Most of us could not expect of how limited the range of applicability of mathematical grounds, given in textbooks in electronics, are.
The Shannon's theoreme of 1949 (russian analog of this theoreme from 1933, by Kotel'nikov) is valid for strictly periodic functions, with limited frequency spectrum. Mr. Kotelnikov is still alive, he is more than 90 years old. They are not applicable for arbitrary musical signals.
Not many of us are awared of Ageev's theoreme (1957) saying the following:
arbitrary function, with LIMITED frequency spectrum, can have some time intervals, within which the function demonstrates an arbitrarily HIGH slew rate
Unbelievable? Yes, but serious mathematicians double and triple checked this theoreme.
Another matematician, Fink, has proven this theoreme in an independent way, in the years 1970-s.
In other words, real musical signal, that has limited frequency spectrum, can nevertheless demonstrate time periods with deliberately high slew rates.
Using of more valid mathematical approaches are not popular, since they produce a shadow over CD and other digital formats.
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Is a real music signal an arbitrary function? I doubt it. Also, a real music signal will always be voltage limited too. I doubt if a voltage-limited spectrum-limited signal can have arbitrarily high slew rate. And over what time interval? I think this is a red herring.VladimirK said:
I don't think the sampling theorem (by Shannon et al) is only for periodic functions. The only restriction is band limiting (and, possibly, the existence of a Fourier transform) and infinite time. Infinite time is not possible in the real world, but we can get close enough for practical purposes.
From the memories of other scientists, when Mr. Ageev first reported his theoreme at the meeting of russian radiotechnical society in 1957, Mr. Kotel'nikov was a head of this society, and all members shouted and wanted put Mr. Ageev into a fire.
Professional engineers in electronics, they are usually not extremely professional in mathematical analysis. At present, Ageev's theoreme was checked many times by serious mathematicians.
Another question, what kind of signals do we have at the output of CD player, after DAC. One should check, whether Ageev's theoreme is applicable to such signals. Devil is always in the range of applicability.
Vladimir,
The slew rate capability of an amplifier is determined by how fast the internal capacitances in the amplifier can be charged/discharged. It is not under influence of feedback or not. If the amplifier has enough slew rate capability, that doesn't change with or without feedback.
Anyway, these days it is really trivial to make a fast slew rate amp, feedback or not; this is no great deal.
jan didden
you forgot to throw in Chaos theory too...
the mathematics of EE textbooks, Signal theory do "take shortcuts" in the view of serious mathematicians
like assuming we are describing things that occur in the physical world, involving sufficiently "macroscopic" conditions that Classical Mechanics, Continuous representations are accurate enough for the subject of the discussion
musical signals propagating in air, at microphone, or listener's ears distances do not involve Mach Fronts, full Vacuum
the motion of membranes having mass, stiffness, like our eardrums, microphones are Locally Lipschiz
recorded musical performances are limited in time, the frequencies that propagate through the air, are captured by microphones, electronics are limited in amplitude and bandwidth
these real world conditions greatly constrain the required math - we can safely assume there is no need to check for "an arbitrarily HIGH slew rate" representing a musical signal from any recording medium
I actually find much of EE theory, practice match the real world to a degree that the rest of science and engineering can only be envious of - in fact almost all of the other fields rely on electronic instrumentation, ADC, DSP to collect, process their data
the mathematics of EE textbooks, Signal theory do "take shortcuts" in the view of serious mathematicians
like assuming we are describing things that occur in the physical world, involving sufficiently "macroscopic" conditions that Classical Mechanics, Continuous representations are accurate enough for the subject of the discussion
musical signals propagating in air, at microphone, or listener's ears distances do not involve Mach Fronts, full Vacuum
the motion of membranes having mass, stiffness, like our eardrums, microphones are Locally Lipschiz
recorded musical performances are limited in time, the frequencies that propagate through the air, are captured by microphones, electronics are limited in amplitude and bandwidth
these real world conditions greatly constrain the required math - we can safely assume there is no need to check for "an arbitrarily HIGH slew rate" representing a musical signal from any recording medium
I actually find much of EE theory, practice match the real world to a degree that the rest of science and engineering can only be envious of - in fact almost all of the other fields rely on electronic instrumentation, ADC, DSP to collect, process their data
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True, but at least this amateur electronics engineer once had a background in theoretical physics so I am aware of both the power and limitations of mathematical theorems. I can cope with counter-intuitive results. I am not questioning the theory, but expressing doubt about its relevance to real audio signals.VladimirK said:
This is voltage-limited, then band-limited (except in a simple filterless NOS DAC). One could perhaps regard the bare DAC output as having infinite slew rate (although not in reality) but as it is voltage-limited any low-pass filtering (whether deliberate or accidental) will ensure that there is an upper slew-rate limit. Someone putting a simple unfiltered NOS DAC output straight into an opamp audio input might experience IM problems, but may then misattribute them to improved "air".
Hi Tom,
Fully agree with your reasoning. I put a few numbers to it:
The induced voltage from a step current on the supply wiring V = L* Di/Dt.
Take a 10A current change in 50uS. Somewhat loosely related to a full power 20kHz signal, which is very rare, but what the heck.
For a wiring inductance of 10uH, an inch of wire or track to the nearest cap, that's 20mV induced ripple. Not a whole lot I would say.
But it does support your call for good local decoupling. Even the best no-holds-barred super-duper-fast supply is a waste of money if you take 10 inches of wire to connect it to the output stage!
jan didden
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Many limitations and model-based approaches are undoubtedly justified. But, sometimes, we break out heads, why that amp sounds better? According to official grounds in electronics it is not possible, hence, what we listen, is a bull-..., important is what scope see.
I wanted simply to remember, all academic knowledges, including in electronics, are limited and present a kind of religion.
A person can not check validity, be aware of applicability, of all knowledge in relevant textbooks, most frequently one simply believes in books content, a sort of religion, or propaganda ...
I wanted simply to remember, all academic knowledges, including in electronics, are limited and present a kind of religion.
A person can not check validity, be aware of applicability, of all knowledge in relevant textbooks, most frequently one simply believes in books content, a sort of religion, or propaganda ...
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I think it is not always possible to relate what people like in an amp to how it measures. For instance, some sort of IM distortion often gives an impression of more 'air' around instruments. So a designer can say: I measure a lot of IMD, but the listener can say: I like this amp.
It all depends a lot on your goals in designing an amp. Do you want to design an amp that is most transparent, does not take anything away, does not add anything? If that is the case, you can get a long way with just measuring.
Would such an amp sound good? I believe it would, but some people used to other amps might call it 'clinical' or 'clean'.
Could someone come up with an amp that people like more, but measures worse? Yes, definitely.
jan didden
OK, I accept that; I just had 10uH in my head (figuratively speaking...).
So, it that local bypassing just folklore? I do it all the time, but maybe more out of routine.
jan
This is a sweeping generalisation, and rarely true. It is sometimes claimed by people who eitherVladimirK said:
a) disagree with what the textbooks say, or
b) don't understand what the textbooks say.
Problems can occur in areas where the scientific consensus impinges on people's political, philosophiocal or religious beliefs but electronics is not one of those areas. Therefore there is no reason to doubt the texbooks, except where they present approximations as the whole truth. A good textbook will show you enough of the derivation of important results (or refer you to the literature) so that you can see any wrong assumptions or unwarranted short cuts.
Speaking about audio reproduction, nobody disagrees with classics in electronics, in what most general terms are concerned, output power, THD, etc.
We usually discuss tiny details, that are not easily explained, and hidden in small details.
I simply put attention, that tiny detailes - are not the subject of classical electronics.
10 inches of wire, or even kind of isolation plastic - and sound can be lost.
If one do not look forward and refuses thinking about tiny details - then what to improve?
Just buy 0,001% THD Hi-Fi amp, and be shure that it is the best, from widely recognized grounds in electronics.
I have read somewhere, that the Head of MBL company, was pressing his engineers many years, until they produced a SOUNDING device, and he refused all their justifications, that some device already measures more than perfectly. Noway, the target - it must sound good. And this target is solved more by intuition and non-traditional thinking.
We usually discuss tiny details, that are not easily explained, and hidden in small details.
I simply put attention, that tiny detailes - are not the subject of classical electronics.
10 inches of wire, or even kind of isolation plastic - and sound can be lost.
If one do not look forward and refuses thinking about tiny details - then what to improve?
Just buy 0,001% THD Hi-Fi amp, and be shure that it is the best, from widely recognized grounds in electronics.
I have read somewhere, that the Head of MBL company, was pressing his engineers many years, until they produced a SOUNDING device, and he refused all their justifications, that some device already measures more than perfectly. Noway, the target - it must sound good. And this target is solved more by intuition and non-traditional thinking.
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The problem with that is that there is no accepted standard for 'sound good'. It is very personal, changes over time and with circumstances and if you ask three listeners you get four different opinions.
jan didden
Hi davygrvy,
Thanks for your kind words about my book.
Your example of TIM is a good one. Matti Otala coined the term, blamed it on high negative feedback and low open-loop bandwidth, and came up with an objective way to measure TIM.
Indeed, thanks to Matti, TIM is very measurable, so there need be no mystery about it or subjective arguing. But guess what? Measurements of TIM generated by real power amplifiers with different amounts of NFB and/or open loop bandwidth showed that NFB and low open loop bandwidth did not exacerbate TIM.
For example, the MOSFET amplifier with error correction that I wrote up in the JAES in 1983 had very high NFB at low frequencies and very low open-loop bandwidth, yet it had virtually unmeasurable TIM. Why? Because it had very high linear slew rate and very low high-frequency distortion. Those matter the most.
The same is true for modern audio op amps like the LM4562 - lots of open-loop gain, low open-loop bandwidth, and virtually unmeasurable TIM.
BTW, here's another dirty little secret. Do a TIM measurement on a no-feedback amplifier or a vacuum tube amplifier. You'll see TIM.
While we cannot or do not measure everything, good measurements often can confirm or disprove some audio lore. TIM and NFB is one of them.
Cheers,
Bob
Vladimir,
I don't see why Mr. Ageev met with so much resistance, since it is just an other angle of looking at a Fourier series approximation of a square wave. High rise times can be generated with heavily truncated series of sinoids.
It cannot be excluded that in random signals such as music, at a given moment so many sinoid signals get aligned at their zero crossings that they will generate very high rise times. It is a statistical excersise to quantify this into a specific probability, but it could conceivably happen. Intuitively, it makes me think of monkeys and typewriters.
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