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Re: Primary and copper (fwd)
---------- Forwarded message ----------
Date: Mon, 30 Mar 1998 23:12:23 -0800
From: Bert Hickman <bert.hickman-at-aquila-dot-com>
To: Tesla List <tesla-at-pupman-dot-com>
Subject: Re: Primary and copper (fwd)
Tesla List wrote:
>
> ---------- Forwarded message ----------
> Date: Sun, 29 Mar 1998 14:07:53 -0800
> From: "Antonio C. M. de Queiroz" <acmq-at-compuland-dot-com.br>
> To: Tesla List <tesla-at-pupman-dot-com>
> Subject: Re: Primary and copper (fwd)
>
> Bert, Jim Lux, Malcolm, all:
>
> Thank you for the comments. I will see if I find or derive a better
> expression for rac.
> For awhile, what I am using is (MKS units, essentially the same as in the
> Ref. Data for Radio Eng.):
> sd=skin depth=sqrt(2*r/(w*u0))
> where w=2*pi*frequency; u0=permeability=pi*4e-7; r=resistivity=1.724e-8 (Cu).
> Assuming a tubular uniform layer with thickness=sd around the wire:
> Rac=length*r/(pi*(diameter-sd)*sd)
> This reduces to Rdc when sd=diameter/2.
>
> The problem is that this alone doesn't give correct results for long coils. I have
> a secondary coil, made with rather thin wire, where I get Rdc~=Rac=142 Ohms
> (Rdc measured, Rac calculated) at the resonance frequency. Measurements of
> the coil characteristics by several methods give a consistent result of
> Rac~=1000 Ohms at the resonance.
> I know that the formula is imprecise at this condition, and that the proximity
> of other wires in a closewound coil increases Rac by a good factor, that
> dielectric losses in the PVC form add some resistance too, and that there is some
> radiation resistance. But I don't know yet how to take these effect in account.
>
> Antonio Carlos M. de Queiroz
> http://www.coe.ufrj.br/~acmq
Antonio,
The best reference I've found, for solenoidal coils at least, is
Frederick Terman's out of print book "Radio Engineer's Handbook",
McGraw-Hill Book Company, 1943, 1019pp. Unlike most other references, he
deals with BOTH skin effect and proximity effects.
About 18 months ago I ran through a calculation (versus measured value)
for my 10" (31" winding, 21 AWG, 90 kHz) secondary, and found that the
impact of skin effect and proximity effect were about the same,
resulting in a total ratio of about 2.4:1 for Rac/Rdc. Terman's classic
goes into very great detail to estimate Rac/Rdc for various coil
geometries. Unfortunately, most of these use empirically-derived
nomagrams and charts combined with equations, and most are not in the
form of true closed-form equations.
For the more general case of skin effect for various geometries
including solenoids, G. A. Schneerson's book "Fields and Transients in
Superhigh Pulse Current Devices", Nova Science Publishers, 1997, 561pp
may be useful. It is, unfortunately, not a very readable book.
Hope this help!
-- Bert --