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[email protected] dane_walther@hotmail.com is offline
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Default Distortion... why/how is it created?

(It was suggested that I bring my question over here....)

While so many people run around with their hands in the air talking
about this amp and that amp, their distortion measurements,
tube-vs-transistor, yadda-yadda-yadda, I'm concerned with something
much more fundamental.

If the phrase is true "all amplifiers cause distortion," which I
believe is the case, my question is simple...


How is it created?


For instance, let's take the scenario of an all-analog, all pure
class-A staged amplifier.. My *assumption* is that in an ideal model,
this scenario would generate no distortion, but in using real-world
components, distortion is still generated.


I understand that there exist what are called "nonlinearities" in the
amplifier, where at some input levels, a change of the input voltage
causes a particular change in the output voltage, but at some other
input level voltage, the same change in voltage (just offset from the
original) would cause a different amount of change in the output.


So is distortion's root this nonlinearity?


And if so, why does this nonlinearity always manifest itself as n-order

harmonics?


And how does clipping come into the picture?


I've read that class-A tube distortion is "more pleasing" because most
of its generated harmonic content are low-order fundamentals with a
steep rolloff (n 5), but push-pull (transistor-based but even
apparent in push-pull tube) topologies have a less-steep rolloff, with
harmonics still of decent amplitude even with the higher-order
harmonics (n10).


Even if that is assumed to be true, what causes the tube to have a
steeper harmonic rolloff? One article I read seemed to imply it had to

do with a tube being a "high impedance" amplifier. Not sure what that
means, if you compare a 30W tube amp to a 30W transistor amp, what's
different? Could you adapt a transistor-based circuit topology to act
as a higher impedance amplifier?


Some quick background-- I've got an EE degree in electrical and
computer engineering with emhpasis on the digital realm of circuit
design. But I've been trying to go back and "fill in the details" in
the analog world due to my heavy interest in audio. So while I easily
understand some EE topics, others I may not have as fundamental a grasp

on.


Any and all input would be greatly appreciated!


...dane

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Todd H. Todd H. is offline
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Default Distortion... why/how is it created?

writes:

How is it created?


Any time you go through a non-linear component in the audio chain, you
have the potential for distortion.

For instance, let's take the scenario of an all-analog, all pure
class-A staged amplifier.. My *assumption* is that in an ideal model,
this scenario would generate no distortion,


Yup, whatever came out would be exactly X dB louder than the input,
and no new frequencies would be generated.

but in using real-world components, distortion is still generated.a


Correct. It has to do with the non-linear nature of transistors and
tubes that we have to use to take energy out of a power supply and add
it to an audio signal to make that audio signal bigger.

I understand that there exist what are called "nonlinearities" in
the amplifier, where at some input levels, a change of the input
voltage causes a particular change in the output voltage, but at
some other input level voltage, the same change in voltage (just
offset from the original) would cause a different amount of change
in the output.

So is distortion's root this nonlinearity?


I'd say that's a good way to look at it.

And if so, why does this nonlinearity always manifest itself as n-order
harmonics?


Great question. To appreciate it, math is involved, and that math
involved functions that have squared terms in them, among other
things. In the time domain, if you have a component whose transfer
function introduces

And how does clipping come into the picture?


Take an input of sine(t). The ideal output would G*sine(t) where G
is a linear multiplier representing the gain of the amplifier stage.

Clipping results when the the amplifier runs into the supply rail. In
the extremest case of clipping your sine wave looks like a square
wave. If you do a Fourier transform on a square wave you get a very
long equation that shows the square wave as a summation of sine waves
all harmonically related t othe original.

If the original input is at say 100Hz, the frequency components of
the square wave will be weighted sum of 100Hz 200Hz 300Hz 400Hz, ad
infinitum. I forget the specifics of the math, but mentally
envision an equation that takes the original sine wave, and adds sine
waves and successive harmonics. That's where you begin to
appreciatiate how clipping introduces new frequenies in the signal
that are multiples of the original. And hence, the term harmonic
distortion.

Some quick background-- I've got an EE degree in electrical and
computer engineering with emhpasis on the digital realm of circuit
design. But I've been trying to go back and "fill in the details" in
the analog world due to my heavy interest in audio. So while I easily
understand some EE topics, others I may not have as fundamental a
grasp


My EE had a bit of DSP but focused quite a big on analog signal
processing. Such a broad field, so no shame in it!

Think in terms of a fourier sreies representation of a square wave, or
how a fourier series' coefficients for higher frequencies would be
changed when you try to represent a clipped signal as a function of an
undistorted sine wave, and your brain will wrap around it pretty
quickly.

Best Regards,
--
/"\ ASCII Ribbon Campaign | Todd H
\ / |
http://www.toddh.net/
X Promoting good netiquette | http://triplethreatband.com/
/ \ http://www.toddh.net/netiquette/ | http://myspace.com/mytriplethreatband
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Default Distortion... why/how is it created?

Todd H. wrote:

So is distortion's root this nonlinearity?


I'd say that's a good way to look at it.

And if so, why does this nonlinearity always manifest itself as n-order
harmonics?


Great question. To appreciate it, math is involved, and that math
involved functions that have squared terms in them, among other
things. In the time domain, if you have a component whose transfer
function introduces

And how does clipping come into the picture?


Take an input of sine(t). The ideal output would G*sine(t) where G
is a linear multiplier representing the gain of the amplifier stage.

Clipping results when the the amplifier runs into the supply rail. In
the extremest case of clipping your sine wave looks like a square
wave. If you do a Fourier transform on a square wave you get a very
long equation that shows the square wave as a summation of sine waves
all harmonically related t othe original.

If the original input is at say 100Hz, the frequency components of
the square wave will be weighted sum of 100Hz 200Hz 300Hz 400Hz, ad
infinitum. I forget the specifics of the math, but mentally
envision an equation that takes the original sine wave, and adds sine
waves and successive harmonics. That's where you begin to
appreciatiate how clipping introduces new frequenies in the signal
that are multiples of the original. And hence, the term harmonic
distortion.



Thanks Todd for that reply. So let me rephrase so ensure I'm along the
right path:

- unwanted distortion is due to nonlinearities

- some nonlinearities exist even within the "linear" operation range of
the amplifier

- some nonlinearities exist when approaching the real-world limits
(power rails) of the amplifier

- It is not that the amplifier does anything special to add distortion
in terms of fundamental multiples, but rather when mathematically
transformed into the frequency domain (FFT) the distortion is
manifested that way.

Another question that comes to mind, then, is that if a wave is made up
of fundamental pure sines with different phases and frequencies (that
makes sense, I knew that one already), I guess I'm wondering why
amplifying, say a 1 kHz sine, doesn't introduce some 1.05 kHz sine as
some distortion coefficient. It would seem to me that if distortion is
caused by nonlinearities, then there must be an infininte collection of
possible nonlinearities that could incur the creation of a harmonic of
some decimal-multiple instead of whole-multiple of the fundamental.

Your thoughts?

...dane

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Karl Uppiano Karl Uppiano is offline
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Default Distortion... why/how is it created?


wrote in message
oups.com...
(It was suggested that I bring my question over here....)

While so many people run around with their hands in the air talking
about this amp and that amp, their distortion measurements,
tube-vs-transistor, yadda-yadda-yadda, I'm concerned with something
much more fundamental.

If the phrase is true "all amplifiers cause distortion," which I
believe is the case, my question is simple...


How is it created?


This might help: http://en.wikipedia.org/wiki/Amplitude_distortion
This article has lots of links to other resources as well.


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Karl Uppiano Karl Uppiano is offline
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Default Distortion... why/how is it created?


wrote in message
ups.com...
Todd H. wrote:

So is distortion's root this nonlinearity?


I'd say that's a good way to look at it.

And if so, why does this nonlinearity always manifest itself as n-order
harmonics?


Great question. To appreciate it, math is involved, and that math
involved functions that have squared terms in them, among other
things. In the time domain, if you have a component whose transfer
function introduces

And how does clipping come into the picture?


Take an input of sine(t). The ideal output would G*sine(t) where G
is a linear multiplier representing the gain of the amplifier stage.

Clipping results when the the amplifier runs into the supply rail. In
the extremest case of clipping your sine wave looks like a square
wave. If you do a Fourier transform on a square wave you get a very
long equation that shows the square wave as a summation of sine waves
all harmonically related t othe original.

If the original input is at say 100Hz, the frequency components of
the square wave will be weighted sum of 100Hz 200Hz 300Hz 400Hz, ad
infinitum. I forget the specifics of the math, but mentally
envision an equation that takes the original sine wave, and adds sine
waves and successive harmonics. That's where you begin to
appreciatiate how clipping introduces new frequenies in the signal
that are multiples of the original. And hence, the term harmonic
distortion.



Thanks Todd for that reply. So let me rephrase so ensure I'm along the
right path:

- unwanted distortion is due to nonlinearities

- some nonlinearities exist even within the "linear" operation range of
the amplifier

- some nonlinearities exist when approaching the real-world limits
(power rails) of the amplifier

- It is not that the amplifier does anything special to add distortion
in terms of fundamental multiples, but rather when mathematically
transformed into the frequency domain (FFT) the distortion is
manifested that way.

Another question that comes to mind, then, is that if a wave is made up
of fundamental pure sines with different phases and frequencies (that
makes sense, I knew that one already), I guess I'm wondering why
amplifying, say a 1 kHz sine, doesn't introduce some 1.05 kHz sine as
some distortion coefficient. It would seem to me that if distortion is
caused by nonlinearities, then there must be an infininte collection of
possible nonlinearities that could incur the creation of a harmonic of
some decimal-multiple instead of whole-multiple of the fundamental.

Your thoughts?


No, a pure sine wave can only have integer harmonics. With a 1KHz pure
sinewave input, 2KHz is the next lowest frequency distortion component you
will ever see, no matter what.


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Default Distortion... why/how is it created?


Karl Uppiano wrote:

No, a pure sine wave can only have integer harmonics. With a 1KHz pure
sinewave input, 2KHz is the next lowest frequency distortion component you
will ever see, no matter what.


Playing the child's voice... "why?"

I do understand the definition of a harmonic is an integer multiple,
but throwing away terminology for a moment, I do not understand why
distortion is always manifested in integer harmonics.

Is it just a mathematial fact, or a physics fact, or something else...
?

And thanks for your Wiki link, I'll look into that and follow its
links, also.

...dane

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Karl Uppiano Karl Uppiano is offline
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wrote in message
oups.com...

Karl Uppiano wrote:

No, a pure sine wave can only have integer harmonics. With a 1KHz pure
sinewave input, 2KHz is the next lowest frequency distortion component
you
will ever see, no matter what.


Playing the child's voice... "why?"

I do understand the definition of a harmonic is an integer multiple,
but throwing away terminology for a moment, I do not understand why
distortion is always manifested in integer harmonics.

Is it just a mathematial fact, or a physics fact, or something else...
?


Ecch. You would have to ask that :-)

I could take the easy way out, and say it is just a physical fact (or a
mathematical one, since the mathematics describes the physics) - which it
is. But I should explain it better than that. If you feed a 1KHz sinewave
into a nonlinear amplifier (that is to say, any amplifier), the
non-linearity will bend and distort the original sinewave into a new shape.
But the bends and distortions can only occur along the original sinewave,
not along something else that was not there to begin with.

Let's say that you *did* detect a 1.05KHz signal distortion product. That
signal would be in phase at some point, but it would drift in and out of
phase, resulting in a slowly changing amplitude at the output. The only way
that can happen is if you put in two signals, or if the *nonlinearity* is
constantly changing. But that contradicts our given conditions, that we put
in only a single frequency, and the unspoken condition that the amplifier's
linearity is a constant (it probably isn't exactly, but that's a different
problem).

On the other hand, any integer multiple of the 1KHz input sinewave will have
a fixed phase relationship with the input, and the output waveshape will be
constant.

This is not a rigorous answer, but I think it provides an intuitive grasp of
the big issues.


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Default Distortion... why/how is it created?


Karl Uppiano wrote:
No, a pure sine wave can only have integer harmonics. With a 1KHz pure


Playing the child's voice... "why?"


Ecch. You would have to ask that :-)


Well, I am an engineer, and the son of an engineer... It is a phenomina
that both my mother and my wife roll their eyes at, but accept as fact
nevertheless. :-)

Karl Uppiano wrote:
I could take the easy way out, and say it is just a physical fact (or a
mathematical one, since the mathematics describes the physics) - which it
is. But I should explain it better than that. If you feed a 1KHz sinewave
into a nonlinear amplifier (that is to say, any amplifier), the
non-linearity will bend and distort the original sinewave into a new shape.
But the bends and distortions can only occur along the original sinewave,
not along something else that was not there to begin with.

Let's say that you *did* detect a 1.05KHz signal distortion product. That
signal would be in phase at some point, but it would drift in and out of
phase, resulting in a slowly changing amplitude at the output. The only way
that can happen is if you put in two signals, or if the *nonlinearity* is
constantly changing. But that contradicts our given conditions, that we put
in only a single frequency, and the unspoken condition that the amplifier's
linearity is a constant (it probably isn't exactly, but that's a different
problem).

On the other hand, any integer multiple of the 1KHz input sinewave will have
a fixed phase relationship with the input, and the output waveshape will be
constant.

This is not a rigorous answer, but I think it provides an intuitive grasp of
the big issues.


W-O-W. (big light blinds on above head)

That's about the best explanation I could have asked for. You're
right-- since the phase of the 1 kHz and 1.05 kHz signals would have to
drift, one could not have been created "from" the other. Unless, as
you theorized, the nonlinearity itself drifted (which can be assumed
false for any sort of modern electronics, esp. over such a short
timeperiod as the harmonic under discussion would exist in the system).

I didn't figure on getting all my questions so thouroughly answered in
one day. Now I'll have to let my brain work on it for a few weeks to
ensure I retain it all.

Thanks for all the help and great answers.
...dane

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Todd -- yours and Karl's replies have been extremely helpful in my
comprehension of the issues around distortion, and fundamentally why it
is created in the first place. I applaud you both and would buy you
both steak dinners if I was able.

thanks so much to you and everyone else.

...dane



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Todd H. wrote:

Ah ha--Karl said the magic word here.

I think a _time varying_ system is what's needed to generate
frequencies other than harmonics. So basically you'd need to be
playing with circuitry involving a 2nd signal source, delay lines,
and/or an oscillator and such to create these non-harmonic
frequencies.


Which sounds like based on yours and Karl's posts, that if two signals
are used, or a time-varying transfer function is used, either way we
are beginning to transition into inter-modulation distortion aspects
rather than harmonic distortion... If the input is stable but the
reference changes (transfer function varying with time), or if the
input is stable along with a secondary input, both situations will
cause modulation distortion (beat noises, I think they are also called)
in the output.

Chorus effect explained (delay+pitch modulation mixed with original signal):
http://www.harmony-central.com/Effects/Articles/Chorus/

A nifty bucket brigade device I've never seen befo
http://www.doepfer.de/A1881.htm


You would have to give me MORE references to look up, wouldn't you??
:-)

Okay, on to my next question, but I'll post a new reply on that one.

...dane

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Default Distortion... why/how is it created?


wrote in message
oups.com...
(It was suggested that I bring my question over here....)

While so many people run around with their hands in the air talking
about this amp and that amp, their distortion measurements,
tube-vs-transistor, yadda-yadda-yadda, I'm concerned with something
much more fundamental.

If the phrase is true "all amplifiers cause distortion," which I
believe is the case, my question is simple...


How is it created?



Please see http://www.pcavtech.com/soundcards/techtalk/nlinear/


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Default Distortion... why/how is it created?

Since you two (Todd and Karl) are being so responsive to my questions,
I want to pull another one in.

I originally posted on rec.audio.opinion, but was suggested to move it
over here so I did. But I did get a response over there that I wanted
to quote here and ask about.


Trevor Wilson wrote:

Even if that is assumed to be true, what causes the tube to have a
steeper harmonic rolloff?


**Output transformer.


Is that due solely to the frequency response (higher freq. rolloff) of
the output transformer?

IOW, if you used an "ideal transformer" with a flat FR from 0-infinity,

would the tube amp's harmonic content be the same as a transistor amp
(with no xfmr) of the same topology?

Of course that would not make sense if the input frequency was
relatively low in the audio band (say, 1 kHz), because surely the
transformer would still exhibit fairly nice frequency response out to
at least 10 kHz if not higher....

I suppose now that I understand "WHY" harmonics are created as
whole-order multiples of the fundamental, now I'd like to consider
topologies of audio amplifiers and their harmonic content differences.

And here I'm not quite sure the questions to ask, so I'll just put back
out there again that "I read somewhere" that a class-A tube amp (with
output xfrmr) has a steeper harmonic content rolloff than a
transistor-based push-pull amp with no xfmr. Granted there are at
least three variables here (tube/transistor, class A/class AB, and
xfmr/no-xfmr) if not more, but I'd like to dive in and learn what I can
learn...

...dane

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Default Distortion... why/how is it created?


Ron Capik wrote:

Ah but don't let your brain rest too much yet. ;-)


of course not!

Non harmonic distortion can be created by microphonics
in a vacuum tube. Forces can be created by the signal
that cause the elements of the tube to move and thus
create modulation effects linked to mechanical resonances
in the tube ...not a likely effect for solid state devices.


Can you provide any measured data about the magnitude of such
modulation distortion?

Don't assume I doubt you, I have heard the term microphonics with tubes
and while I didn't know its definition, I can understand the principals
you describe. I am curious though as to how much they really play a
part (assuming of course the tubes are *physically* isolated from
external mechanical forces like the rumbling of the speakers).

Hmmm... that being said, I wonder if microphonics are more commonly
caused from air coupling of the speaker outputs shaking the tubes
(similar to a feedback equation with delay), and how much is due to
internal system issues in-time with the signal being amplified?

...dane



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Arny Krueger Arny Krueger is offline
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Default Distortion... why/how is it created?


wrote in message
oups.com...

Ron Capik wrote:

Ah but don't let your brain rest too much yet. ;-)


of course not!

Non harmonic distortion can be created by microphonics
in a vacuum tube. Forces can be created by the signal
that cause the elements of the tube to move and thus
create modulation effects linked to mechanical resonances
in the tube ...not a likely effect for solid state devices.


Actually, there are two effects

(1) Modulation distortion in the form of modulation of an audio signal being
amplified at the same time.

(2) Noise caused by modulation of the bias voltages present in the tube.

Can you provide any measured data about the magnitude of such
modulation distortion?


IME (1) is pretty small, and (2) is quite a bit larger.

Don't assume I doubt you, I have heard the term microphonics with tubes
and while I didn't know its definition, I can understand the principals
you describe. I am curious though as to how much they really play a
part (assuming of course the tubes are *physically* isolated from
external mechanical forces like the rumbling of the speakers).


Hmmm... that being said, I wonder if microphonics are more commonly
caused from air coupling of the speaker outputs shaking the tubes
(similar to a feedback equation with delay),


Or mechanical vibration propigated through furniture and room structure.

and how much is due to internal system issues in-time with the signal
being amplified?


Now we're back to the more common form of distortion due to the nonlinearity
of the tube.


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Dave Platt Dave Platt is offline
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Default Distortion... why/how is it created?

Is it just a mathematial fact, or a physics fact, or something else...
?


It's a mathematical fact, _if_ the transfer function of the device
is a function of the input value, and only the input value.

You can prove this via a simple method: that of contradiction. That
is, assume that it's not true, follow this assumption logically, and
show that the conclusions of this line of thought contradict one of
your starting assumptions.

So, let's assume the following three things:

[1] The output value (i.e. the amp's output voltage) is a deterministic
function of the input value (i.e. the input voltage), and nothing else.

Vout = f(Vin)

[2] Vin is a sinusoidal function of time,

Vin(t) = sin(rate * t)

where "rate" is a constant

[3] Vout, the output, contains one or more sinusoidal frequency
components which are not members of the set

sin(rate * t)
sin(2*rate * t)
sin(3*rate * t)

That is, Vout(t) contains some nonzero (and of course not
necessarily integer) amount of

sin(X*rate * t)

where "X" is not an integer.

Now, let's follow these assumptions forwards.

Let's evaluate Vout at various times. Let's look at times t=Q and
t=Q+2*pi, where Q is any starting time value you want to choose.

Vout(Q) = f(sin(Q))

Vout(Q+2*pi) = f(sin(Q+2*pi))

Fair enough? We're simply evaluating the output of the amp's transfer
equation, precisely one cycle apart in the input sinewave.

Now, we can make use of the fact that sin(X) = sin(X * N*2*pi) for any
integer N - that is, any sinusoidal function repeats its value once
per cycle. This means that

sin(Q) == sin(Q*2*pi)

which further means that

Vout(Q) == Vout(Q+2*pi)

That is to say, since we're feeding the same value into the function
at these two points in time, and since the function's output depends
only on this one input (our assumption #1), we know that the
function's output must be the same at these two moments.

Here's where the fun kicks in. We've also assumed that the output
function has some frequency component which is not an integral
harmonic of "rate". In other words, we've assumed that

Vout(t) = a*sin(rate*t) + b*sin(2*rate*t) + c*sin(3*rate*t) + ...
+ w*sin(X*rate*t))

where "w" is the relative amount of this particular non-harmonic.

But, our knowledge of the behavior of the sin(x) function leads us to
an uncomfortable conclusion. If X is not an integer, then

sin(X*rate * t) != sin(X*rate * (t+2*pi))

except on special occasions. If there's any nonzero amount of such a
non-harmonic in the signal, then its presence would cause the output
voltage to be different at two points in the output cycle which are
precisely one input period apart... points at which we know that the
inputs to the transfer function are identical.

Or, in other words, the presence of a nonharmonic component in the
output means that

Vout(Q) != Vout(Q+2*pi)

So, combining our set of initial assumptions in different ways have
led us to two conclusions: that the output voltages at two specific
points in time must be identical, and must not be identical. We've
got a logical contradiction. The initial assumptions, taken as a
group, are incompatible with one another.

The only way to resolve this contradiction, and create a consistent
set of conclusions, is to eliminate one of the initial assumptions.
We can either give up the requirement that the system be able to
generate non-integral harmonics, or we can give up the requirement
that the output be a function of only the input value, or we can give
up the requirement that the input value be a strict sinusoidal
function of time.


--
Dave Platt AE6EO
Hosting the Jade Warrior home page: http://www.radagast.org/jade-warrior
I do _not_ wish to receive unsolicited commercial email, and I will
boycott any company which has the gall to send me such ads!
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Karl Uppiano Karl Uppiano is offline
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Default Distortion... why/how is it created?


wrote in message
ups.com...
Since you two (Todd and Karl) are being so responsive to my questions,
I want to pull another one in.

I originally posted on rec.audio.opinion, but was suggested to move it
over here so I did. But I did get a response over there that I wanted
to quote here and ask about.


Trevor Wilson wrote:

Even if that is assumed to be true, what causes the tube to have a
steeper harmonic rolloff?


**Output transformer.


Is that due solely to the frequency response (higher freq. rolloff) of
the output transformer?

IOW, if you used an "ideal transformer" with a flat FR from 0-infinity,

would the tube amp's harmonic content be the same as a transistor amp
(with no xfmr) of the same topology?

Of course that would not make sense if the input frequency was
relatively low in the audio band (say, 1 kHz), because surely the
transformer would still exhibit fairly nice frequency response out to
at least 10 kHz if not higher....

I suppose now that I understand "WHY" harmonics are created as
whole-order multiples of the fundamental, now I'd like to consider
topologies of audio amplifiers and their harmonic content differences.

And here I'm not quite sure the questions to ask, so I'll just put back
out there again that "I read somewhere" that a class-A tube amp (with
output xfrmr) has a steeper harmonic content rolloff than a
transistor-based push-pull amp with no xfmr. Granted there are at
least three variables here (tube/transistor, class A/class AB, and
xfmr/no-xfmr) if not more, but I'd like to dive in and learn what I can
learn...


This starts to get into areas where I do not have specific knowledge about
specific devices. Triode tubes and transistors have remarkably different
transfer characteristics (bipolar junction transistors and field effect
transistor curves are shaped a bit more like tetrodes, but you can't even
take that to the bank). The differences in transfer characteristics alone
are enough to give rise to different harmonic content. That is a reasonable
starting point, anyway.

My personal opinion (flame bait) is that both amplifier types (tubes or
transistors), when linearized using properly-designed negative feedback
should have such low distortion characteristics as to be indistinguishable.
Perhaps theoretical or measurable, but my opinion (again, flame bait) is
that if you can actually *hear* a difference between two amplifiers of
similar power and bandwidth, then one of the amplifiers is poorly designed.
:-)


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Arny Krueger wrote:

Actually, there are two effects

(1) Modulation distortion in the form of modulation of an audio signal being
amplified at the same time.

(2) Noise caused by modulation of the bias voltages present in the tube.


Wouldn't a low-impedance bias driver help reduce the levels of (2)
above? (Granted I don't know amplifier design theory, so I'm not sure
that the bais point CAN be low impedance. But it would seem to me if
the current flowing through the bias point was substantial (10x)
compared to that flowing(leaking) into the tube bias, that the bias
point voltage would therefore not change much as a function of the
leakage through the tube grid.

Or mechanical vibration propigated through furniture and room structure.


of course; I assumed physical structure isolation, but did not mention
it.

and how much is due to internal system issues in-time with the signal
being amplified?


Now we're back to the more common form of distortion due to the nonlinearity
of the tube.


Ah. Very good. yes.

...dane

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Dave Platt wrote:

....[a lot!]...

Wow, Dave. Excellent response. Well-done. Not much to reply to
there, seems fairly straightforward (as most math proofs are, I
suppose)

...dane



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writes:

Thanks Todd for that reply. So let me rephrase so ensure I'm along the
right path:

- unwanted distortion is due to nonlinearities


Yup.

- some nonlinearities exist even within the "linear" operation range of
the amplifier


Yes. Because no matter how brilliant the design, how carefully biased
the transistors are to work in the linear portion of their transfer
curves, we're strill trying ot make linear output using non-linear
devices.

- some nonlinearities exist when approaching the real-world limits
(power rails) of the amplifier


Absolutely.

- It is not that the amplifier does anything special to add distortion
in terms of fundamental multiples, but rather when mathematically
transformed into the frequency domain (FFT) the distortion is
manifested that way.



Or, alternatively, it's just the nature of the beast, that you're
using nonlinear devices (transistors/tubes) doing everything you can
to confine their state to the linear portion of their transfer curves,
but necessarily you're going to have nonlinearities when the input
pushes outside of the limits of "linear" operation.

I put linear in quotes because it's not entirely linear.

Here's a paper I found that talks in terms of the non-linearities
introduced by the components and talks about things in the terms
you're grappling with
http://www.passlabs.com/downloads/articles/cascode.pdf

Another question that comes to mind, then, is that if a wave is made up
of fundamental pure sines with different phases and frequencies (that
makes sense, I knew that one already), I guess I'm wondering why
amplifying, say a 1 kHz sine, doesn't introduce some 1.05 kHz sine as
some distortion coefficient. It would seem to me that if distortion is
caused by nonlinearities, then there must be an infininte collection of
possible nonlinearities that could incur the creation of a harmonic of
some decimal-multiple instead of whole-multiple of the fundamental.

Your thoughts?


The problem is that to create arbitrary non-harmonic frequencies like
that, you need a transfer function that is not readily available in
the transfer characteristics of the components involved.

I'd need to back to my notes of my third analog electronics classes
and my communication engineering class to see the math again, but I
think it's basically because the transfer function of transistors is
polynomial, you're simply not able to create non-harmonic frequencies
without really going out of your way to do so (e.g. synthesis).


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Todd H. wrote:

IOW, if you used an "ideal transformer" with a flat FR from 0-infinity,

would the tube amp's harmonic content be the same as a transistor amp
(with no xfmr) of the same topology?


No, I don't think so. #include the even'odd harmonics stuff.

If it were this simple, you'd see transistor amps transformer coupled
and sold as botique. :-)


I've been convinced through my research thus far that the even/odd
harmonic stuff between tubes and transistor amps is hogwash, that it's
much () more related to the topology (class A, push/pull,
feedback/no-feedback, etc) than the technology (tube vs transistor).

Your last statement is what I'm getting at... Albeit added expense and
unnecessary for sales, I wonder if a transformer-coupled push-pull
transistor amp would sound more like a class-A tube amp. This of
course assumes that a good bit of signal shaping is done by the
transformer... which may itself be hogwash.

...dane
on a never-ending quest

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Karl Uppiano wrote:

This starts to get into areas where I do not have specific knowledge about
specific devices. Triode tubes and transistors have remarkably different
transfer characteristics (bipolar junction transistors and field effect
transistor curves are shaped a bit more like tetrodes, but you can't even
take that to the bank). The differences in transfer characteristics alone
are enough to give rise to different harmonic content. That is a reasonable
starting point, anyway.


I guess we're close to me having to start digging up some datasheets..
:-)

My personal opinion (flame bait) is that both amplifier types (tubes or
transistors), when linearized using properly-designed negative feedback
should have such low distortion characteristics as to be indistinguishable.
Perhaps theoretical or measurable, but my opinion (again, flame bait) is
that if you can actually *hear* a difference between two amplifiers of
similar power and bandwidth, then one of the amplifiers is poorly designed.
:-)


I would agree with your assessment, with the only caveat that when the
output approaches clipping, differences will occur due to nonlinearity
differences outside of the feedback's area of operation. But that
would be expected.

What's interesting (e.g. yet another tangent road I'd like to travel
down further) is that traditional tube designs, or so I hear, don't use
feedback, but to design a transistor-based method without feedback
would be dangerous (unstable). Again, haven't gone down that road yet,
so that comment could be hogwash also. :-)

I guess I gotta get home to let the dog out. Thanks for all the
feedback today; back here on Monday. Have a great weekend.

...dane

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"Karl Uppiano" writes:

Let's say that you *did* detect a 1.05KHz signal distortion product. That
signal would be in phase at some point, but it would drift in and out of
phase, resulting in a slowly changing amplitude at the output. The only way
that can happen is if you put in two signals, or if the *nonlinearity* is
constantly changing. But that contradicts our given conditions, that we put
in only a single frequency, and the unspoken condition that the amplifier's
linearity is a constant (it probably isn't exactly, but that's a different
problem).


Ah ha--Karl said the magic word here.

I think a _time varying_ system is what's needed to generate
frequencies other than harmonics. So basically you'd need to be
playing with circuitry involving a 2nd signal source, delay lines,
and/or an oscillator and such to create these non-harmonic
frequencies.

Electric guitarists familiar with teh "chorus" effect are familiar
with these shimmering introduction of frequencies around an original
frequency, and its done by adding analog delay lines (bucket brigade
devices) that are clocked by an oscillator to perform the magic.

Chorus effect explained (delay+pitch modulation mixed with original signal):
http://www.harmony-central.com/Effects/Articles/Chorus/

A nifty bucket brigade device I've never seen befo
http://www.doepfer.de/A1881.htm

Best Rgards,
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wrote:

Ron Capik wrote:

Ah but don't let your brain rest too much yet. ;-)


of course not!

Non harmonic distortion can be created by microphonics
in a vacuum tube. Forces can be created by the signal
that cause the elements of the tube to move and thus
create modulation effects linked to mechanical resonances
in the tube ...not a likely effect for solid state devices.


Can you provide any measured data about the magnitude of such
modulation distortion?


Sorry, that's way out of my realm of expertise. Most of my experience
with microphonic tubes goes back to my high school days as a TV
repair person. I have heard tubes "sing" and thus extrapolated
that observation. As tubes age they can become vibration sensitive
and forces in the tubes can make the sensitized tubes "sing."

Don't assume I doubt you, I have heard the term microphonics with tubes
and while I didn't know its definition, I can understand the principals
you describe. I am curious though as to how much they really play a
part (assuming of course the tubes are *physically* isolated from
external mechanical forces like the rumbling of the speakers).

Hmmm... that being said, I wonder if microphonics are more commonly
caused from air coupling of the speaker outputs shaking the tubes
(similar to a feedback equation with delay), and how much is due to
internal system issues in-time with the signal being amplified?

..dane


You asked a very broad question. This is but another aspect. ;-)

Oh, and there may also be thermal relaxation effects in solid
state systems. ...or maybe not.

Can we add switching power supply interactions to the list?


Later...

Ron Capik cynic in training
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wrote in message
ups.com...

Karl Uppiano wrote:

My personal opinion (flame bait) is that both amplifier types (tubes or
transistors), when linearized using properly-designed negative feedback
should have such low distortion characteristics as to be
indistinguishable.
Perhaps theoretical or measurable, but my opinion (again, flame bait) is
that if you can actually *hear* a difference between two amplifiers of
similar power and bandwidth, then one of the amplifiers is poorly
designed.
:-)


I would agree with your assessment, with the only caveat that when the
output approaches clipping, differences will occur due to nonlinearity
differences outside of the feedback's area of operation. But that
would be expected.


There are tons of caveats and provisos in my assertion, which is why I
labeled it "flame bait". It might be a design goal to produce a certain
amound of distortion. Musical instrument amplifiers tend to be designed this
way, or at least, they don't try to design out all the distortion.

Also, while most amplifiers used for playback don't clip much, many
professional applications do, because the sound level is not known in
advance. So designers must take clipping into account. Soft clipping vs.
hard clipping, and what happens if an amplifier doesn't come out of clipping
cleanly are all things we have to think about.

What's interesting (e.g. yet another tangent road I'd like to travel
down further) is that traditional tube designs, or so I hear, don't use
feedback, but to design a transistor-based method without feedback
would be dangerous (unstable). Again, haven't gone down that road yet,
so that comment could be hogwash also. :-)


Tube amps use feedback, starting in the 1920's I think. The phone company
used tube amplifiers as repeaters to increase long distance service, and
they found that by the time the audio made it through several of these
devices, it was almost unitelligible. They started using feedback. Problem
solved.

In my first engineering job, I had to maintain lots of tube amps as well as
solid state amps, and I can guarantee that they *all* had feedback.
Degenerative cathode feedback, overall feedback, RIAA equalization using
feedback, you name it.

I guess I gotta get home to let the dog out. Thanks for all the
feedback today; back here on Monday. Have a great weekend.


Thanks :-)

..dane



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wrote in message
ups.com...

What's interesting (e.g. yet another tangent road I'd like to travel
down further) is that traditional tube designs, or so I hear, don't use
feedback,


False. Feedback has been part of tubed amplifier designs going back to the
1930s.

but to design a transistor-based method without feedback
would be dangerous (unstable).


False, sort of.

Audio amplfiers are actually designed in two domains - AC and DC. The DC
design of an audio has traditionally related to stabilizing operating points
for the active components. The AC design relates of course to how the
amplifier amplifies audio. In some cases the AC and DC designs converge and
the amplfier operates the same at all frequencies including zero frequency
or DC.

If you don't stabilize the operating points of either a tubed or SS circuit
it will be prone to either drift to a high distortion operating point, or
drift to saturation and perhaps overheat, or drift to cutoff and not amplify
at all.



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writes:

Since you two (Todd and Karl) are being so responsive to my questions,
I want to pull another one in.

I originally posted on rec.audio.opinion, but was suggested to move it
over here so I did. But I did get a response over there that I wanted
to quote here and ask about.


Trevor Wilson wrote:

Even if that is assumed to be true, what causes the tube to have a
steeper harmonic rolloff?


**Output transformer.


Is that due solely to the frequency response (higher freq. rolloff) of
the output transformer?


Yes. The output transformer has all the nifty properties we've come
to love from ferromagnetic materials. Yeah, there's the rolloff
among them, soft compression/saturtion in tape is another nice
property. Some studios still track drums to tape because there's no
good digital equivalent to nice tape compression.

IOW, if you used an "ideal transformer" with a flat FR from 0-infinity,

would the tube amp's harmonic content be the same as a transistor amp
(with no xfmr) of the same topology?


No, I don't think so. #include the even'odd harmonics stuff.

If it were this simple, you'd see transistor amps transformer coupled
and sold as botique. :-)

And here I'm not quite sure the questions to ask, so I'll just put back
out there again that "I read somewhere" that a class-A tube amp (with
output xfrmr) has a steeper harmonic content rolloff than a
transistor-based push-pull amp with no xfmr. Granted there are at
least three variables here (tube/transistor, class A/class AB, and
xfmr/no-xfmr) if not more, but I'd like to dive in and learn what I can
learn...


Start lurking rec.audio.tubes and alt.guitar.amps

And google tube solid state harmonics for a lot of stuff on that.

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"Karl Uppiano" wrote in message
news:Ir85h.53$xD.38@trndny08...

In my first engineering job, I had to maintain lots of tube amps as well
as solid state amps, and I can guarantee that they *all* had feedback.
Degenerative cathode feedback, overall feedback, RIAA equalization using
feedback, you name it.


Agreed.

In the Army I maintained 3 Hawk CW radars that were pretty much entirely
tubed*. They had audio-like circuits for handling the Doppler and the
modulation of the transmitter, and they had DC-coupled circuits for antenna
servos, and numerous other things. The largest had about 400 tubes.

As you say, these tubed circuits were full of every kind of local and loop
feedback one could imagine. We had one feedback loop that essentially
traversed the entire radar from transmitter to receiver with numerous
subloops that stabilized segments of the overall loop. IOW this feedback
loop passed through about 350 tubes. The other 50 or so tubes were in
regulated power supplies and other service circuity. MTBF was about 1 day.

* there were some solid state tubed replacements that were packaged as tubes
and were socketed. Most were in the regualted power supplies. They were 300B
replacements. There was also some SS-based built-in test equipment.
Ironically the SS built-in test equipment was a bit marginal in places and
would not work when it was really cold, because the beta of some critical
transitors would fall off too much.


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wrote in message
oups.com...

Todd H. wrote:

IOW, if you used an "ideal transformer" with a flat FR from 0-infinity,

would the tube amp's harmonic content be the same as a transistor amp
(with no xfmr) of the same topology?


No, I don't think so. #include the even'odd harmonics stuff.

If it were this simple, you'd see transistor amps transformer coupled
and sold as botique. :-)


I've been convinced through my research thus far that the even/odd
harmonic stuff between tubes and transistor amps is hogwash, that it's
much () more related to the topology (class A, push/pull,
feedback/no-feedback, etc) than the technology (tube vs transistor).


Even/odd harmonic differences are generally due to the use of push-pull
versus single-ended circuitry. Push-pull or balanced circuits can reduce
even harmonics very dramatically, depending primarily on how well the halves
are matched.

Your last statement is what I'm getting at... Albeit added expense and
unnecessary for sales, I wonder if a transformer-coupled push-pull
transistor amp would sound more like a class-A tube amp.


No, but as Nelson Pass tries to show, a single-ended SS circuit can produce
harmonic structure that is similar to a single-ended tube circuit.

This of course assumes that a good bit of signal shaping is done by the
transformer... which may itself be hogwash.


Transformers are for impedance matching, They can shape the signal by adding
nonlinear distortion and also by adding phase shift and frequency response
variations. Most tube amp output transformers are marginal and start losing
efficiency at the low end, but still inside the audio band.

..dane
on a never-ending quest





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wrote in message
oups.com...

Arny Krueger wrote:

Actually, there are two effects

(1) Modulation distortion in the form of modulation of an audio signal
being
amplified at the same time.

(2) Noise caused by modulation of the bias voltages present in the tube.


Wouldn't a low-impedance bias driver help reduce the levels of (2)
above? (Granted I don't know amplifier design theory, so I'm not sure
that the bais point CAN be low impedance. But it would seem to me if
the current flowing through the bias point was substantial (10x)
compared to that flowing(leaking) into the tube bias, that the bias
point voltage would therefore not change much as a function of the
leakage through the tube grid.


By definition, tube grids in linear amplifiers draw essentially no current
and are therefore always high impedance.

From practical experience I can tell you that a tube with a grounded grid
(hard to imagine a lower impedance source!) can be microphonic.



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Arny Krueger wrote:

"Ron Capik" wrote in message
....snip..
Sorry, that's way out of my realm of expertise. Most of my experience
with microphonic tubes goes back to my high school days as a TV
repair person. I have heard tubes "sing" and thus extrapolated
that observation. As tubes age they can become vibration sensitive
and forces in the tubes can make the sensitized tubes "sing."


Microphonic tubes are most apparent in low level circuits with flat
frequency response. RIAA phono preamps would qualify except for the fact
that they are integral with low pass filtering. Microphonic tubes were more
common in PA system mic preamps.


Ummm, gain structure.


Later...

Ron Capik
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Karl Uppiano wrote:

.....snip...

Tube amps use feedback, starting in the 1920's I think. The phone company
used tube amplifiers as repeaters to increase long distance service, and
they found that by the time the audio made it through several of these
devices, it was almost unitelligible. They started using feedback. Problem
solved.


Close, very close. Bell Lab's Harold Black invented/discovered the negative
feedback stabilization technique in 1927. Scribbled his first notes on the
subject
on his New York subway ride to the West Street lab.

Later...

Ron Capik
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See, Dave, unlike me, has not forgotten all the math. :-)

Kudos.

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On Nov 10, 12:26 pm, wrote:
(It was suggested that I bring my question over here....)

While so many people run around with their hands in the air talking
about this amp and that amp, their distortion measurements,
tube-vs-transistor, yadda-yadda-yadda, I'm concerned with something
much more fundamental.

If the phrase is true "all amplifiers cause distortion," which I
believe is the case, my question is simple...

How is it created?

For instance, let's take the scenario of an all-analog, all pure
class-A staged amplifier.. My *assumption* is that in an ideal model,
this scenario would generate no distortion, but in using real-world
components, distortion is still generated.

I understand that there exist what are called "nonlinearities" in the
amplifier, where at some input levels, a change of the input voltage
causes a particular change in the output voltage, but at some other
input level voltage, the same change in voltage (just offset from the
original) would cause a different amount of change in the output.

So is distortion's root this nonlinearity?

And if so, why does this nonlinearity always manifest itself as n-order

harmonics?


You asked why one can't put a 100 Hz sinewave into a some kind of
nonlinear device and get out 100 Hz + 105 Hz.

A steady (reoccuring) wave is composed of a fundamental (sinewave) and
various harmonics. (In a reoccuring wave, every cycle looks exactly
like the previous cycle.) If there was a non-harmonic frequency
component, such as a 105 Hz , added to 100 Hz, the sum of the two waves
would vary in amplititude as the two components went in and out of
phase. That would be a non-reoccuring waveform.

Puting a sinewave into a any nonlinear amplifier can only produce a
reoccuring output waveform. Such a wave will always be composed of a
fundamental and harmonics. No matter how much an amplifier bends and
distorts the sinewave, the output wave will always be a constant
waveform. Thus, it must be composed of a fundamental and various
harmonics, only.

Bob Stanton

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Wow -- thanks to everyone for so much good discussion. I think I'm
good for a while on this topic, I'll come back and revisit as more
questions arise.

thanks again to all!
...dane

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