LC Resonant theory RE: Longitudinal Waves

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

Original poster: "Steve Greenfield by way of Terry Fritz <twftesla-at-qwest-dot-net>" <alienrelics-at-yahoo-dot-com>

Someone remind me who has the website with all the
waveforms of primary vs secondary voltage. It shows
plainly how the energy rings back and forth between
the primary and secondary.

Dave, you might find it helpful to think of the charge
as a pendulum swinging back and forth. If you give it
a kick when nothing is happening, it starts out from
zero and so you don't see a "kick" at the peak. So the
primary gets a kick from an arc, it starts at zero and
the first half sine is the highest. As it rings down,
it is losing energy in three ways: resistive,
radiative, and transfered by magnetic coupling to the
secondary. The secondary, rather than getting one big
kick, gets kinda dragged along. It is not a "kick"
each half cycle. It is more like grabbing the string
near the top of a pendulum and pulling it back and
forth at the resonant frequency of the pendulum,
oscillations build up over several cycles.

Then the reverse happens- some of the field from the
secondary now couples energy back into the primary and
so you see the primary peaks getting higher again.
Then back again. How many times it happens depends on
things like resistive and radiative losses, and
whether or not it arcs out from the top of the
secondary.

Dave, in your question below:
> ...what is the current
> scientific explanation for
> the variation of voltage in a damped sine wave? 
> What force is believed to
> determine when the wave will reverse direction?

You are asking for an explanation of resonance. If I
understand you correctly, you are asking what
determines when a rising sine wave stops rising and
falls, passes through zero, then to another peak where
it stops and reverses direction again.

Again, it may help to think of an LC resonant circuit
as a pendulum. Charge on the capacitance is
represented by displacement of the weight from the
center resting point, and the magnetic field by the
speed of the weight.

You might do yourself some good to study resonant
theory and the operation of LC and RLC parallel and
series circuits. The ARRL Handbook is a good place to
start.

Steve Greenfield

--- Tesla list <tesla-at-pupman-dot-com> wrote:
> Original poster: "David Thomson by way of Terry
> Fritz <twftesla-at-qwest-dot-net>" <dave-at-volantis-dot-org>
> 
> Hi Pete,
> 
> Your explanation is helpful.  At what point of the
> cycle is new energy
> added?  We know there are losses in the system, so
> at some point the energy
> has to be replaced, correct?
> 
> I'm going to jump ahead of your answer, because I
> can't see how energy would
> be efficiently added gradually through the entire
> cycle, it must be added as
> a pulse at a given time.
> 
> Most likely, just a guess, this energy will be added
> shortly after the
> magnetic field begins to collapse in either one or
> both places in the cycle.
> 
> If the energy is added in just one point of the
> cycle, then due to the
> gradual decay in the sine wave (resistance) there
> will be a slightly higher
> voltage in the cycle just after the added pulse than
> just before the added
> pulse.
> 
> Am I correct?
> 
> Whether my assumption is correct or not, that is
> what I had intended to
> convey the first time.
> 
> Now when I see a perfect sine wave floating across
> the screen, and I know
> due to the laws of nature that there must be
> resistance in the circuit, I
> should be seeing a slight bump somewhere in the sine
> wave.  But I don't see
> it.  Was it smoothed out by the oscilloscope?
> 
> Dave
> 
> -----Original Message-----
> From: Tesla list [mailto:tesla-at-pupman-dot-com]
> Sent: Friday, February 15, 2002 12:15 PM
> To: tesla-at-pupman-dot-com
> Subject: RE: (Fwd) RE: Longitudinal Waves
> 
> 
> Original poster: "Pete Komen by way of Terry Fritz
> <twftesla-at-qwest-dot-net>"
> <pkomen-at-zianet-dot-com>
> 
> Dave,
> 
> Consider a circuit consisting of a capacitor (F) and
> an inductor (H)
> connected in series with nothing else in the
> circuit.  Suppose that the cap
> is charged to some voltage V (if you want, imagine a
> switch in the circuit).
> The cap has charge Q = F * V and energy J = F * V^2
> / 2.  When the switch is
> closed the voltage is at a maximum and rapidly falls
> (based on the resonant
> frequency of the circuit) to zero as the current
> rises to its maximum.  At
> this point (1/4 through one cycle), the energy is
> all stored in the inductor
> J = I^2 * H / 2 (I = current)
> 
> V = inductance * dI/dt (voltage is inductance in
> Henries * change in current
> With Respect To change in time.  Note that when
> voltage is zero, the current
> is at a maximum but not changing (instantaneous)
> 
> At this time the inductor starts to give up energy
> as voltage builds in the
> cap and the current changes more and more rapidly
> (falling) as the current
> flow is opposed by the voltage building in the cap. 
> Finally, all energy is
> transferred to the cap (the voltage is reversed from
> the beginning) and the
> current is zero.  This is the end of the first half
> cycle.  This continues
> until all energy is lost.
> 
> Energy is lost in resistance and radiation (is there
> anything else?).  The
> energy lost means a lower voltage in the cap when
> the voltage is at maximum,
> and a lower current when current is at maximum.
> 
> If it is damped, the Q of the circuit is low and
> drop in voltage at each
> peak is less. (or there may be no second peak).
> 
> As usual, I don't know if this is what you were
> looking for.
> 
> Regards,
> 
> Pete Komen
> 
> -----Original Message-----
> From: Tesla list [mailto:tesla-at-pupman-dot-com]
> Sent: Wednesday, February 13, 2002 4:51 PM
> To: tesla-at-pupman-dot-com
> Subject: RE: (Fwd) RE: Longitudinal Waves
> 
> Original poster: "David Thomson by way of Terry
> Fritz <twftesla-at-qwest-dot-net>"
> <dave-at-volantis-dot-org>
> 
> Hi Malcolm,
> 
> >Having spent half a lifetime repairing
> oscilloscopes as well as calibrating
> them I must strongly disagree with the statements in
> that paragraph. Bear in
> mind that you can invert one channel of most if not
> all scopes. The fact
> that there is no DC shift in a pure sinusoidal
> waveform when you do that
> speaks volumes.
> 
> I've been looking for the reference that I derived
> my information from.  I
> cannot find it just yet.
> 
> The DC shift has been shown by some experimenters to
> exist.
> 
> The shift was explained just as I am presenting it,
> that there are two
> opposite polarity waves working together.
> 
> While we are on the topic, what is the current
> scientific explanation for
> the variation of voltage in a damped sine wave? 
> What force is believed to
> determine when the wave will reverse direction?  I
> could use a little
> education on the current theory if you would indulge
> me.  I believe this is
> useful information for Tesla coils in general.
> 
> Dave

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