Re: Transformerless Tesla coil

["Tesla list" <tesla-at-pupman-dot-com>]

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

Tesla list wrote:
> 
> Original poster: "Jolyon Vater Cox by way of Terry Fritz
<twftesla-at-qwest-dot-net>" <jolyon-at-vatercox.freeserve.co.uk>
> 
> Antonio,
> I am sorry to say but I think there may be an error in the formula for the
> "transfer" frequency (fo) as given by equation
> 
>  fo=(1/2*pi)*(L2*C1/L2final*C1final))^(1/2)
> in your document.
> 
> This is because the answer for fo with the given parameters is 296207.4703Hz
> (or 296.207kHz) not 30 kHz as suggested.
> 
> When I entered L1 in place of L2 in the formula I got 31266.34409 Hz or
> 31.266 kHz, which is much nearer to  the 30kHz indicated in the text.
> 
> So should the "L2" actually be replaced by "L1" in the above formula?

The formula is in terms of L2 and C1.
Let's see:
f0=1/(2*pi)*sqrt(1.1049723e-2*90.750693/(28.2e-3*1e-9))
  =1/(2*pi)*sqrt(1.002839/2.82e-11)=30013 Hz

You probably forgot the parenthesis.
What the formula says is that in the normalized circuit, w0norm=1 rad/s.
The use of L2final and C1final instead of L2 and C1 causes a
denormalization in frequency and impedance, by the factors r0 and w0:
L2final=L2*r0/w0
C1final=C1/(r0*w0)
Solving for w0:
w0=sqrt(L2*C1/(L2final*C1final))
and f0=w0/(2*pi) (this formula was wrong, but I corrected it yesterday).

Antonio Carlos M. de Queiroz