Re: Resonance equations (fwd)

["Tesla list" <tesla@xxxxxxxxxx>]

---------- Forwarded message ----------
Date: Sun, 05 Aug 2007 19:54:44 -0500
From: Bert Hickman <bert.hickman@xxxxxxxxxx>
To: Tesla list <tesla@xxxxxxxxxx>
Subject: Re: Resonance equations (fwd)

Hi Dave,

If you were working with a simple lumped LC circuit (not coupled to 
anything else), it will have a single resonant frequency. The secondary 
coil is actually a distributed LC circuit and exhibits significantly 
more complex behavior. For Tesla coil tuning purposes it can be viewed 
as having a single fundamental (i.e., lowest) resonant frequency.

However, if you were working with two coupled resonant LC circuits (like 
a Tesla Coil), you will see two resonant peaks as you adjust the driving 
frequency. This occurs even if each LC circuit was separately tuned to 
the same frequency (when isolated from each other). The act of simply 
coupling the two circuits together (via either magnetic coupling, 
electrostatic coupling, or a combination) will cause two resonant 
"humps" to appear on either side of the original frequency - these are 
sometimes called the upper and lower sidebands. The greater the 
coupling, the wider the separation between the upper and lower 
frequencies. This is sometimes called "frequency splitting" in Tesla 
Coils, and this phenomenon was used extensively to create simple RF 
bandpass filters for older analog (superhet) radios. Trying to 
"instrument tune" coupled resonant circuits is a bit tricky because of 
this effect.

During energy transfer between the primary and secondary (which occurs 
only when the spark gap is firing on a disruptive coil), both the upper 
and lower "sideband" frequencies will be seen. Once the spark gap 
quenches, the secondary will ring down at its own (isolated) frequency. 
If you used a spectrum analyzer when the coil was operating you'd see 
the upper and lower sidebands while the gap was firing, and the middle 
frequency when the secondary rung down. A magnifier can be even more 
complex since it actually has three LC circuits, but its behavior is 
well understood.

Some good theory that ties this together for two coil Tesla Coils can be 
seen on Richie Burnette's site - see the Frequency Splitting section on 
this page:
http://www.richieburnett.co.uk/operatn2.html#quenching

Bert
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Tesla list wrote:
> ---------- Forwarded message ----------
> Date: Sun, 5 Aug 2007 18:04:21 -0500
> From: David Thomson <dwt@xxxxxxxxxxxx>
> To: 'Tesla list' <tesla@xxxxxxxxxx>
> Subject: Resonance equations
> 
> Forgive me for stirring up the pot again, but I have made an
> interesting observation and quantification with regard to resonance.
> As many of you know, I have been working on a new physics theory
> (Aether Physics Model).  Getting to the relevant part for this post,
> the theory predicts that resonance in an LC circuit should be
> calculated as:
> 
> F.apm = sqrt(1 / 4pi * (LC)),
> 
> which is the same as:
> 
> F.apm = sqrt(pi / (4pi^2 * LC)).
> 
> The standard equation for resonance is actually:
> 
> F.standard = sqrt(1 / (4pi^2 * LC)) [often written as 1 / 2pi
> sqrt(LC)]
> 
> While experimenting with 8 different Tesla coil setups, I found that
> resonance can be achieved by both equations in every case.  So I built
> a little test setup that I could drive with my signal generator.  And
> after studying about resonance in a textbook, I found there at least
> two different types of resonance.  For a given inductance and
> capacitance, there is an oscillatory resonance (produces highest
> potential) and a true resonance (produces zero potential).  The
> standard LC resonance equation calculates the oscillatory frequency
> for highest potential.  My resonance equation calculates the true
> resonance of the system.
> 
> After doing further research, I found a third resonance equation,
> which ties to the other two equations using the Pythagorean theorem.
> The relationships of the three resonance equations are such that:
> 
> F.standard^2 + F.third^2 = F.apm^2
> 
> The third resonance equation is:
> 
> F.third = sqrt((pi - 1) / (4pi^2 * LC))
> 
> I have tested these equations for numerous inductance and capacitance
> values and it works every time.  
> 
> Here is my question to the list.  Does standard electrodynamics theory
> identify these three different resonances for any given LC
> combination?  Also, have these three types of resonances been fully
> investigated and their functions identified?
> 
> Dave
> 
> David W. Thomson 
> Quantum AetherDynamics Institute
> 
> 
> 
> 


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***************************************************
We specialize in UNIQUE items! Coins shrunk by huge
magnetic fields, Lichtenberg Figures (our "Captured
Lightning") and out of print technical Books. Visit
Stoneridge Engineering at http://www.teslamania.com
***************************************************