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Skin effect


----------
From:  Bill the arcstarter [SMTP:arcstarter-at-hotmail-dot-com]
Sent:  Thursday, April 02, 1998 3:47 PM
To:  jimlux-at-earthlink-dot-net; tesla-at-pupman-dot-com
Subject:  Re: Skin effect

It was written:

>> 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.

Who wrote this? I missed the start of this thread...  Sounds like fun!

I do know that, for a series lumped RLC - where you are viewing the 
impedence across the terminals of the lumped cap - it can be shown that, 
at resonance (note 1), the net system impedence is equal to Z0 = L/RC, 
where R,L,C are the lumped values, and Z0 is the system impedence across 
the cap.

I'm curious if perhaps the measurement of Rac is being confused with the 
measurement of Z0 = L/RC.  This resonant circuit will transform the 
actual "lumped" ac resistance by the L/((Rac)C) operation.

(NOTE 1) Notice that, for the above discussion, "resonance" is defined 
as the frequency at which the net impedence is purely resistive.  This 
is NOT the same as the frequency which yields the peak voltage (although 
it is close).  This frequency, expressed in rad/sec is W0 = sqrt( 
(L-R^2*C)/(L^2*C) ).  Note that if R ==0 then this is equivalent to the 
classic W=sqrt(1/LC), etc.

I'm working on a derivation for W1 and Z1 such that output voltage is 
peaked, which is more to the needs of us coilers...  Anyone want to 
maximize a ratio of a 6th and a 4th order polynomials?!  Where's a 
freshmen when you need one??? :)

I can provide the derivations for all this, if needs be.  Comments 
welcome!

-Bill the arcstarter
Starting arcs in Cinci, OH
http://www.geocities-dot-com/CapeCanaveral/Hangar/6160