Re: Non-Linear Coil Winding Experiment. (and more tests!)

---------- Forwarded message ----------
Date: Thu, 16 Oct 1997 19:21:59 -0600
From: terryf-at-verinet-dot-com
To: Tesla List <tesla-at-pupman-dot-com>
Subject: Re: Non-Linear Coil Winding Experiment. (and more tests!)   

At 03:21 PM 10/16/97 -0600, you wrote:
>---------- Forwarded message ----------
>Date: Fri, 17 Oct 1997 08:31:02 +1200
>From: Malcolm Watts <MALCOLM-at-directorate.wnp.ac.nz>
>To: tesla-at-pupman-dot-com
>Subject: Re: Non-Linear Coil Winding Experiment. (and more tests!)  
>Hi Terry,
>> high Z source the Q (bandwidth) should broaden as you describe but Fo should
>> stay the same.  Of course with non-linear coils there may be unknown factors
>> at work, but my results with different resistances did not show anything
>> unusual.
>>         Terry
>Fo shouldn't stay exactly the same and measurement by myself and 
>others show it doesn't. The popular 1/[2PI.SQRT(LC)] formula assumes 
>zero resistance. The real formula 1/[2PI.SQRT(LC - R^2/4L^2)] takes
>this resistance into account. The resistance is the Effective Series 
>Resistance at the frequency being measured.

If      L=10 mH
        C=10 pF

I get:  LC = 10^(-13)     R^2 = 2500    4*(L^2) = 0.0004

Fo = 1/[2*pi*SQRT(10^(-13) - 2500/0.0004)] = 0 - 0.00006366i

Can you clarify this equation?  It isn't making sense to me.

The  R^2/4L^2  part must be different???

Ahhh...... perhaps you meant the frequency of a decaying impulse response of
a coil.

Fo = SQRT(1/LC-(R/2L)^2)/(2*pi)  This equation is correct only for an
impulse response (capacitive discharge).  My measurements were steady-state
AC.  Trying the numbers:

1/(2*pi*SQRT(L*C)) = 503292.546158 Hz

SQRT(1/LC-(R/2L)^2)/(2*pi) = 503292.38888 Hz

A difference of 0.157278 Hz

How would one measure such a subtle difference?   Perhaps, I have made an
error or wrong assumption?