Re: Frequency splitting (fwd)

["Tesla list" <tesla@xxxxxxxxxx>]

---------- Forwarded message ----------
Date: Sun, 19 Aug 2007 22:46:23 -0500
From: resonance <resonance@xxxxxxxxxxxx>
To: Tesla list <tesla@xxxxxxxxxx>
Subject: Re: Frequency splitting (fwd)




The arc itself is a conductor.  The intervening air between the arc and 
ground is an insulator, ie, a dielectric.  The ground is also a conductor, 
so you have two conductive "plates" with a dielectric sandwiched into 
between.

Yes, this would form a crude capacitance with a cap value in the pF range. 
typically, 1 pF per foot of spark length.  With our Big Bruiser coil we have 
to adjust tuning to compensate for the additional 32 pF of capacitance in 
the secondary system.

It's not the arc itself independent of it's environment that forms the total 
capacitance, but with all things considered a definite capacitance to ground 
is involved which does effect tuning.


Dr. Resonance

Resonance Research Corp.
www.resonanceresearch.com


----- Original Message ----- 
From: "Tesla list" <tesla@xxxxxxxxxx>
To: <tesla@xxxxxxxxxx>
Sent: Sunday, August 19, 2007 6:53 PM
Subject: Frequency splitting (fwd)


>
> ---------- Forwarded message ----------
> Date: Sun, 19 Aug 2007 15:22:28 -0400
> From: Jared Dwarshuis <jdwarshuis@xxxxxxxxx>
> To: Pupman <tesla@xxxxxxxxxx>
> Subject: Frequency splitting
>
>                                                    Frequency splitting
>
>
>
> If we build a circuit with two identical parallel LC oscillators that have
> been coupled with a third capacitor ( which we will label as C') we can
> easily describe the beat frequency as being comprised of two individual
> frequencies: w+ = 1/sqrt(LC) and w- = 1/sqrt( L( C + 2(C') )
>
>
>
> We can make remarks about the charge amplitude and show the beat frequency
> as being comprised of w+ and w-
>
>
>
> q = 2 q0 sin [ ( w+ +  w-  )/2   t ] cos [ (w+  - w- )/2   t  ]
>
>
>
> We can also model a pair of identical mass /spring's  coupled with a 
> central
> spring labeled k'  by using the exact same mathematical underpinnings.
>
>
>
> In this case w+ = sqrt (k/m) and w- = sqrt [(k + 2k')/m]
>
>
>
> Wall-----Spring k---Mass--- Spring k' ----Mass--- Spring k -----Wall
>
>
>
> We can make remarks about the amplitude and show the beat frequency as 
> being
> comprised of w+ and w-
>
>
>
> x = 2 x0 sin [ ( w+ +  w-  )/2   t ] cos [ (w+  - w- )/2   t  ]
>
>
>
> Now to give some physicality. We find the two fundamental modes of this
> coupled mass spring system by examining two special cases of motion.
>
>
>
> When we move both mass the same direction and distance, we find that the
> central spring k' remains flaccid and does not contribute to the frequency
> of the system. In this case the term k' disappears and we get w = sqrt 
> (k/m)
>
>
>
> When we move both mass in opposite directions and equal distance. We are
> stretching the center spring k'. This is where we get the second 
> frequency:
> w- = sqrt( (k + 2k') /m)
>
>
>
> Now if we were to introduce dampening to one side of our mass spring 
> system
> we could no longer make these simple remarks. We would need to write all 
> of
> this using decaying exponential functions.
>
>
>
> But in a pinch we could always get a lightly dampened system to respond
> decently to the driver by tweaking one or more of: m, k, or  k'
>
>
>
> Now does it makes sense to use the phrase "frequency splitting". Not 
> really
> since it is already implied that we have a superposition of two 
> frequencies
> in a coupled system. The beat envelope increases as we diminish k'. this 
> is
> no surprise since:
>
> w- = sqrt( (k + 2k') /m) becomes: w = sqrt (k/m) as k' goes to zero.
>
> End.
>
>
>
> Commentaries:
>
>
>
> It has come to my attention that many experts on Pupman are now describing
> the plasma arc from the secondary capacitor  as having a capacitance. They
> are tuning coils as if the capacitance was really there.
>
>
>
> There is no such capacitance in the arc. Capacitors do not increase
> capacitance when they arc out. Arcs do not have an ability to store 
> charge.
> Arcs  do not have plates nor can they be described with a fixed geometry.
>
>
>
> Nor can we describe an arc as having an appreciable inductance. The 
> geometry
> is not much good for inductance.
>
>
>
> Nope!;  you are altering C or C'  to make up for changes in frequency 
> caused
> by dampening. (dampening from  the non linear resistance of the arc)
>
>
>
> Empirical corrections are wonderful, my hats off!  I am sure that a great
> deal of effort was involved in arriving at a useable correction factor. 
> But
> there is no capacitance in the arc. There is only non linear resistance 
> and
> perhaps a tiny bit of inductance.
>
>
>
>
>
> Jared Dwarshuis  August 07
>
>
>