Re: Resonance equations (fwd)

["Tesla list" <tesla@xxxxxxxxxx>]

---------- Forwarded message ----------
Date: Tue, 07 Aug 2007 22:03:13 -0500
From: Shaun Epp <scepp@xxxxxxx>
To: Tesla list <tesla@xxxxxxxxxx>
Subject: Re: Resonance equations (fwd)

I think what your measuring is a result of mutual impeadance (Xm).  Your 
driving you test setup with a coil magnetincally coupled to your test 
circuit, when doing this your going to get mutual impedance reflected 
between your two coils which will change the resonant frequency. Depending 
on the degree of coupling you may get more that one resonant point, 
ie -sidebands.  Note that the refected impeadance with be opposite from 
primary coil to secondary.  In other words if you secondary is inductive at 
a given frequency, it will be reflected as capacitive in the primary 
circuit.

why don't you try direct drive and take your measurements:



Derivation of resonance:


Resonance occurs when capacitive reactance (Xc) and inductive reactance (Xl) 
are equal.  So Xc = Xl

        Xc =       1
                  --------
                    2 pi f c

and   Xl = 2 pi f l

so at resonance with no resistance.

       1
----------  =  2 pi f l
 2 pi f c


now reange for to solve for f

f^2 =           1
            ------------
            4 pi^2 l c

now take the square root of both sides and simplify:

f =          1
     --------------
      2 pi  sqrt(l c)

voila we have the standard resonance equation.

Shaun Epp


----- Original Message ----- 
From: "Tesla list" <tesla@xxxxxxxxxx>
To: <tesla@xxxxxxxxxx>
Sent: Sunday, August 05, 2007 8:55 PM
Subject: RE: Resonance equations (fwd)


> ---------- Forwarded message ----------
> Date: Sun, 5 Aug 2007 20:53:57 -0500
> From: David Thomson <dwt@xxxxxxxxxxxx>
> To: 'Tesla list' <tesla@xxxxxxxxxx>
> Subject: RE: Resonance equations (fwd)
>
> Hi Bert,
>
> Thanks for the explanation and link.
>
> The coils I'm using in the test setup are inductively coupled.
> However, the equations I'm using to produce resonance are different
> from the values in frequency splitting.
>
> Whereas frequency splitting is about multiple frequencies in a
> particular Tesla coil run, I can produce true resonance (as indicated
> by an oscilloscope) at three different operating frequencies and
> inductances, all else being the same in the circuits.
>
> Let me try to explain it this way.  I measure the inductance of one
> coil with a signal generator.  Then I can tune the other coil to
> resonance by adjusting the inductance and capacitance to one of three
> different equations.  Each coil has three different resonances, which
> are not harmonics or octaves of the others.
>
> These three frequencies always follow the same proportions.  So if you
> would normally calculate your resonance using the standard resonance
> equation, there is also a resonance at 1.463 times the first frequency
> and also 1.772 times the first frequency.  Of course, we see the value
> of 1.772 all the time, such as in John Freau's empirical spark length
> formula.
>
> Dave
>
> David W. Thomson
> Quantum AetherDynamics Institute
>