[sdiy] Fixed filter bank questions

mskala at ansuz.sooke.bc.ca mskala at ansuz.sooke.bc.ca
Tue May 14 02:01:50 CEST 2019

On Mon, 13 May 2019, David G Dixon wrote:
> When I look at, say, those little blue or yellow film caps, it is simply
> inconceivable to me that they could be made 10% different from one another.
> If you've ever seen a continuous automated industrial process that cranks
> out millions of the same thing, the key feature is repeatability.  In order
> for every part of the process to work, and for every piece of the assembly
> to fit together, every part has to be identical from one piece to the next.
> That is a recipe for 1% tolerance, not 10% or 20%.

Well, maybe.  I was mostly responding to the suggestion that things should
be different "in 2019."  It doesn't look to me like much has changed in
capacitor manufacturing recently, that would justify the expectation of
better results now compared to the past.  If it was 10% in 1959, there's
not much reason to expect it to be much better than 10% in 2019 - although
as I said, I think there *has* actually been some considerable improvement
and it's just less visible because we usually see lower prices for the
same tolerance rather than a better tolerance.

So why was it 10% in 1959?

I think part of the answer may be that capacitance is a higher-order
effect.  Consider the plate capacitor formula C = k e_0 A / d where C is
capacitance, k is permittivity of the dielectric, e_0 is permittivity of
vacuum, A is area, and d is separation.  The value of e_0 is a natural
constant but everything else is subject to manufacturing tolerances.  If
you can achieve 1% on the dielectric and 1% on every length, then you've
got 2% on A because it's the product of two lengths, another 1% on d, and
4% on the capacitance.  I don't know how realistic those made-up numbers
are; my point is only that because it's the consequence of multiple
dimensions that all need to be controlled, the tolerance on capacitance
ends up naturally looser than the tolerance we expect on mechanical

Matthew Skala
mskala at ansuz.sooke.bc.ca                 People before tribes.

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