[Amps] Capacitance Amount Formula

[Dr. David Kirkby]

MorgusMagnificen at aol.com wrote:
> 
> Yes, I do think you are wrong. The concept of 'exact' is context sensitive,
> but not altogether meaningless. This is an issue which causes scientists to
> have a great problem communicating with the scientifically illiterate world.
> 
> For practical purposes, I would call an exact analysis/calculation  one whose
> errors can be specified. "Exact" means that the results which we state are
> less than the precribed error. If you insist that the error go right down to
> zero, then there is nothing in the world that can be specified that precisely
> (this is the uncertainty principle in action). Does that mean that we totally
> abandon the concept of exact? Let me give some familiar examples.
> 
> Suppose I go into a high-precision laboratory and measure the voltage across
> the terminals of a standard cell and report it as 1.376899 volts +/-.000001
> volt (this is doable.) Are you rejecting this as non-exact because I cannot
> get closer than 1uVolt?
> 
> The degree of error is the whole gist of exactness, and in practice, we refer
> to measurments, calculations, etc. as 'exact' if their error is very low. How
> low? That requires judgement and adherence to convention.
> 
> In the case which I stated (a power supply calculation) I was making a fairly
> specific statement which would be understood by most experienced design
> engineers. Namely, before the computer became a desktop tool for every single
> person on the planet, many conceptually simple problems were never solved
> exactly. The most important category of same is problems involving non-linear
> elements, which are not well described by standard physical laws and
> formulas. Pre-computer power supply design was based upon picewise-linear
> approximations to linear circuits, which means that even if the mathematics
> were done exactly, the results would still be approximate. But with a
> computer, you can easily solve the necessary circuit equations to any degree
> of precision, limited only by how many significant figures of precision you
> seek. In practice, we don't need 10 or 100 sig. figures to feel that the
> result is exact.
> 
> So in that respect, when I tell you that I have done an exact solution, what
> I am really saying (this is understood to those who do this kind of
> calculation) is I will calculate the results for you to any specified degree
> of precision. You CANNOT make that statement based on an old-style
> (non-numeric) calculation which invokes approximations in the basic circuit
> equations themselves (e.g. piecewise-linear models). That is the difference.
> 
> Eric vonValtier K8LV

First I would say Eric sent some comments on this subject to me
personally. As far as I could tell, they were NOT copied to the 'amps'
mailing list, hence I only replied to Eric. Therefore others may have
some difficulty in knowing what this is all about.

In essence, Eric said that he had written a program to give an EXACT
solution of this problem. The last paragraph I sent to Eric was: 

* I would add that any EXACT analysis is likely to be an approximation. 
* Do you consider the change of forward voltage drop with junction
* temperature for example ??? Of course it's insignificant, but it does
* mean your analysis is likely not to be exact. Correct me if I'm wrong. 

Clearly Eric feels I am wrong and wants to correct me.

I've not seen Eric's program, but if, like I expect, it is a spice-type
model, where components, such as diodes are modelled as non-linear
equations, then I would maintain the solution it NOT exact. To me at
least, any computer program that models the non-ideal behaviour of
electronic components is not EXACT.

Personally, I don't think one could ever obtain an answer to 100
significant places (as claimed) since there is no way anyone could
possibly know the characteristics of a components that closely. To me at
least, such methods are numerical approximations. I use numerical
approximations in a program of mine
http://atlc.sourceforge.net/
and I would never say the solutions are exact. I can't even say for sure
what the bounds of the errors are (I would like to), I can only say I
have run tests and state the errors found in those tests.
http://atlc.sourceforge.net/accuracy.html
For some problems, one can admittedly state bounds on the errors - I
can't on my program.

If I write a cheque for $101.34, then it is exactly $101.34, but a
numerical approximation of a power supply can never be exact - in my
opinion anyway. Eric feels differently. 

Not only do I think an exact solution is impossible, but neither do I
think it's possible to get a solution to an arbitrary degree of
precision in this case. I would not like to put a figure on how accurate
such an approximation could be, but I doubt a solution could be found to
say better than 4 significant digits, simply because there is no model
that is better than that. Variability between components is likely to be
more than that. 

I would add:

I don't have the interest in pursing the capacitance problem myself. As
far as I'm aware, this has been done many years ago and I don't
personally at this moment in time wish to spend time on the issue.
Anyone seeking an analytical solution should first check the past issues
of journals, as I know this has been done before. I believe the author's
name was something like Schade, but I doubt I have the spelling EXACTLY
right. 

I just made a passing comment that I thought Jeff's analysis was too
simple. If I recall correctly, using a 3-phase supply, the ripple is
about 4% or so with no capacitance at all. Hence I maintain you must
consider the circuit. At least Eric and I agree on that, even if we
don't agree on the definition of EXACT. 


PLEASE NOTE:

If this message was sent to a newsgroup or mailing list, please 
reply to there. Personal e-mail is always welcome, but unless 
I have received e-mail from you previously, you may be sent 
an automatically generated reply, requesting that you send the
message again, adding a password in the subject line. Sorry,
but this action has been taken to prevent unsolicited 
commercial emails (spam mail). 

Dr. David Kirkby PhD,
Senior Research Fellow,
Department of Medical Physics,
University College London,
11-20 Capper St, London, WC1E 6JA.
Tel: 020 7679 6408 Fax: 020 7679 6269
Internal telephone: ext 46408
e-mail davek at medphys.ucl.ac.uk  
Web page: http://www.medphys.ucl.ac.uk/~davek