Transfer functions

[Ethan]

Any EE's out there ever actually use transfer function theory in pedal design?

[rodriki1]

I think transfer function is a good consideration when thinking of
tube emulation or transistor distortion.

But filtering must be considered too. Treble booster before distortion.

Or bass atenuation.

see my example of personal research.

http://geocities.yahoo.com.br/rmfidelis/vox1.jpg

I am using CIRCUITMAKER student edition.

My first objective is to get tube distortion emulation.

To make my computer tests i am considering to emulate
vox ac30 12ax7 stages.

Each stage has its own harmonical characteristics.

So we must have one simulation for each stage.

But i only got 12ax7 the harmonical reproduction with fet (in my tests i use bf245a)

when i use high value fet source resistor.

That way i have strong negative realimentation.

So i get at the end some atenuation of signal, or in another way
no amplification at all.

I discovered that for tube simulation i can not think of getting
gain at my stages of simulation.

Something i believe now based on my simulation is that i have to think of
my simulation as if it is the real tube amp.

So i have to get some good booster before simulation, giving me some volts at output.

I have op amps ideas for distortion too.

Op amps for tube distortion simulation must not have high gain.
The gain i got is about 2 or 3.

Hope anybody could confirm that ideas.....

Thanks

[Paul Perry (Frostwave)]

THe thing with zeners like this, is that you are getting a function built up from a number of straight lines. With ordinary (Si or Ge) diodes, if you get everything right, you are approximating the desired transfer function from curves, so you can possibly get closer.
Pretty tricky, though... I suspect thta ther emay still be some relatively simple unorthodiox transistor arrangements that just happen to give a useful function!!!!
The old book "Function circuits: design and applictions" by Wong & Ott might inspire. And any of the Korn (no, not THAT Korn!!) analog computing books. I'm not an EE, but luckily Wong, Ott & Korn were :wink:

[Ardric]

I suspect thta ther emay still be some relatively simple unorthodiox transistor arrangements that just happen to give a useful function!!!!

Is that what this is?  I found this interesting clipping section in the Musicman 1600-B amp:



It seems to be an attempt to do that.  The opamp is a TL072 at +/-16V, and the other section of the gain pot controls the pre-EQ gain stage.

I guess it's attempting to emulate a PP power stage, not a 12AX7, so it's not really the same thing.  I'm still curious to know if anyone has any comments about it.

[Paul Perry (Frostwave)]

THanks Ardric, now my brain hurts :wink:  Maybe someone can emulate this & see what happens? I *think* it's going to give a compressed kind of distortion, but?!

[R.G.]

Any EE's out there ever actually use transfer function theory in pedal design?

Yes. At least one I know of.

But filtering must be considered too.

This another way of saying that for a good emulation, you have to consider both the tranfer function and the frequency response.  It is true. Transfer function tell you at what level you have nonlinearities.Frequency response tells you what PART of your signal you clip.

THe thing with zeners like this, is that you are getting a function built up from a number of straight lines. With ordinary (Si or Ge) diodes, if you get everything right, you are approximating the desired transfer function from curves, so you can possibly get closer.

The real problem with matching transfer functions is that the circuit complexity grows out of bounds for anything except the simplest functions. Close matching may take many inflection points, and you the run into the problem that it's hard to get the inflection points close together without interaction. The standard biased-transistor curve matcher is probably the simplest thing to do the general job, and even then it's complex.

I suspect thta ther emay still be some relatively simple unorthodiox transistor arrangements that just happen to give a useful function!!!!

Me too - especially since a lot of the whole technology of simple FX relies on the "side effects" of a simple circuit to do some fairly complex effect.

Is that what this is? I found this interesting clipping section in the Musicman 1600-B amp:
I guess it's attempting to emulate a PP power stage, not a 12AX7, so it's not really the same thing. I'm still curious to know if anyone has any comments about it.

It's a transistor clipper based on the Vbe multiplier circuit.

The two 1N914's isolate the transistor stages so that one operates with one polarity, the other with the reverse polarity - no side effects from reverse conduction.

A single Vbe multiplier has a resistor from the collector of a bipolar to the base and another resistor from base to emitter. The voltage at the base must be equal to the resistor divider voltage of Rc with Rb. However, the transistor physics force the voltage across Rb to be one junction voltage. If you do the math, the Rc/Rb divider makes the collector find a voltge that is 1+Rc/Rb times the base-emitter voltage. Less than that and the resistors don't let the base conduct. More than that and the transistor conducts until it's true.

In this case the transistors are symmetrically arranged for a clipping at 1+(470+22)/22   = 23 times Vbe. Vbe is usually low for such low currents, about 0.5V, so the stage will clip symmetrically at about +/-11.5V.

The knee of the Vbe characteristic is amplified too, so the knee is softer that you'd get with 11V zeners.

Yes, it's probably an attempt to emulate the clipping behavior of a PP amp. This is not the first time this has been done. All of the old Thomas Vox amplifiers had what they called a limiter in front of the power amp. It worked at low voltages, but the intent was probably the same - clip the signal below where the power amp would clip by itself and so the clipper transfer function would show through, not the feedback-sharpened clipping of the power amp itself.

[George Giblet]

It depends what you mean by transfer function?

By far the most common meaning is the output/input ratio in the s-domain (Laplace Transforms).  The full term is continuous-time linear-time-invariant transfer function. Engineers use this all the time and so would engineers designing pedals.  In simple terms this is the same as frequency response when s is replace by j*omega and j is the complex number sqrt(-1).

DSP people use discrete-time linear-time-invariant transfer function.  Pretty much all DSP engineers use this to design stuff, that goes for DSP effects too.  Here the transfer function is the output/input ratio except you use the z-domain.  It's possible to convert the z-domain to the frequency domain, which for example would give you the frequency response of a digital equalizer.

Another transfer function is the non-linear transfer function which is the one people seem to be stuck on here.  It is less common to use this term, and many text books avoid it by using the term transfer characteristic.  It is more common to plot output vs input, or define a function which describes the behaviour output = f(input), as opposed to defining an output/input ratio.   Engineers do use non-linear behaviour to design things.  It is more common to use a plot or ball-park/approximate shape of the non-linearity than to write down equations.  It is usually difficult to derive such equations and they often aren't very revealing to a designer - of course there are cases where it makes a lot of sense.

[Ardric]

Awesome explanation, RG.  I can understand it!  Thanks muchly.  I'll go check out the Thomas Vox schematics.

What's the general consensus on the sound of this approach?  I'm planning a combo amp based on the LM4780 with a couple of ROG emulators and/or Accoustic 360 pre up front for the tone, and no doubt letting the chip clip will sound like ass.  My first thought was to just fix the maximum level with a trimmer, so that 100% volume on the pre-out would be just below power amp clipping.

But AFAIK the actual clip level would wander around with speaker impedence, and the chip PS wasn't going to be regulated either.  To leave a safe margin would mean throwing away much of the amps potential output.

A clipper like the MM above has the same problem, doesn't it?  We don't really know what's happening in the output section without fixing the particular speaker, cabinet and PS voltages used, and the PS for the chipamp was to be unregulated.  A few dB of headroom represents half of our output power.  It seems like a very expensive solution.  Besides, I don't yet know if I'd even like the sound of it.

So I guess I'd be better off with a clipping detection circuit that lights up a LED when the output swings close to the PS rails.  That could then kick a limiter, or get the operator to tweek the master volume.  Does that sound like the most reasonable approach?

[Ethan]

Thanks George,  Yes I was referrring to the classic use of transfer functions.
I was wondering if it would be usefull to go back and dig up my notes on how to do transefer functions and laplace transforms.  I haven't used that stuff since school and have since forgotton it.