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# Re: topload questions

Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz <teslalist-at-qwest-dot-net>" <acmq-at-compuland-dot-com.br>

Tesla list wrote:
>
> Original poster: "Godfrey Loudner by way of Terry Fritz
<teslalist-at-qwest-dot-net>" <ggreen-at-gwtc-dot-net>
>
> Hello Antonio
>
> I am getting the following:
>
> 16" x 7"------------19.2035 pF
> 16" x 1"------------13.9494 pF
> 16" x 0.1"----------9.87011 pF
> 16" x 0.01---------7.50278  pF
> 16" x 0.001"-------6.03675  pF
>
> Let x = (D - d)/d. If x is large, then a good approximation to C is given
> below.
>
> C = 35.4 d (x^2 - 1)^(1/2) Q[-1/2, x]/P[-1/2, x], where C is in pF, D and d
> in inches.
>
> Q and P are the Legendre functions, commonly used in EE.

This formula looks better, but still appears to give zero as d -> 0.
The term (x^2-1)^(1/2) could be x without difference if x is large.
I know the Legendre polynomials Pn(x), that I have seen in some rare
cases of filter design, and also the functions Qn(x), that also
satisfy Legendre's equation. If the functions that you mention
are these, what means the -1/2 in the formulas?

Antonio Carlos M. de Queiroz