Big Muff circuit. Don't let anyone claim that the second clipping stage is a "hard clipper". It's just as soft as the first one but it displays the composite effect.

Agreed sir,

Since the component values of each Big Muff stage with diodes is exactly the same, they have to behave exactly the same. The only difference is that the second stage is being fed the signal from the first stage which has already processed it once.

> Opamp driving shunt diodes: at the opamp overdrive threshold you get composite of shunt diode clipping and brickwall clipping, brickwall being dominant in the composite.

This is the basis of so many pedals : Rail Saturated Opamp driving shunt diodes.

> And yes, in guitar effects things can get very lively and dynamic when DC bias points between these clipping stages shift.

Could you suggest a way to get dynamic DC shift in a BMP ?

[Steben]

Could you suggest a way to get dynamic DC shift in a BMP ?

Asymmetrical clipping

[Rob Strand]

I guess the problem with these analysis is you have to ask what you want out of it.    To me that's
- the process of finding what makes it tick,  ie. what circuit aspects affects what signal aspects
- Then pick and choose the circuit aspects that push things towards what you think sounds good.

The other angle is you can just build two circuits and keep one as the best so far and another where you play with the values.  You just keep tinkering around until you get sick of it.

After that is despair because you end up with things that sound different but not different enough to be awesome.   That's for both the analysis and the playing with circuit.

What should I try next ?

1Vp 1Khz signal clipped at 0.5v and then passed through a LPF at 3Khz
versus

Both hard clipping and soft clipping ?

Somehow that does not seem to be an Apples to apples comparison with additive effect of 2 LPF in the multi-stage Amp. How to make it more equal ?

Soft clipping is going to give you more options but then you end-up with with a lot more combinations to try.   I end-up spending days messing with this stuff and finally decide to stop at some point - to continue another day.

As for apples to apples.  When I add filters my argument is for non-clipped signals those filters are active.  So any two circuits up for comparison most contain the same filtering.   If you have filters f1, f2 and clipper c1, c2 you can create many combinations which have both f1 and f2 in the signal path.
pre filtering:                 f1 ---> f2 ---> c1 --->  c2
post filtering:               c1 --->  c2  ---> f1 ---> f2     ; perhaps the most common
Inter-stage filtering:    c1 ---> f1  --->  c2  ---> f2

And for Intermodulation ?
How about a composite signal of 1VP 1Khz + 0.5Vp 3.14159 Khz with a phase shift

A ) Passed through clipper at 0.5V

B ) passed through clipper at 0.85V and then 0.5V

First Hard clipped and then Soft clipped
and see the intermodulation harmonics ?

or can you peer into your crystal ORB and predict the results in advance ?

For intermodulation it's best to start with one stage and look soft and hard clipping.  See how harmonic distortion can stay relatively fixed and intermodulation can vary with softness and filtering.

You always end-up with with messy spectra and the way you interpret the spectra is with some loose intuition, sometimes perhaps not 100% agreeing with what you hear or like.

I started putting something together but I was trying not to put up "something" but put up something which has an apples to apples element.     I was using 100Hz @ 1V + 3000Hz or 3025Hz or 3040Hz  @ 100mV to 500mV.   Having some patterns in the frequencies lets you workout where the frequency components come from.

The biggest observation is if you look the spectrum from 100Hz and 3kHz alone you just see the same old harmonic spectra we are used to seeing.    However when you have 100Hz + 3kHz (or whatever) the spectrum is *much* more complex.   It's also much more difficult to just judge what is good.

One prediction is soft-clipping reduces the level intermodulation components away from the fundamentals.   If you do a simulation you will see what I mean.