BSIAB I Waveform Study

[Paul Marossy]

Well, once I again, I didn't see anything that I expected when looking at these waveforms. It did confirm that FETs have softer clipping characteristics than other types of solid state device.

As usual, the scope used was my trusty Tektronix 453 with the Volts/Div switch set at 20mV, Time/Div set at 0.5mS, chop mode on with no input on B to give a ground reference to the signal. 1M/13pF probe. Input signal was 600Hz at 20dB attenuation.


This is with Level at 1:00, Drive between 10:00 & 11:00 and the Tone between 1:00 & 2:00. This is the settings I keep mine on for use with my rig. I expected to something more like the classic tube clipping, but instead it was more of a triangle wave...



This is with Level at 5:00, Drive between 10:00 & 11:00 and the Tone between 1:00 & 2:00. Not much change from the previous shot. This is how the waveform looks at pretty much all settings, the amplitude is what changes the most.



This is with Level at 1:00, Drive between 10:00 & 11:00 and the Tone at 7:00.



This is with Level at 1:00, Drive between 10:00 & 11:00 and the Tone at 12:00. Finally, we are getting some rounded edges. No hard clipping going here...



This is with Level at 1:00, Drive between 10:00 & 11:00 and the Tone at 3:00. Tops and bottoms are still round, amplitude has increased some more.

Hope this was interesting. It's surprising how different the waveforms look from what you think they should be. I am starting to see some patterns in the way things sound to me vs. how they look on a scope. So, I guess I am learning something from all of this after all...  

[bazzwazzle]

speaking of waveforms, does an electric guitar playing clean have a square wave form?

[Paul Marossy]

It's closer to a triangle wave than a sine wave. You can get a square wave by amplifying the hell out of a sine wave and then whacking the tops and bottoms off really hard.

[bazzwazzle]

well i remember reading a book which showed some circuits which would take in a square wave and produce another type, whter it be sawtooth or something. But if I were to connect this circuit to 2 jacks for the input and output waves, could I possibly have an effect on my hands?

EDIT: I've also seen the same with the input as a triangle wave and sine wave with various output forms. Could i create an effect out of it?

[Paul Marossy]

A square to sawtooth is probably what you are talking about. It's possible to manipulate your guitar signal by turning it into square waves, and other types of waveforms. A square wave is probably the easiest to accomplish. Getting mixed waveforms gets quite a lot more complicated.

[WGTP]

Once again, thanks for the great pic's.  I think the forum needs a library of those things.

Doesn't a triangle wave consist of mostly even ordered harmonics, as opposed to a squarewave being odd ordered harmonics???

If the tone control is cutting the highs, it will round off the edges of the squarewaves, or other waves too I guess.  Very interesting.  

[Transmogrifox]

Doesn't a triangle wave consist of mostly even ordered harmonics, as opposed to a squarewave being odd ordered harmonics???

Actually, a triangle wave has purely odd-ordered harmonics.  The thing that makes it different from a square wave is the relative amplitude of each harmonic.

This is why filtering so drastically changes the wave-forms of signals.  If you filter a square-wave with an op amp integrator, you get a triangle wave--and if you filter a square wave well enough, you can get a sine-wave, which is very soft looking compared to a square wave.

Scoping a filtered signal is somewhat deceptive in terms of viewing actual clipping curve of a device. Low-pass filtering will always make a clipped sine wave look more rounded while high-pass filtering makes it look sharper (as above).  You see this very dominantly in the above pictures.

If you want to know whether a device produces soft or hard clipping, you need to scope the signal right at the output of the device itself before it's filtered.

A place where distortion gets more interesting is when the signal is clipped, then filtered, then distorted again.  This is very common not only within the preamp stage of a tube amp, but also very noticeable where the preamp is filtered by the tone stack, then the signal is clipped again in the power amp stage.

[Paul Marossy]

So, if a triangle wave is mostly odd harmonics, then this is a curious thing, because I think this circuit sounds pretty good the way it looks in the first picture. Maybe it is what happens to the waveform in the amp that makes it sound so good? I know that to get a closer representation of what is happening with the waveform is to look at it right at the device, but on these studies, I am mainly interested in the final outcome more than anything else. I guess on this particular circuit, I ought to go back and look at what is happening at all five stages...

[Transmogrifox]

Paul-  remember that your guitar signal is not composed of a single sine wave (though the really high notes are more pure).  In ANY circuit, tube or not, there are some intermodulation cross terms added by nonlinear distortion.

Another thing to consider is that with the same drive level, you got all those different wave-forms.   That wasn't a representation of the harmonics *ADDED* by the distortion, that was a representation of how the relative phase and amplitude of those harmonics were changed by the tone stack.

The FETs in BSIAB add both even and odd harmonics to the signal.  If you feed a pure sine wave into a high-gain circuit like that, you get something very square-wave like, and the waveform generally will not look terribly different from a filtered square wave from a sythesizer.  Asymmetrical clipping is like varying the pulse-width--that is, in terms of a pure sine wave.

This all changes when you have something like a guitar signal that is a sum of many frequencies.  Not only that, but the overall amplitude of the signal is changing with time AND the relative frequency/ harmonic content of the original signal is all changing with time.

This is what makes distortion so interesting.  When you dig in, you have a lot more of the wave-form clipped.  As you let a chord ring out, you hear what happens as the signal fades out away from the rails and eventually becomes clean ( in a less high gain pedal like BSIAB).

Therefore, not only the harmonic content and envelope of the original guitar signal are changing, but also the harmonics added by the distortion circuit are changing non-linearly with the input signal.  

Pre-filtering drastically effects the spectral content of the distortion device output as it is changing the relative spectral content of the input signal before a non-linear device.  This is because a nonlinear element ADDS in harmonics that weren't in the original signal.

Now, post filtering changes the VOICING on the harmonics that are there.  You do not add anything spectrally with a filter.  You can only take away frequencies, emphasize others, and de-emphasize certain frequencies.  A filter only changes the magnitude and phase (time) relationship of a signal.  You may note that a filter DOES certainly change the waveform.  A pure sine wave is only effected in phase and amplitude by a filter, but a signal that can be represented by a sum of many sines of different frequencies has a distinct waveform that does not look anything like a sine wave.  Such a signal's waveform will be changed by a filter to look nothing like the original signal even though it contains exactly the same spectral content.

That triangle-esque looking wave in the first picture was not a pure tri-wave and it very well may contain second harmonics---but this could not easily be determined without a spectrum analyzer.

All this said, that is why the effect of the FET itself is best seen by scoping right at the output of the FET.  You have done a good job of showing what the circuit as a whole does to a sine wave.  This is interesting, and a good thing to look at, but I'll guarantee you'll see a lot more if you probe various parts of the circuit from input through to the output and even sweep the frequency of the input signal as this with greatly change the output.  That would demonstrate the nonlinear behaviour of a distortion pedal.

Finally, a good waveform to use for observing the transfer curve of a FET is a triangle wave applied to the gate and the output taken directly at the drain.  The reason is that you have a straight line going in, so what you have on the output is the FET's transfer curve exactly.

Thanks again for your various scope studies and pictures.  It is interesting to see what this all looks like in the time domain. :wink:

Oh, and one last thing:  generate a squarewave at the same frequency as you did the sine and put it through the tone stack and I'll bet the pictures will look very similar to the ones you put up there all except for the last one.

[Paul Marossy]

Thanks for the detailed explanation on that transmogrifox. That is good stuff there. I did notice that the first picture wasn't a true triangle wave. It probably has more second order harmonics than the average transistor, I would imagine. I do wish that I had a spectrum analyzer! At least I have a function generator that produces sine, triangle and square waves...

I think I will look at what's happening in the circuit per your suggestions and see what I find. This should be very interesting!

[Transmogrifox]

You're welcome.  Writing this stuff out also helps me think through it, as well.

Here are a few more tidbits about spectral content added by transistors vs. FETs vs. tubes:

The odd and even-ordered hamonic emphasis in a clipping circuit is primarily due to the symmetry of the clipping, as opposed to the device.  It's in a different thread, but I can't remember which one...I think it was RG replying on the issue.  Either way, it was stated that the more asymmetrical clipping produces even order harmonics; symmetrical clipping produces odd harmonics.  This is absolutely true in the case of a pure sine wave.   As you amplify it and clip it, it approaches a square wave (purely odd).  If you rectify it, you add even harmonics.

The difference between devices is in the convolution of the nonlinear transfer curve of the device on the signal.   Big words, sorry, but all it means is that the input signal is multiplied by the gain of the amplifier.  If the gain of the amplifier changes with respect to the magnitude of the input, it is considered "non-linear", meaning that the output is no longer a linearly scaled input.

Some interesting things happen when an amplifier goes nonlinear.  I covered this in another thread, but the basis is this:

BJT's  :  transfer Ic = Is*exp(Vbe/Vt)

so the output current is an "e" to the power of the input scaled by some constants.

FETs :  Id = (some constants)*(Vthresh-Vgs)^2

so the output is a scaled square root of the input

tubes:

approximately :  Iplate = (Somestuff+Gridvoltage)^3/2


If you understand math, you'll see that the approximate output to input relationships are quite different mathematically.

Signal, sound, distortion-on-guitar-wise, there is a period of time in the clipping where this exponential, or square-root...blah blah blah...dominates the effect on the input.

Basically, when you multiply these nonlinear functions with a signal containing a sum of cosines, you get products that produce frequencies that were not in the original signal.

Furthermore, these nonlinear functions do not always produce harmonically related terms.  This is the case of the BJT.  Do the math, (I haven't, it's very hard with the variable in the exponent) and you'll find some weird stuff that's not very musical.  A well-designed BJT circuit can minimize the nonmusical content and emphasize the musical content--thus some good sounding solid state distortion pedals.

Tubes are noted for even order harmonic content to audiophiles...to us we clip the signal so hard that this phenomenon becomes a mix in the many subtleties that compose tube distortion sound.  This phenomenon I attribute to the multiplication of the tube's particularly nice transfer curve not producing ugly cross-terms.

Like-wise with the FETs.  Squared and Square-Root relationships produce harmonically related spectral content, whereas exponential relationships, as in (constant)^(variable), have some much more dense and complicated spectral consequences.

[WGTP]

Good stuff.  Thanks for the explainations.  

If it is still up, the Blackstone Appliance site had a cool demo of the effect of different harmonics on the wave form.  You could vary the amplitude off each harmonic and see how the waveform changed.  

I guess you also have to factor in the phase of each harmonic as well.

If you think about the guitar producing (conservative guess) the first 5 harmonics upon being picked, which eventually dies down to the fundamental, and the first stage of the distortion producing 5 harmonics of each of those and then the 2nd stage producing 5 of those...  we end up with a bunch of harmonics, theoretically, even though many are duplicates (everyother one being an octive of the fundamental???).

Is that correct?  

[Transmogrifox]

Yes, that's correct WGTP...and if the harmonics aren't enough, there are intermodulation terms as well--which may or may not be musical.  Here's what intermodulation distortion is:

for simplicity sake, suppose you have two signal generators and you set one to produce a sine wave at 83 Hz (Low E fundamental), and the other at its second harmonic, 166 Hz.

You add these two together and  clip the hell out of them.

First, you get harmonics of these frequencies starting to form...but you then get intermodulation terms.

Intermodulation is the sum and difference of the frequencies on the input:

83+166 = 249 Hz---which happens to be harmonically related.
83 - 166 = -83 Hz which is "folded" to 83 Hz, also related harmonically.

Now let's see what happens in the case of 83 Hz and A at 440 Hz:

Sum = 523 Hz
difference  = 357 Hz

Now, obviously, these terms aren't harmonically related, and when you start putting really high frequencies and really low frequencies together, they aren't even musically related.

Say 2400 Hz and 110 Hz
sum = 2510
diff =  2290

At that point it's like having something out of tune in a messy way.

Now imagine having, like you said, like 5 frequencies at once.  You get all those harmonics AND all of the sums and differences of the 5 frequencies.

That's called fuzz.

Now does it make more sense why it usually sounds better when you boost the highs a whole bunch and filter out the lows before you distort a signal?

[WGTP]

Makes sense to me.  I guess we need some spectrum analyzer pics as well.  

Won't it be nice when we can digitally model and manipulate all of this?  Or maybe not!    Filter out the IM products and adjust the balance/phase/over time of harmonics or whatever.

Computers need a quarter inch jack on the front panel.   :twisted:

[Paul Marossy]

I had a dream that someone gave me a spectrum analyzer. I hadn't been that happy in a dream for quite a while!  :wink: