Hi Andy,
What a sad debachle this is for an otherwise edifying thread.
Maybe the shortened form meaning from a definition I reported about linearity is not acceptable to you, but that still cannot excuse you making false statements in your Posts#582 and 593 related to me being actively involved with 'fabrication', 'bluff' and 'brazen misrepresentation'.
I have looked up, and herewith take the trouble that your unwarranted accusation obliges me make, to copy - word by word - text from a book in front of me from a NY publisher.
Linear - denoting any system, device, or apparatus that has an output directly proportional to the value of the input and varying continuously with it, as in a linear amplifier.
No more; no less. That's it !
If you check back to my Post#544 to you, you will see that all I am guilty of is writing adjectivally in order to be able to post in a shortend form, and that because I was not actually copying from this same book now in front of me.
That was not 'fabrication', 'bluff' or the 'brazen misrepresentation' you wrongly accuse me of.
Or do I need to prove that I am not lying now by posting a scan copy ?
Anyway, what is actually wrong with this definition, or my shortened form, because others and the publisher would need to be informed ?
Or would you prefer to furnish us with a better definition that we should all be abiding by ?
(Sorry Jan, unable to make genuine reply to your most worthwhile posts whilst Andy's accusations are distracting me.)
Cheers ......... Graham.
What a sad debachle this is for an otherwise edifying thread.
Maybe the shortened form meaning from a definition I reported about linearity is not acceptable to you, but that still cannot excuse you making false statements in your Posts#582 and 593 related to me being actively involved with 'fabrication', 'bluff' and 'brazen misrepresentation'.
I have looked up, and herewith take the trouble that your unwarranted accusation obliges me make, to copy - word by word - text from a book in front of me from a NY publisher.
Linear - denoting any system, device, or apparatus that has an output directly proportional to the value of the input and varying continuously with it, as in a linear amplifier.
No more; no less. That's it !
If you check back to my Post#544 to you, you will see that all I am guilty of is writing adjectivally in order to be able to post in a shortend form, and that because I was not actually copying from this same book now in front of me.
That was not 'fabrication', 'bluff' or the 'brazen misrepresentation' you wrongly accuse me of.
Or do I need to prove that I am not lying now by posting a scan copy ?
Anyway, what is actually wrong with this definition, or my shortened form, because others and the publisher would need to be informed ?
Or would you prefer to furnish us with a better definition that we should all be abiding by ?
(Sorry Jan, unable to make genuine reply to your most worthwhile posts whilst Andy's accusations are distracting me.)
Cheers ......... Graham.
I can't believe there's so much bantering about the definition of linearity. Graham Maynard had it right.
A linear system obeys the function f(x) = mx + b
Where: m is the constant of proportionality
b is ideally zero in the case of audio amplifiers
The output must be equal to the input times the constant of proportionality, and independant of any and all previous values of input.
As for oscillators, linearity is just as important as in amplifiers. An oscillator that was not linear would have an output frequency that is dependant on the amplitude.
A linear system obeys the function f(x) = mx + b
Where: m is the constant of proportionality
b is ideally zero in the case of audio amplifiers
The output must be equal to the input times the constant of proportionality, and independant of any and all previous values of input.
As for oscillators, linearity is just as important as in amplifiers. An oscillator that was not linear would have an output frequency that is dependant on the amplitude.
Hi !
Ok, please don't hurt me too bad, i just wanted to know...
I had learned that "linear distortions" are distortions that can
be represented as a transferfunction, means creating harmonics
that have a phaseshift of +/-180° or 0°, and "unlinear distortions"
are the ones that can't be described by a transferfunction and are
caused by PIM or asymetric slewrates, creating harmonics at wild
phasehifts. (but typically like +/- 90°)
Is this definition wrong ?
I can post pics of waveforms later if you don't understand what i mean...
Mike
Ok, please don't hurt me too bad, i just wanted to know...
I had learned that "linear distortions" are distortions that can
be represented as a transferfunction, means creating harmonics
that have a phaseshift of +/-180° or 0°, and "unlinear distortions"
are the ones that can't be described by a transferfunction and are
caused by PIM or asymetric slewrates, creating harmonics at wild
phasehifts. (but typically like +/- 90°)
Is this definition wrong ?
I can post pics of waveforms later if you don't understand what i mean...
Mike
Well guys, when you start to discuss with passion, even beeing a little bit excessive
in heat, the oportunitty appear to me to learn many things that i do not understand.
Give some time as a break, to avoid a high level discussion be transformed in a street figth.
And, inside this kind of conflict, i cannot enter to figth aside my friends, as there are many friends envolved and both sides.
A small brake may put all things into the track again.
You are all great guys, very special knowledge people, wonderfull researchers and owners of incredible quality designs, and in my opinion, all of you may be rigth in some aspect, as evaluating referenced the things you all produce, no doubts, all of you are great.
But please, do not loose the interest to defend your ideas, to make big Charlie less ignorant.
regards,
Carlos
in heat, the oportunitty appear to me to learn many things that i do not understand.
Give some time as a break, to avoid a high level discussion be transformed in a street figth.
And, inside this kind of conflict, i cannot enter to figth aside my friends, as there are many friends envolved and both sides.
A small brake may put all things into the track again.
You are all great guys, very special knowledge people, wonderfull researchers and owners of incredible quality designs, and in my opinion, all of you may be rigth in some aspect, as evaluating referenced the things you all produce, no doubts, all of you are great.
But please, do not loose the interest to defend your ideas, to make big Charlie less ignorant.
regards,
Carlos
Graham Maynard said:
Yes, but ...
In one dimensional mathematical world, linear means
y = kx + q /multiplied + shifted/
where y = f(x) /y is a function of x/
But we live in a world of complex variable in electronic circuits, i.e. variable s or jw (w = 2*pi*f, j is complex unit). It is a world of amplitudes and phase shifts, when in frequency domain.
The circuits with R, L and C are linear, if the values of R, L and C are fixed and do not depend on time, voltage, current etc. Their circuit connection always creates a linear circuit.
Resistors, coils and capacitors may be non-linear as well, in case their values depend on voltage, current etc. Then they create a non-linear circuit. In fact, in a real world, these components are always more or less non-linear, the case is, if the non-linearity is negligible or not. (Depends on application).
STOP THAT
Linear system is when a sum of responses equals response for a sum.
Normal (non-adaptive) filters are linear.
any RLC circuit is linear.
Fourier transform is linear.
...
anything, which can be described by convolution, transmitancy, step/inpulse response is linear.
One of interesting features of linear systems is that they cannot produce new spectrum components, another words adding something new to spectrum is a symptom of non-linearity. Linear systems only amplify, attenuate or shift phase of spectrum components already present in input signal.
I think it is time to read more about Lapunow criterium of stability, 's' (Laplace) transform, Nyquist's principle of stability with feedback Nyquist's Re{Im} hodograf and whole steering/systems theory, (just few term to google up) otherwise the discussion is pointless.
Linear system is when a sum of responses equals response for a sum.
Normal (non-adaptive) filters are linear.
any RLC circuit is linear.
Fourier transform is linear.
...
anything, which can be described by convolution, transmitancy, step/inpulse response is linear.
One of interesting features of linear systems is that they cannot produce new spectrum components, another words adding something new to spectrum is a symptom of non-linearity. Linear systems only amplify, attenuate or shift phase of spectrum components already present in input signal.
I think it is time to read more about Lapunow criterium of stability, 's' (Laplace) transform, Nyquist's principle of stability with feedback Nyquist's Re{Im} hodograf and whole steering/systems theory, (just few term to google up) otherwise the discussion is pointless.
Let me try to formalize a bit what darkfenriz is saying. This is a repeat of what Rodlofo said in an earlier post, but adds some specific examples.
A general operator L is linear if it meets the following two criteria:
(criterion 1) L { a * x } = a * L { x }
(criterion 2) L { x1 + x2 } = L { x1 } + L { x2 }
where a is a constant, x is the input to the system, and L { x } is the output of the system.
Let's take for example L(x) = x2
Check criterion 1 above:
L { a * x } = (a * x)2
= a2 * x2
We see that L { a * x } is not equal to a * L { x } (in fact it's equal to a2 * L { x }) so the operator is not linear.
Let's take a much more useful example, the derivative operator, and let's call the variable t for time instead of x. Note: in the notation below, d/dt{ something } means "the derivative of something with respect to time".
Investigating criterion 1 above, we have
d/dt{ a * f(t) } = a * d/dt{ f(t) }
This follows from the scale factor rule for computing derivatives, so criterion 1 is met.
Let's look at criterion 2 now
d/dt{ f1(t) + f2(t) } = d/dt{ f1(t) } + d/dt{ f2(t) }
This follows from the rule for derivatives that the derivative of a sum is the sum of the derivatives.
So we see that the derivative operator is linear.
We can immediately extend this result to ideal inductors and capacitors. Since for a capacitor,
i(t) = C * d/dt{ v(t) }
we immediately see that the linearity of the ideal capacitor follows directly from the linearity of the derivative operator. Also, the linearity of an ideal inductor can be demonstrated in a similar way.
So the idea of linearity is much more general than simply multiplying something by a constant. I've used the derivative operator as an example because it's complex enough to get some useful results from but not so complex as to muddy the waters.
A general operator L is linear if it meets the following two criteria:
(criterion 1) L { a * x } = a * L { x }
(criterion 2) L { x1 + x2 } = L { x1 } + L { x2 }
where a is a constant, x is the input to the system, and L { x } is the output of the system.
Let's take for example L(x) = x2
Check criterion 1 above:
L { a * x } = (a * x)2
= a2 * x2
We see that L { a * x } is not equal to a * L { x } (in fact it's equal to a2 * L { x }) so the operator is not linear.
Let's take a much more useful example, the derivative operator, and let's call the variable t for time instead of x. Note: in the notation below, d/dt{ something } means "the derivative of something with respect to time".
Investigating criterion 1 above, we have
d/dt{ a * f(t) } = a * d/dt{ f(t) }
This follows from the scale factor rule for computing derivatives, so criterion 1 is met.
Let's look at criterion 2 now
d/dt{ f1(t) + f2(t) } = d/dt{ f1(t) } + d/dt{ f2(t) }
This follows from the rule for derivatives that the derivative of a sum is the sum of the derivatives.
So we see that the derivative operator is linear.
We can immediately extend this result to ideal inductors and capacitors. Since for a capacitor,
i(t) = C * d/dt{ v(t) }
we immediately see that the linearity of the ideal capacitor follows directly from the linearity of the derivative operator. Also, the linearity of an ideal inductor can be demonstrated in a similar way.
So the idea of linearity is much more general than simply multiplying something by a constant. I've used the derivative operator as an example because it's complex enough to get some useful results from but not so complex as to muddy the waters.
Rodolfo,
I see, you meant it the other way around - not 'oscillatory capability implies a nonlinear cause', but 'real life oscillation will lead to a nonlinear effect because of real life limitations'.
Still, I thought resonances were modeled as linear (minimum phase) phenomena. I thought of resonances as damped oscillations. So if you have a damped resonance, you'd still have a linear phenomenon (minimum phase). In your wording, you would call only undamped resonant behavior "oscillation". Do I interpret this correctly?
Hi, PMA,
Could you give me a hint how to built V-I openloop converter for the front end of NP-PMA
In your theread, you didn't finish it. If you need direct email, my email is lumanauw@bdg.centrin.net.id
Actually I'm about to finish designing an amp with NP-PMA. I'm still not determined about the front end. Now it is using differential. I wanted to build something like your V-I converter without feedback for its front end, but don't know how. I will be building amp with +/-45V rail.
Could you give me a hint how to built V-I openloop converter for the front end of NP-PMA
In your theread, you didn't finish it. If you need direct email, my email is lumanauw@bdg.centrin.net.idBah... 
The better does when the discourses are done unproductive are leave the thread ( and I what will do ).
I recommend to all of takes a "bath of reality" and remember that this is not a forum on the mathematical maximum systems. Among a lot will discover that the amp and the spks have not THD and if there the haves are "linear" because produced from a together of linear elements, for which goes well things!
Ps: if at least some of the mathematical experts are able to think ( and build ) to a "decent" amp with technology of this century...
goodbye
Mauro
The better does when the discourses are done unproductive are leave the thread ( and I what will do ).
I recommend to all of takes a "bath of reality" and remember that this is not a forum on the mathematical maximum systems. Among a lot will discover that the amp and the spks have not THD and if there the haves are "linear" because produced from a together of linear elements, for which goes well things!
Ps: if at least some of the mathematical experts are able to think ( and build ) to a "decent" amp with technology of this century...
goodbye
Mauro
Hi Jan,
From your explanations I have said I now understand how you have come to use the term 'linear distortion', but to me the term was completely meaningless.
I have just looked through the same publication I copied from for Andy and it does not list 'linear distortion', possibly because use of the term is not universally acceptable, and as we know, it has failed to communicate information clearly.
To me what you know as 'linear distortion' has always been 'phase distortion';- where there is an introduced phase change that is not a linear function with frequency, the result being that output voltage cannot continuously retain direct proportionality with input at the frequencies where there is the phase change. Thus a composite music waveform will become voltage amplitude distorted if there is phase change in the passband, and ditto to an amplifier's NFB response to loudspeaker back-EMF (which is already phase distorted by the loudspeaker) as it attempts to control output terminal error.
You have quoted from 'masteraudio.com' -
some frequencies are emphasised more than others;
to this I add - this must be due to the output carrying a frequency dependent error potential (often hf) that was not present at input.
Clearly the voltage 'amplitude' resonse during 'phase' distortion is not continuously linear in 'time'; ie. phase distortion disturbs the coherence of waveform components and this arises as waveform voltage error.
Those who accept the term 'linear distortion', could be confused by that terminology in a manner that enables them to think there is 'linearity of amplitude response' where actually a fractional voltage amplitude error can exist within the time period of the composite waveform !
I'm not trying to be awkward - but I believe that is all valid comment.
'masteraudio.com' could give this more thought !
Clearly different understandings of terminology have already led to misunderstandings.
(I am not trying to lecture other readers who are already learned and well experienced, but I am here trying to illustrate why first cycle waveform examination has value because of the composite nature of a suddenly starting first sinewave cycle, that is missing with steady sine, and should not overcome an amplifier's slew rate, as with square wave. Ditto via reverse suddenly starting sine injection into the output terminal to observe amplifier NFB loop control in time.)
Hi MikeB,
But I see that you are already hurting yourself ?
What a stuggle it is for you to try to communicate your terms of 'linear distortion' and 'unlinear distortion'. I now know what you are trying to explain, but you are having very real trouble trying to say it !
Hi Carlos,
A well aimed bucket of water to each protagonist !
Cheers mate !
Now that I have looked through this 1980's 600 page reference dictionary I see it might be worth *copying* a couple of the 'distortion' definitions. I had not realised they were here, though I am bound to have read them years ago.
'Nonlinear' distortion is produced in a system when the instantaneous transmission properties depend on the magnitude of the input. Amplitude, harmonic, and intermodulation distortions are all results of nonlinear distortion.
'Amplitude' distortion occurs when the ratio of the root-mean-square value of the output to the r.m.s. value of the input varies with the amplitude of the input, both waveforms being sinusoidal. If harmonics are present in the output waveform only the fundamental frequency is considered.
'Harmonic' distortion is due to harmonics not present in the original.
'Intermodulation' distortion results from spurious combination-frequency components in the output of a non-linear transmission system when two or more sinusoidal voltages, applied simultaneously, form the input. Intermodulation distortion of a complex waveform arises from intermodulation within the waveform.
'Phase' distortion occurs where the phase change introduced is not a linear function of frequency.
'Delay' distortion is a change in the waveform because of the variation of the delay with frequency.
___________________________________________
I've lost the thread, and see there is new argument, but I will go back in case I owe any answers.
Your last comment rings true David.
Cheers ......... Graham.
From your explanations I have said I now understand how you have come to use the term 'linear distortion', but to me the term was completely meaningless.
I have just looked through the same publication I copied from for Andy and it does not list 'linear distortion', possibly because use of the term is not universally acceptable, and as we know, it has failed to communicate information clearly.
To me what you know as 'linear distortion' has always been 'phase distortion';- where there is an introduced phase change that is not a linear function with frequency, the result being that output voltage cannot continuously retain direct proportionality with input at the frequencies where there is the phase change. Thus a composite music waveform will become voltage amplitude distorted if there is phase change in the passband, and ditto to an amplifier's NFB response to loudspeaker back-EMF (which is already phase distorted by the loudspeaker) as it attempts to control output terminal error.
You have quoted from 'masteraudio.com' -
some frequencies are emphasised more than others;
to this I add - this must be due to the output carrying a frequency dependent error potential (often hf) that was not present at input.
Clearly the voltage 'amplitude' resonse during 'phase' distortion is not continuously linear in 'time'; ie. phase distortion disturbs the coherence of waveform components and this arises as waveform voltage error.
Those who accept the term 'linear distortion', could be confused by that terminology in a manner that enables them to think there is 'linearity of amplitude response' where actually a fractional voltage amplitude error can exist within the time period of the composite waveform !
I'm not trying to be awkward - but I believe that is all valid comment.
'masteraudio.com' could give this more thought !
Clearly different understandings of terminology have already led to misunderstandings.
(I am not trying to lecture other readers who are already learned and well experienced, but I am here trying to illustrate why first cycle waveform examination has value because of the composite nature of a suddenly starting first sinewave cycle, that is missing with steady sine, and should not overcome an amplifier's slew rate, as with square wave. Ditto via reverse suddenly starting sine injection into the output terminal to observe amplifier NFB loop control in time.)
Hi MikeB,
But I see that you are already hurting yourself ?
What a stuggle it is for you to try to communicate your terms of 'linear distortion' and 'unlinear distortion'. I now know what you are trying to explain, but you are having very real trouble trying to say it !
Hi Carlos,
A well aimed bucket of water to each protagonist !
Cheers mate !
Now that I have looked through this 1980's 600 page reference dictionary I see it might be worth *copying* a couple of the 'distortion' definitions. I had not realised they were here, though I am bound to have read them years ago.
'Nonlinear' distortion is produced in a system when the instantaneous transmission properties depend on the magnitude of the input. Amplitude, harmonic, and intermodulation distortions are all results of nonlinear distortion.
'Amplitude' distortion occurs when the ratio of the root-mean-square value of the output to the r.m.s. value of the input varies with the amplitude of the input, both waveforms being sinusoidal. If harmonics are present in the output waveform only the fundamental frequency is considered.
'Harmonic' distortion is due to harmonics not present in the original.
'Intermodulation' distortion results from spurious combination-frequency components in the output of a non-linear transmission system when two or more sinusoidal voltages, applied simultaneously, form the input. Intermodulation distortion of a complex waveform arises from intermodulation within the waveform.
'Phase' distortion occurs where the phase change introduced is not a linear function of frequency.
'Delay' distortion is a change in the waveform because of the variation of the delay with frequency.
___________________________________________
I've lost the thread, and see there is new argument, but I will go back in case I owe any answers.
Your last comment rings true David.
Cheers ......... Graham.
Hi, Moderators,
Here is full with quality brains (John Curl, Charles Hansen, Graham Maynard, AndyC, JCX, Rodolfo, PMA, AKSA, Steven, PRR, SwedishChef, Jorge, MikeB, Mauro, JockoHomo, ElsoKwok, Janneman, Nelson Pass, SonnyA, Lars Clausen, etc...etc...[so many of them]). So many that can be learned from them.
Is there any way to make discussion still exist, but prevent anyone of them disappearing due to too much heated discussions? Texas section is growing rapidly nowdays. Bad wheather is happening in all parts of the world?
Here is full with quality brains (John Curl, Charles Hansen, Graham Maynard, AndyC, JCX, Rodolfo, PMA, AKSA, Steven, PRR, SwedishChef, Jorge, MikeB, Mauro, JockoHomo, ElsoKwok, Janneman, Nelson Pass, SonnyA, Lars Clausen, etc...etc...[so many of them
]). So many that can be learned from them.Is there any way to make discussion still exist, but prevent anyone of them disappearing due to too much heated discussions? Texas section is growing rapidly nowdays. Bad wheather is happening in all parts of the world?
Hi Lumanauw,
I left diyAudio once before, and it was not because of necessary discussion, but due to 'minority attitude' and the intemperate manners that detract from the friendliness that might otherwise arise.
I have seen a need to pass on information that might not have otherwise been discussed, and I have gained by learning there is a different understanding that is not incorrect, but which does not lead to the same results and conclusions by as easy a route.
That need to discuss and present my views (with a quite understandable suggestion of stubborness in so doing) has been on a 'while I am able' basis.
I still feel that there is a need for further discussion, but it is now more important that I get away from the unresolved and personally directed friction, for my long term ill health is catching up with me, and the effort necessary to battle against such unnecessary adversity has been quite exhausted.
I will follow Carlos' friendly and humourous threads, but that is all.
Au revoir ............. Graham.
I left diyAudio once before, and it was not because of necessary discussion, but due to 'minority attitude' and the intemperate manners that detract from the friendliness that might otherwise arise.
I have seen a need to pass on information that might not have otherwise been discussed, and I have gained by learning there is a different understanding that is not incorrect, but which does not lead to the same results and conclusions by as easy a route.
That need to discuss and present my views (with a quite understandable suggestion of stubborness in so doing) has been on a 'while I am able' basis.
I still feel that there is a need for further discussion, but it is now more important that I get away from the unresolved and personally directed friction, for my long term ill health is catching up with me, and the effort necessary to battle against such unnecessary adversity has been quite exhausted.
I will follow Carlos' friendly and humourous threads, but that is all.
Au revoir ............. Graham.
MBK said:
Well, OK, you said, it doesn't correct the error. Now you say, it doesn't correct the error completely. To that last statement I can agree. And, that is fully taken care of in the formulas, it is not like something hidden has been missed all the time.
You take an amp with gain of 1000 and apply 40dB feedback. Errors are corrected to 99%. No magic, simple engineering math since 1932 or thereabouts. Just take 10 minutes with google to check for feedback principles.
Jan Didden
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