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Old Yesterday, 3:44 pm   #321
WaveyDipole
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

Root -1 on my vintage calc = E (error). On the modern one I get 'Math ERROR'. Seems my calculators do not like it either!

This also speaks for itself I think!
http://www.decoaudio.com/deco_audio_...on.html#Copper
Stumbled across it today while looking at valve amps.
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Old Yesterday, 3:53 pm   #322
GrimJosef
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

Are you familiar with the expression

exp(i*theta) = cos(theta) + i*sin(theta) ?

If so then you can see that if the exponent goes from real to imaginary - i*theta - then our exponential growth/decay becomes a periodic oscillation. More generally if the exponent is complex, which it is in the case of underdamping, we will get a combination of a periodic term and a pure exponential term - damped oscillation.

Getting to grips with functions of a complex variable can be hard work. But the payoff is that we don't have to handle three 'different' solutions. We can just write one general solution which covers the underdamped, critically damped and overdamped cases. Dropping the numbers for L, C and R into the equation for the exponent automatically generates the right answer.

There's a treatment here http://galileo.phys.virginia.edu/cla...s_Lectures.pdf although I confess even they start out by specialising to the overdamped case, which turns out to be an unnecessary specialisation, as they show when they go on to consider the other two cases.

Cheers,

GJ
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Old Yesterday, 4:17 pm   #323
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

I was reading a review of some 'high-end' (read very expensive but the companies lowest priced model) speakers and was surprised that the article spent most of the time talking about the various cables tried and how only the very best cable (read most expensive) was required to bring them to life.

Bearing in mind these speakers were floor standing with open baffle mid and treble, I am struggling to understand how the cables could ever be the most notable aspect of the setup. The source and amplifier got no mention at all.

This left me to the only reasonable conclusion, that the reviewer had absolutely no interest in the speakers and the article was merely a vehicle for getting payments against his marketing deal with cable manufacturers.
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Old Yesterday, 4:21 pm   #324
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

Well said GJ, that what comes from teaching simplified equations for specific cases where one variable tends to zero leading people to think that for each "case zero" there is a different equation and source for it (that is the important bit).

Charging a capacitor and swinging pendulum have the same equation, different bits are zero (or near enough for practical use) a charging cap. can 'boing' at the end (sine wave) as a pendulum will in the real world would reduce amplitude (exponential).

It is all about e's i's and pi's, all the same thing looked at from different directions.
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Last edited by merlinmaxwell; Yesterday at 4:22 pm. Reason: may have made more sense
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Old Yesterday, 4:23 pm   #325
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

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This left me to the only reasonable conclusion, that the reviewer had absolutely no interest in the speakers and the article was merely a vehicle for getting payments against his marketing deal with cable manufacturers.
One is surprised!
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Old Yesterday, 5:09 pm   #326
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

Unlike the trig identities above, there will be no proof of a financial linkage ;-)
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Old Yesterday, 5:15 pm   #327
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

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Unlike the trig identities above, there will be no proof of a financial linkage ;-)
“beyond reasonable doubt” M’lud?
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Index:
recursive loop: see recursive loop
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Old Yesterday, 5:18 pm   #328
GrimJosef
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

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Originally Posted by merlinmaxwell View Post
It is all about e's i's and pi's ...
A very long time ago I was the maths tutor for my college's undergraduate physicists at a well-known local university. They shared the maths part of the course with the engineers so I (used to) know how to wield a Laplace transform as well as being reasonably competent at matrix algebra and vector calculus. Like Argus I also own a copy of Kreyszig, although mine's the 3rd edition . which was current when I was doing this stuff !

Cheers,

GJ
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Old Yesterday, 7:22 pm   #329
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

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I sometimes get to feeling this way- but then think, much of it probably doesn't cause actionable harm and it's another thing that keeps disposable income, VAT etc. swilling around the economy. (Though there has been mains/primary side "foo" that has me muttering, "Please, no...." from time to time). After all, just about any leisure activity has after-market products associated with it that range from eminently practical good value to indulgent bling.

And who would want to be the civil servant or Government minister associated with "Control and limitation of products that bring comfort through faith"!
You say it causes no harm but have you tried to hang out in a hifi forum recently? It's no place for the sane, feet on the ground, long in the tooth, experienced, 'science-based' (old fashioned?) hifi enthusiast. You get bombarded by 'know-all' audiophools telling you that you need to buy this piece of kit, upgrade your cables, your amp doesn't match your speakers, your speakers are showing their age now, you need this vital accessory to get the most information out of your deck, etc etc ad infinitum. So yes, in my opinion, for those reasons audiophools do cause 'trouble'. They are tainting and polluting established, mainstream, audio technology and beliefs, I'm talking about the kind of stance that the BBC would take on audio technology; a million miles away from smoke, mirrors, snake oil and voodoo. And there's no going back, the audiophool and the companies making the stuff that he buys are here to stay, audiophoolery has become hifi mainstream. Like dry rot it is insidious and contagious.
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Old Yesterday, 7:40 pm   #330
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

Matrix maths, (well arithmetic, doing sums that is) easy to understand, easy to write down what you want and a complete b****er to calculate by hand. Praise the HP15C or indeed a computer.
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Old Yesterday, 8:00 pm   #331
G8HQP Dave
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

The discussion about how many different solutions there are to damped harmonic motion reminds me of a time I was supervising a maths class for engineers in one of our lesser universities. An engineering lecturer popped in for a while to assist. He asked the class to tell him the most general form of the sine function. In my mind I thought "sin Z" where Z could be a complex matrix, but at least "sin z" where z is any complex number/function etc. I kept quiet while the class pondered. Eventually he told them that the answer is "sin( wt + theta)". To me as a physicist that was one of the least general forms of a sine because it specifies periodic time-based motion. I learned that day that (some) engineers see maths from a very different viewpoint from physicists.

Solving damped harmonic motion eventually leads to solving a quadratic equation. The standard formula applies to every possible case and there are always two roots, although sometimes they can coincide. The two roots move along either the real or imaginary axis until they meet at the double root and then shoot off orthogonally again. I am surprised if Kreyszig is confused about this, but his book is aimed at engineers so maybe he had to go gently?
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Old Yesterday, 9:11 pm   #332
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

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Originally Posted by G8HQP Dave View Post
The two roots move along either the real or imaginary axis until they meet at the double root and then shoot off orthogonally again. I am surprised if Kreyszig is confused about this, but his book is aimed at engineers so maybe he had to go gently?
Kreyszig is not confused about this at all.

I was pointing out though that if you were using the equations for damped SHM or those that define the behavior of damped resonant circuits, that if you don't select the correct form of the equation by testing the damping conditions, the equation will not solve and produce a mathematical error.

You can't for example express angular frequency as a complex number and that value have any real meaning. At the point were its over damped and the solution using the case for an oscillatory system fails, the result is imaginary, and there is no such thing for example as an imaginary angular frequency, or an imaginary displacement an object along its real displacement axis. That is also obvious from the fact that as the equation starts to report that the value is imaginary, the angular frequency formula fails to work.

So to make this point even clearer, the idea that this represents a type of "discontinuity" in the way mathematics describes reality, lets go back to the simple resonant circuit of L, C and R in series, with a step applied voltage V to it placed across this network. There is no single (one equation) which will give the voltage across the capacitor, with time after the voltage is applied.

You have to select the correct one of the three possible solutions, or the equation will fail to solve for a meaningful value on your computer or calculator for the capacitor's voltage with time, even if your calculator is displaying the result as a complex number like merlinmaxwells calculator can.

If you have a single equation solution that doesn't suffer from this limitation and works with every value of L, C and R, I'd like to see it.

(one of the great things about an iterative Spice transient analysis for this situation you can vary the damping conditions across the boundaries of the three solutions and it doesn't snag the process)
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Old Yesterday, 9:29 pm   #333
Craig Sawyers
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

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Matrix maths, Praise the HP15C or indeed a computer.
I was so paranoid that my trusty old HP15C would give up the ghost that when the limited edition reissue came out with an ARM processor I squeezed my wallet and bought one. It goes like stink - an order of magnitude or more faster than the original. They kept the memory allocation, functions etc all the same though.
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Old Yesterday, 10:33 pm   #334
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

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Originally Posted by GrimJosef View Post

Getting to grips with functions of a complex variable can be hard work. But the payoff is that we don't have to handle three 'different' solutions. We can just write one general solution which covers the underdamped, critically damped and overdamped cases. Dropping the numbers for L, C and R into the equation for the exponent automatically generates the right answer.

although I confess even they start out by specialising to the overdamped case, which turns out to be an unnecessary specialisation, as they show when they go on to consider the other two cases.

Cheers,

GJ
HI,

I had a look at the paper.

You say there is a solution where you can drop in any values of L, C & R in the exponents and that there is a general solution for all values. (And therefore the damping values don't have to be checked first). This would be very handy for a project I have.

Can you then cite (attach on your next post) a single equation which will give the value with time of the voltage across the capacitor Vc(t) (initial value zero if you like) for the series R,C,L resonant circuit, after a fixed step voltage V is applied across the circuit, where your equation will accept any values of R,C, & L without attempting for some combinations of R,C & L, to take the square root of a negative number and give a meaningless result and abort the process on most computers and calculators ?

Thanks,
Hugo.
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Old Yesterday, 10:38 pm   #335
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

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Originally Posted by Argus25 View Post
Kreyszig is not confused about this at all.

I was pointing out though that if you were using the equations for damped SHM or those that define the behavior of damped resonant circuits, that if you don't select the correct form of the equation by testing the damping conditions, the equation will not solve and produce a mathematical error.

You can't for example express angular frequency as a complex number and that value have any real meaning ...
Kreyszig is not confused. What he has done is to show three solutions, each of which is a different version of the general solution. All of Kreyszig's solutions are functions of real variables. If we are only familiar with functions of real variables then we'll need to select the correct one of these three solutions and use it.

But once we've learnt how to work with functions of complex variables then we find we only need the general solution and that works in all cases. You can express angular frequency as a complex number - G8HQP Dave implicitly did so with sin z in the post before yours (z is a complex number). I'm not surprised you haven't come across this way of doing things. Many people haven't. But that doesn't mean that functions of complex variables are somehow impossible or erroneous.

EDIT - Sorry, we were writing at the same time so I didn't see your request until I'd finished this post. I'll start a new post to avoid being cut off by the edit time limit.

Cheers,

GJ
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Old Yesterday, 10:44 pm   #336
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

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I'm talking about the kind of stance that the BBC would take on audio technology; a million miles away from smoke, mirrors, snake oil and voodoo.
Even the BBC has put out some pretty silly stuff about audio technology in the past few years, both editorially in news programmes and in its stance over the alleged superiority of DAB. Agreed, time was when the Corporation was a beacon of good sense and a pioneer in real advances in technology, but its reputation in these areas has sadly diminished. Agreed, also, that the audiophool blogosphere has little to do with reality, or indeed with pleasure.
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Old Yesterday, 11:21 pm   #337
GrimJosef
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

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Can you then cite (attach on your next post) a single equation which will give the value with time of the voltage across the capacitor Vc(t) (initial value zero if you like) for the series R,C,L resonant circuit, after a fixed step voltage V is applied across the circuit, where your equation will accept any values of R,C, & L without attempting for some combinations of R,C & L, to take the square root of a negative number and give a meaningless result and abort the process on most computers and calculators ?
There is a general solution, but it doesn't satisfy the bold part of your request because it's not based on the premise that taking the square root of a negative number gives a 'meaningless' result.

I should take a step back. Just to be clear, I'm not saying that the three distinct versions of the general solution that are so commonly used are in any way wrong. The general solution contains terms of the form A*exp(z) where A and z are both (potentially) complex. Interpreting the 'real world' meaning of those terms requires a familiarity with complex variables which people who use them regularly have. Unfortunately I stopped using them regularly a little more than 30 years ago, so I'd need to spend some time re-familiarising myself with them before I could write down the general solution reliably. Even more unfortunately I don't have that time to spare these days.

What brought me into this discussion was the debate about whether the three representations of the answer were distinct or not. They're really not distinct other than in terms of their ease of use with respect to calculators. They're fundamentally the same thing. But if you're constrained to using a calculator that can't handle complex variables (I've never owned one that can) then I fear you can't avoid the need for something cleverer (a human) to intervene and work out which of the three representations the calculator will be able to work with.

Cheers,

GJ
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Old Yesterday, 11:42 pm   #338
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

The audio industry has a poor record when it comes to misleading marketing. Look at maximum power ratings, distortion and power measurements taken at 1kHz, and so on. Listening to test tones is not to everybody's taste and there is a need for a specification that reflects normal operating conditions (sounds like dieselgate?).

The reality is two systems with identical specification are not going to sound the same. Inter-modulation distortion in speakers must far outweigh any other distortion contributor but it gets no mention and the trend for smaller and longer excursion bass drivers must be making this worse.

Engineering and science has failed to provide meaningful standards for audio so it is perhaps unsurprising that consumers resort to blindly following the marketing twaddle.
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Old Today, 12:07 am   #339
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

I quite regularly express frequency as a complex variable in equations representing the transfer function of a network. The roots of the equation then can be analysed fairly easily and the patterns they make relate to recognisable solutions.

For example the roots of the equation defining a butterworth filter lie on a semicircle on an Argand diagram of frequency. A Chebyshev response distorts the circle into half an ellipse. A complete cauer looks like a Chebyshev with transmission zeroes outside the half-ellipse, along the real axis.

Can I make imaginary frequencies? Not really, but putting a mundane variable as a complex number turns complex solving into pattern geometry. It is the basis of loop stability analysis, filter design and some antenna design.

It would also blow the average audiophool's mind.

David
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Old Today, 12:24 am   #340
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Default Re: Audiophoolery. 'Cable Break In' - I never knew that!

Quote:
Originally Posted by GrimJosef View Post
But if you're constrained to using a calculator that can't handle complex variables (I've never owned one that can) then I fear you can't avoid the need for something cleverer (a human) to intervene and work out which of the three representations the calculator will be able to work with.

Cheers,

GJ
It is not so much being constrained by using a calculator (it could be merlinmaxwell's one that displays complex results) it is that the voltage with time, across the capacitor, is not imaginary, it is real for any & all values of R,C and L. Any imaginary result won't inform you of the actual voltage at time t.

The imaginary solutions which occur under certain combinations of L,C, & R, using just one of the equation solutions are no help in telling anyone what the actual capacitor voltage will be at some time. They merely inform you that you have used (selected) the incorrect version of the solution to solve the problem.

So, for example, if you use a computer program running the solutions, you have to check the damping first and apply the correct equation format, or alternatively you can run the R,C,L data through the three equations and after that pick the one with the real results.

That is why I would be very interested to see a single equation that didn't suffer from this for this application, but I don't think there is one, but like I say I'd love to see it if you can resolve it.

In nature of course you could have an object oscillating in the breeze, and the damping dynamically changing across the boundaries, to describe that, even though it seems simple is very tricky for this reason.
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