Normally when I get responses like this I assume the problem is that English is not their native language and the error is in translation. The word "Linear" has multiple meanings and apparently you haven't even bothered to test the math for your comment.
But to make this clear If you take the first derivative of a square wave you get a Dirac Delta function. If you take the integral you get a triangle wave.
Now if you care to listen to these you will find they do not sound the same.
If you would like to look at the the Fourier representation they are quite different.
If you would like to describe the difference in harmonic components and the resultant distortion you would see that they are not "Linear!"
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I don't have the proceedings right now and I didn't mean to contradict anything there only point out that a simple passive circuit that has a second order non-linearity that can differentate between music and sine waves is extraordinary. I was involved in the bridge null test with John and Walt, it is very powerful, but when I wanted to discuss how to use it to extract the Pease ladder model for the cap no one was interested. After all they were making 5 1/2 - 6 1/2 digit integrating A/D's by some simple compensation techniques. I never found DA alone to do anymore than cause minor frequency response deviations and as usual one had to insert truely horrible examples to get large results. Is high DA an indicator of high voltage coefficient, I don't know?
I have not changed my mind on the matter at all. This work was very useful but most of the time it pointed out the awful components or bad things that folks knew to avoid in the first place. As a justification for substituting a good $2 film cap with an $80 hand made teflon one I don't agree (and never have).
BTW I disliked that DSP conference because David Rich expected an onslaught of objectivism aimed at debunking the audiophile "myths". I didn't cooperate, if you remember I even said good things about SET amps which incited a member of the audience to think I spoke against feedback. David Rich never spoke to me again. You also might remember when I pointed out the conventional I/V had rising output impedance that was an open door for RFI the feathers also flew. Don't knock the 5532.
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They don't sound the same because they represent very different frequency responses, but a triangle, square and Dirac delta have exactly the same frequency components and can (in an ideal world) be transformed back and forth with no loss or addition of information by purely linear circuits. No distortion needed! You have helped me make my point.
At frequencies several decades above its rolloff point a low pass filter is virtually indistinguishable from an integrator. If an integrator introduced distortion then all opamp and standard SS power amp circuits would be useless for audio. Integrators and differentiators really don't create distortion, but they do fiddle with frequency response in a major way. However, a coupling cap is chosen to alter frequency response either in a selected way or as little as possible so the 'differentiation' aspect of it is minimal. You really ought to think through what you are saying before confusing people with misunderstandings about calculus.
At frequencies several decades above its rolloff point a low pass filter is virtually indistinguishable from an integrator. If an integrator introduced distortion then all opamp and standard SS power amp circuits would be useless for audio. Integrators and differentiators really don't create distortion, but they do fiddle with frequency response in a major way. However, a coupling cap is chosen to alter frequency response either in a selected way or as little as possible so the 'differentiation' aspect of it is minimal. You really ought to think through what you are saying before confusing people with misunderstandings about calculus.
A square wave by one definition is a maximally distorted sine wave and integration or differentiation are simple first order filtering functions. BTW the derivative of a square wave is a train of +/- impulses the spectrum simply the square waves filtered by a first order zero, The tri-wave simply the square wave filtered by a first order pole. Integration and differentiation do not distort i.e. they do not create new harmonics.
In Fourier space the integral or derivative of a series sum of sines or cosines are just another sum of sines or cosines (at the same omegas).
(Sorry DF96 out outdrew me by seconds I guess)
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Scott,
I am aware that they are all a series of odd harmonics, however the amplitude of each of the harmonics changes. If you compare the original amplitude to the post process amplitudes of each harmonic, the difference is the definition of classic harmonic distortion as used in audio.
The process is reversible, but the issue was that when you pass a sine wave through a capacitor the current is a cosine wave. That is also called phase shift or a lagging response. The result looks and sounds the same.
When you pass a complex waveform, particularly one that is not periodic, the derivative is by the audio use of the word distorted. Even though the spectrum is the same the waveform is not. That may not not look or sound the same.
ES
Changing the shape of a waveform by using a filter does not correspond to the normal audio use of the term 'distorted', as no new frequency components are introduced. Comparing 'before' and 'after' harmonic amplitudes can be a useful way of detecting distortion provided that there is little or no filtering going on as well. Strictly speaking, you should also see how harmonic amplitudes vary with signal level: a filter will give fixed ratios of out/in, while distortion will give varying ratios. I think you may be confusing methods of measuring harmonic distortion with definitions of what HD actually is.
What if you want to avoid 'Fourier' (although I can't think why you would)? Then perhaps you could define distortion as some change in the waveform which cannot be brought about by any linear filter.
Filters do change the sound, which may be why they are used, but 'change' and 'distortion' are not synonyms.
What if you want to avoid 'Fourier' (although I can't think why you would)? Then perhaps you could define distortion as some change in the waveform which cannot be brought about by any linear filter.
Filters do change the sound, which may be why they are used, but 'change' and 'distortion' are not synonyms.
Sorry ED we don't just disagree this time, you're wrong
. By that definition any filter has distortion and an RIAA is nothing but distortion except at exactly 1kHz.This is definately not any definition of harmonic distortion, there are NO NEW HARMONICS.
Sorry ED we don't just disagree this time, you're wrong
This is definately not any definition of harmonic distortion, there are NO NEW HARMONICS.
Scott,
The issue is slipping into the side argument.
The issue is that any capacitor is driven by a source resistance and into a load resistance and why that places limits on the circuit performance.
As any source resistance produces a finite current the charging and discharging of the capacitor is exponential not linear. Now when the amplitudes of the harmonics are varied so will the charging current available for those harmonics. That deviation is what I started with. It is not an issue with a single sine wave. Yes I know it is a very small side effect.
Now some designers use capacitors of at least ten times the value required to pass the designed low frequency cut-off citing improvements from this. Others have used high impedance loads. Both approaches reduce the issue.
The reason why I am looking at the issue is that of a musical note's ADSR (Attack, Decay, Sustain, and Release) provides a high level (or full scale for practical purposes) sharp initial envelope that is of very low frequency and is not continuous. It is the modulation between that and the "tone" (or carrier frequency) that creates artifacts that are not as low in level.
No. A filter can't create anything. This is the basic fact you seem to miss. A CR circuit, even with DA, is just a filter. It might be a more complicated filter than an ideal CR, but it is still a filter. Dielectric or resistor nonlinearity is a separate issue. No matter how unlike the output waveform is from the input or how much it sounds different, there is no distortion. If it sounds too different then it merely means that the frequency rolloff is in the wrong place.simon7000 said:
The charging of a cap from a square wave had better be exponential, not linear, otherwise it will introduce distortion through slew-rate-limiting. There is no "modulation" between a transient and a tone, as filters are linear.
Yes, the issue is that the best AC voltage across a cap is no AC voltage. But the true distortion at the -3dB point is due to dielectric properties other than just DA even though they might be related. As for -120dB artifacts being audible please read Dick Burwen's editorial in Linear Audio. Finishing half your beer is more audible in more ways than one.
EDIT - Probably more audible if it was a glass of beer.
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If the output is not the same as the input in some fashion, what adjective do we use?
An exxample:
Badly built speakers produce refractive components that sound bad above, say, 80 - 85 dB and sound progressively worse as SPL's increase. On the speaker side it's a linear phenomenon; on the hearing side it's non-linear.
There was a bust up on a speaker thread when a participant (an extremely well qualified engineer/physicist) referred to this as 'linear distortion'. No such thing said another engineer and in so many words accused the first of being incompetent. So what do I call it? said the first guy, there are components in the sound that weren't in the original signal. Yada yada.....
An exxample:
Badly built speakers produce refractive components that sound bad above, say, 80 - 85 dB and sound progressively worse as SPL's increase. On the speaker side it's a linear phenomenon; on the hearing side it's non-linear.
There was a bust up on a speaker thread when a participant (an extremely well qualified engineer/physicist) referred to this as 'linear distortion'. No such thing said another engineer and in so many words accused the first of being incompetent. So what do I call it? said the first guy, there are components in the sound that weren't in the original signal. Yada yada.....
Yes, the issue is that the best AC voltage across a cap is no AC voltage. But the true distortion at the -3dB point is due to dielectric properties other than just DA even though they might be related. As for -120dB artifacts being audible please read Dick Burwen's editorial in Linear Audio. Finishing half your beer is more audible in more ways than one.
EDIT - Probably more audible if it was a glass of beer.
Scott,
Using common professional values of 10 microfarads and 600 ohms for a source/load impedance, then the attack wavefront from a drum strike would approach 20% distortion!
You are welcome to try your own measurements or simulations, I would quite legitimately like to see others try it.
ES
ED, I'm sure when we get down to it, it's semantics. Rearranging the phase and amplitude of the frequency components could "dull" a transient 20%, no problem. This is not distortion.
26Hz really? Even Peavy specs -.5dB @ 10Hz which is well below 5Hz corner.
10 microfarads at 600 ohm source and load is 13 Hz. That actually happens in pro gear, but that is just a typical value. If you go lower the distortion does drop. We I think can agree on those issues.
But let me ask the question:
If you pass the same compound signal (ADSR x Carrier) through two different high pass RC filters R & C vs R & 100C and compare the waveforms is there a difference in the first cycle of the carrier? (You can use a carrier frequency of 3,000 Hz and an attack of 10db/msec. for 60 db.)
That to me is the issue.
Interesting point in and by itself. I wouldn't call this distortion however, since refraction leads to local dips and peaks in the FR at different angles from the loudspeaker.
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Thanks, you answered my question about the NPO/COG capacitors.
By the way, what choices are left ?
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Yes.
A reference I've found very helpful: Blinchikoff and Zverev, Filtering in the Time and Frequency Domains. It was out of print for a long time, then reissued; not sure what the status is now.
If it were to be revised, today we'd likely have a CD ROM or a website with lots more examples, maybe some animations and even acoustical examples.
Brad
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