No, a 1000 Hz and 1001 Hz sine wave added linearly might sound like and have an amplitude envelope at 1Hz but there is no 1Hz content at all. Your example could be HP brickwall filtered at some frequency like say 50Hz without affecting the envelope at all (assuming none of the instruments are <50Hz). I think you get the idea.
Yes Gerhard,
The amplitude variation is closer to a Dirac impulse and the amplitude change can be treated as the music frequencies being the carrier for AM modulation.
The basic issue is does high pass filtering of the music signal change the content in a perceptable manner. The issue of adding sidebands to the AM carrier is one that some research indicates is perceptable.
What other changes that are perceptual is an open issue.
The simplification that the high pass frequency of concern is 20 hertz has been addressed by many audio designers. Some have included in their design rules to set the high pass an order of magnitude lower others as mentioned express this as a voltage across the capacitor. (Lacking data on the signal magnitude comparison is difficult.)
I think the conclusion of avoiding even perfect capacitors in the signal path when practical is a reasonable design goal.
The bits about the limits of practical Fourier analysis of a finite signal cloud the issue of is there a clean mathematical model that illustrates artifacts that occur on a non periodic signal that is high passed which are perceived?
The amplitude variation is closer to a Dirac impulse and the amplitude change can be treated as the music frequencies being the carrier for AM modulation.
The basic issue is does high pass filtering of the music signal change the content in a perceptable manner. The issue of adding sidebands to the AM carrier is one that some research indicates is perceptable.
What other changes that are perceptual is an open issue.
The simplification that the high pass frequency of concern is 20 hertz has been addressed by many audio designers. Some have included in their design rules to set the high pass an order of magnitude lower others as mentioned express this as a voltage across the capacitor. (Lacking data on the signal magnitude comparison is difficult.)
I think the conclusion of avoiding even perfect capacitors in the signal path when practical is a reasonable design goal.
The bits about the limits of practical Fourier analysis of a finite signal cloud the issue of is there a clean mathematical model that illustrates artifacts that occur on a non periodic signal that is high passed which are perceived?
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I forgot that, most SOTA recordings get transformers, electrolytics, or both right at the beginning. I prefer FET's, high Meg resistors and readily available and cheap PS caps whenever possible.
Dick - You forgot to add phantom powered, lots of chaff there, only ones likes Wayne's flying supply version qualify. I don't think you will find many in commercial use.
EDIT - Make that any.
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The answer to the basic issue is that a linear high pass filter composed of linear components can't give a nonlinear output (can't have a nonlinear transfer function). That's the fundamental nature of linearity. We don't need Fourier transforms to know that.
It follows that if sidebands are being produced, it can only be due to nonlinearity of some type. Voltage coefficient for caps would qualify.
Now, undesired alteration of frequency response with a linear filter can produce linear distortion. That is, if you don't like the sound of a linear HP filter and you don't want it there, then for your purposes it is creating linear distortion. But, no sidebands can be produced in that case.
Edit: I should add that an RC ladder network composed of linear components is linear. It is a type of linear filter. That's why I said to the extent DA can be accurately modeled by a linear ladder network it is linear. If it produces sidebands the one or more components in the model must be nonlinear, thus the model must not be fully accurate.
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maybe. I don't know. haven't looked. But, if so, there is an area which could use some clever design. BTW -- the transformers' likeness to DA is hysteresis..... Some transformers have it. Lower is better. None is best.
See my references above (99603). New, better designs don't use either.
THx-RNMarsh
Uh, I think the reason that particular newer, better design hasn't caught on is because it doesn't sound better to anyone. You may notice it has a lot of op-amps in it, depending on how you feel about that. Don't know if that's why. But, sure, in principle getting rid of capacitors and transformers would be nice. The easiest way is simply not to use phantom power. Condenser mics have been made that have dedicated power wires in the cable, but even then most of them are single polarity supply and use caps to get back to ground referenced output. Unfortunately, there is no wiring standard for such cables, so each mic and a special cable and a remote power supply. Apparently, they aren't worth the trouble to most people.
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If you have a DC source charging a capacitor through a resistor the voltage across the resistor is an exponent.
So at what frequency does the voltage become linear?
It is linear in the sense of being time-invariant, and there is a Laplace transform for it. It is time invariant because the exponential curve is solely a function of time (time is the only variable), R and C are constants. If R and/or C aren't constants, then we get a nonlinear differential equation.
And when you pass a triangle waveform through the capacitor into the resistor you do not get the same shape out. It is not just the phase shift but the fundamental frequency is reduced.
What is the difference between a sum of sines where the fundamental is reduced and one where the harmonics are increased?
What is the difference between a sum of sines where the fundamental is reduced and one where the harmonics are increased?
Changing the amplitude of a fundamental or existing harmonics can be done with linear filters, voltage dividers, linear amplifiers, etc. It is the creation of new harmonics or other frequencies that didn't exist before that requires nonlinearity.
where do you get that idea? 😕
Using minimum number of coupling capacitors and when needed, use low value, low DA film types.
-RNM
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I don't see them being sold commercially, there are some DIYer's using them. I tried googling to see if there were any serious reviews, ideally with some measurements included. Didn't find anything. Maybe it's only a matter of time, if so we'll have to wait and see.
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https://web.eecs.umich.edu/~fessler/course/316/rc1.pdf
I'm still not sure what you're trying to drive at. This is the frequency response of an RC circuit (nothing fancy, just the clearest link I could quickly find), and then you need to multiply it by sinc^2(f) function (fourier transform of a triangle wave) in frequency domain.
For a short interlude during the all-important issues of capacitors:
Most of us know Henrik Bode's 1945 book on feedback systems. But in 1940 Bode published a monpograph Relations between Attenuation and Phase in Feedback Amplifier Design which was included in the Bell Systems Technical Journal in that year. Although this field was relatively new, he very precisely delineates what can and what cannot be done with feedback, and how to do it. The insight that you need an open loop bandwidth that is as much larger than the closed loop bandwidth by the amount of feedback used is something you see rarely mentioned these days, yet is a very useful insight for a designer.
I suggest you read at least the 1st page to appreciate the humor of this technological giant.
Jan
Most of us know Henrik Bode's 1945 book on feedback systems. But in 1940 Bode published a monpograph Relations between Attenuation and Phase in Feedback Amplifier Design which was included in the Bell Systems Technical Journal in that year. Although this field was relatively new, he very precisely delineates what can and what cannot be done with feedback, and how to do it. The insight that you need an open loop bandwidth that is as much larger than the closed loop bandwidth by the amount of feedback used is something you see rarely mentioned these days, yet is a very useful insight for a designer.
I suggest you read at least the 1st page to appreciate the humor of this technological giant.
Jan
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Looking at those Google searches I can't immediately see anything other than Wayne's designs that are trying to break the stranglehold of phantom power on the microphone space. Likewise not sure H&H have had hundreds of studios build their ultralownoise ribbon preamp.
That there are multiple reasons why the changes in the audio signal caused by capacitor coupling change the perceived sound.
Obvious to most is that if you reduce the fundamental but not the harmonics you change the measured and perceived sound.
The second issue is what does linear mean. Manfred Schroeder did a series of experiments where he generated waveforms that contained the same harmonics with different amounts of phase shift but maintaining the same peak amplitude. His conclusion was that 5 degrees at 20,000 hertz was perceptable.
Rupert Neve had two "identical" circuits that sounded different. Close examination showed one differed by the other by 5 degrees of phase shift at 20,000 hertz. Two folks arriving at the same conclusion quite independently. I have not been able to replicate Schroeders work at 20,000 hertz but require a bit more at lower frequencies.
What is clear is that when phase shift causes amplitude variations this is perceived at levels as low as 1 decibel of change! So what a mathematical definition calls linear, can still change our perceived sounds. Of course graphing a straight line versus an exponential curve is what most folks would consider to be non-linear.
The issue of how dielectric absorption affects this perception is not one of increased harmonic distortion, it can be one of wave shape modification or even some of the issues that change perception. The test for audio effects of DA was quite simply a wave shape distortion detector. The capacitors that did poorly clearly would have changed peak amplitude of some music signals.
The third issue is why many golden ear designers use the order of magnitude lower corner frequency. That can be from reduction of fundamental or AM modulation artifacts. So the next experiment is to modulated a complex harmonic structured signal and then use a simple RC high pass filter and look at the result for issues such as sidebands, wave shape changes, increases in the noise floor etc. Note that the question is how these issues change with real capacitors not theoretically perfect ones.
In the mean time use as few capacitors in your audio circuit designs as possible and use quality ones. Either desicate them or allow burn it time.
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I did the measurements, we are not talking 5 degrees but 0.05 degrees or less not 1dB but .1dB or less. This all will go back to the "dramatic" audibility of ppm level phenomena. BTW a priory why would burn in favor improvement over degradation of any given parameter? For instance Ib and Vos in IC's is stabilized some get better some get worse.
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Ed, I agree with most of what you say.
However, linear and nonlinear in engineering refer to types of differential equations, the applicability of linear models, linear systems analysis, etc. Most of the powerful and useful engineering math applies to linear systems, which are those that can be modeled by linear differential equations. Most physical things in the real world are not actually perfectly linear in the the mathematical sense, but linear math is the math we have and so we use it knowing that it is an approximation of reality. However, most of the time the approximation is pretty darn close, at least expressed in terms of a percentage error.
Also, I don't know why you find it okay that a sine wave can be considered linear but not an exponential function. Both are possible solutions to linear differential equations, as are sine waves with exponential envelopes, either decaying or growing envelopes.
In addition, people can hear and find objectionable both linear and nonlinear distortion, although not everybody hears everything the same way. Earl Geddes says linear distortion in loudspeakers is much bigger problem than nonlinear distortion.
One important factor in the conversation and argument that has been going on is that it is crucial that we all speak the same language. Otherwise we just end up talking past each other and accusing each other of being wrong. Regarding the definition of linear used in engineering, it's already baked into decades or centuries of literature and we are stuck with it.
However, linear and nonlinear in engineering refer to types of differential equations, the applicability of linear models, linear systems analysis, etc. Most of the powerful and useful engineering math applies to linear systems, which are those that can be modeled by linear differential equations. Most physical things in the real world are not actually perfectly linear in the the mathematical sense, but linear math is the math we have and so we use it knowing that it is an approximation of reality. However, most of the time the approximation is pretty darn close, at least expressed in terms of a percentage error.
Also, I don't know why you find it okay that a sine wave can be considered linear but not an exponential function. Both are possible solutions to linear differential equations, as are sine waves with exponential envelopes, either decaying or growing envelopes.
In addition, people can hear and find objectionable both linear and nonlinear distortion, although not everybody hears everything the same way. Earl Geddes says linear distortion in loudspeakers is much bigger problem than nonlinear distortion.
One important factor in the conversation and argument that has been going on is that it is crucial that we all speak the same language. Otherwise we just end up talking past each other and accusing each other of being wrong. Regarding the definition of linear used in engineering, it's already baked into decades or centuries of literature and we are stuck with it.
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