Einstein published peer reviewed papers. He will have been asked that exact question by the few peers who understood what he was describing (and 100 years ago it was very few).
Completely is relative, it enabled 20bit integratiing A/D's (ppm level linearity) ~40 yr. ago with this simple model.
Here is an historical overview and Cadences' models. Ken is a smart guy, this is more than you would ever want to know and the most complete DA modeling treatment I have seen. I could not find any non-linear elements here not that I read every word.
http://www.cktsim.org/Modeling/da.pdf
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Actually I liked the battle of dictionary definitions, it almost brings to light one of the issues here.
I did this before but the peanut gallery made so much noise I had to give up. They were really confusing folks and as technical issues are not determined by voting there was no point. Now that the same issues are back and the same noise is present I'll give it one more go.
The DEFINITION of distortion is a change in the signal. This should not be confused with harmonic distortion which is caused by non-linear system response.
The DEFINITION of capacitance is C=q/V. (C is capacitance, q is charge and V is Voltage. Upper case means static values lower case is dynamic values normally q is an exception.)
The DEFINITION of current is dq/dT (T is time.)
Therefore C x dv/dt + V x dc/dt = dq/dt = i (This is a simple derivative and as basic a calculus gets.)
Now if you are building a condenser microphone the V x dc/dt term means if you place a DC voltage on the diaphragm (one plate of a capacitor) and it moves that will change the capacitance and current will flow. Now in normal circuit component capacitors this term is very low for most capacitors. (Some ceramics excepted.) However as this is a theoretical analysis we will assume the capacitor is perfect and the dc/dt value is zero.
Now if we have a simple circuit when an AC voltage signal source feeds a resistor through a capacitor the voltage across the resistor is i x R. (Ohms Law) We will also use a theoretically perfect resistor.
So we have an output based on current with an input of voltage. It is when the signal passes through the capacitor that the current = C x dv/dt.
In simple terms the faster the voltage changes for a given time period the more current flows. The more current the higher the output voltage. This is why a capacitor feeding a resistor is a high pass filter.
Now when the input is a sine wave the first derivative of that is a cosine wave. That is why there is "phase shift" going through this filter. When the voltage across the capacitor is equal to the voltage across the resistor then the phase is split between sine and cosine equally or there is 45 degrees of phase shift.
Now if we run sine waves through a high pass filter we will notice level and phase changes. But if we run a single musical note there is a difference. A note will have a fundamental frequency and harmonics above that frequency. So the lower fundamental frequency will be reduced in level and the harmonics less so. THIS IS DISTORTION. It is a change in the signal and it is not harmonic distortion...
Now when you have dielectric absorption (DA) it is recognized that the capacitor retains a charge (q) from the prior application of voltage. We call this a result of DC voltage. But as this is theory we can state there actually is no such thing as DC, as we are not eternal. In other words a low frequency (Say .000001 hertz) signal has lost energy charging a capacitor. The worse the DA the more energy lost and the higher in frequency the effect will still be large enough to affect our desired complex musical note. All that would be observed on a sine wave is an attenuation at low frequencies. Again distortion!
Now the part that really gets the peanut gallery going is confusing Fourier theory with Fourier analysis.
Fourier theory states that any repetitive signal may be expressed as a sum of sine waves. Thus when we have a capacitor passing signal the dv/dt means that these sine waves are converted to cosines and we have phase shift but no harmonic distortion.
Music is not a repetitive signal! Now this is where the peanut gallery confuses analysis with theory. If the piece of music is 100 seconds long according to theory you could splice it into an infinite repeating peace and analyze that. In practice you need to really only start the analysis at time zero and end your sample capture at a time of 100 seconds. This will provide a Fourier spectrum of that piece of music. Therefore they conclude the music is a series of sine waves and will pass through a capacitor without distortion. What they ignore is the resultant analysis will show frequency components related to the inverse of the time component. As time is 100 seconds you require a frequency response without attenuation below 1/100 of a second (Actually half that.)
Now for an IEC standard load of 20,000 ohms what size capacitor is required to keep the fundamental loss below 3% at .005 hertz?
Now as has been stated many times when there is no voltage across the capacitor there is no distortion and the math shows that to be true.
I'll let the peanut gallery scream for a bit and then I will go on to why power supplies benefit from power line filters even thought Dick has already let the first cat out of the bag.
I did this before but the peanut gallery made so much noise I had to give up. They were really confusing folks and as technical issues are not determined by voting there was no point. Now that the same issues are back and the same noise is present I'll give it one more go.
The DEFINITION of distortion is a change in the signal. This should not be confused with harmonic distortion which is caused by non-linear system response.
The DEFINITION of capacitance is C=q/V. (C is capacitance, q is charge and V is Voltage. Upper case means static values lower case is dynamic values normally q is an exception.)
The DEFINITION of current is dq/dT (T is time.)
Therefore C x dv/dt + V x dc/dt = dq/dt = i (This is a simple derivative and as basic a calculus gets.)
Now if you are building a condenser microphone the V x dc/dt term means if you place a DC voltage on the diaphragm (one plate of a capacitor) and it moves that will change the capacitance and current will flow. Now in normal circuit component capacitors this term is very low for most capacitors. (Some ceramics excepted.) However as this is a theoretical analysis we will assume the capacitor is perfect and the dc/dt value is zero.
Now if we have a simple circuit when an AC voltage signal source feeds a resistor through a capacitor the voltage across the resistor is i x R. (Ohms Law) We will also use a theoretically perfect resistor.
So we have an output based on current with an input of voltage. It is when the signal passes through the capacitor that the current = C x dv/dt.
In simple terms the faster the voltage changes for a given time period the more current flows. The more current the higher the output voltage. This is why a capacitor feeding a resistor is a high pass filter.
Now when the input is a sine wave the first derivative of that is a cosine wave. That is why there is "phase shift" going through this filter. When the voltage across the capacitor is equal to the voltage across the resistor then the phase is split between sine and cosine equally or there is 45 degrees of phase shift.
Now if we run sine waves through a high pass filter we will notice level and phase changes. But if we run a single musical note there is a difference. A note will have a fundamental frequency and harmonics above that frequency. So the lower fundamental frequency will be reduced in level and the harmonics less so. THIS IS DISTORTION. It is a change in the signal and it is not harmonic distortion...
Now when you have dielectric absorption (DA) it is recognized that the capacitor retains a charge (q) from the prior application of voltage. We call this a result of DC voltage. But as this is theory we can state there actually is no such thing as DC, as we are not eternal. In other words a low frequency (Say .000001 hertz) signal has lost energy charging a capacitor. The worse the DA the more energy lost and the higher in frequency the effect will still be large enough to affect our desired complex musical note. All that would be observed on a sine wave is an attenuation at low frequencies. Again distortion!
Now the part that really gets the peanut gallery going is confusing Fourier theory with Fourier analysis.
Fourier theory states that any repetitive signal may be expressed as a sum of sine waves. Thus when we have a capacitor passing signal the dv/dt means that these sine waves are converted to cosines and we have phase shift but no harmonic distortion.
Music is not a repetitive signal! Now this is where the peanut gallery confuses analysis with theory. If the piece of music is 100 seconds long according to theory you could splice it into an infinite repeating peace and analyze that. In practice you need to really only start the analysis at time zero and end your sample capture at a time of 100 seconds. This will provide a Fourier spectrum of that piece of music. Therefore they conclude the music is a series of sine waves and will pass through a capacitor without distortion. What they ignore is the resultant analysis will show frequency components related to the inverse of the time component. As time is 100 seconds you require a frequency response without attenuation below 1/100 of a second (Actually half that.)
Now for an IEC standard load of 20,000 ohms what size capacitor is required to keep the fundamental loss below 3% at .005 hertz?
Now as has been stated many times when there is no voltage across the capacitor there is no distortion and the math shows that to be true.
I'll let the peanut gallery scream for a bit and then I will go on to why power supplies benefit from power line filters even thought Dick has already let the first cat out of the bag.
So the question remains: what is the nonlinear element and how did Dick determine that it was a result of DA?
YOUR definition. Read Ken Kundert's paper, it's really good. It might be useful to consider the RIAA network. I guess by this reasoning it undoes the "pre-distortion" applied at the recording end. Now use the DA model and see how much the accuracy is compromised, you might be surprised at how little.
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Scott,
You are being plain silly. Anyone can find something on the internet to support just about any conclusion. Do you really not know the meaning of the word?
"If F is a linear function, for instance a filter whose gain and/or delay varies with frequency, the signal suffers linear distortion. Linear distortion does not introduce new frequency components to a signal but does alter the balance of existing ones."
So far P.G. 2
Oh yeah. I came across that piece several years ago while in a similar discussion about DA somewhere (might have been here). It's the most complete model I've ever seen.
se
I said look at the model and quantify the "linear distortion" from the addition of the DA. I don't find this linear distortion concept particularly useful.
As to this comment, " Anyone can find something on the internet to support just about any conclusion." Think the guy standing in line in that scene in Annie Hall.
https://www.youtube.com/watch?v=sXJ8tKRlW3E
Ed you have a unique and personal way of looking at things. You could also notch out the fundamental and have huge THD. BTW the cap ladder model for DA works fine at DC (yes I know there is "no" DC
) and AC there is no need to bring in the "time from the creation of the universe". You will find that the DA in most cases contributes small fractions of a dB frequency response anomalies, after all we needed a G100-G1000 amplification to see anything.
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I believe there is a problem with the moon, or the arrival of the spring-time.
I don't know what, but it is strong.
PMA I think the point is, is measuring DA by the simple soakage test correlate at all to dielectric caused distortions. BTW I'm perfectly happy to know from Samuel G's data that cheap film caps that measure <130db THD are available. NPO ceramics might be a good test do they have DA but very little THD.
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