# Re: TC Theory

```Hi Reinhard and Cabbott,

You may want to check out my paper "Modeled and Actual Voltage and Current
Waveforms within a Tesla Coil".  It is in Word and HTML format at:

www.peakpeak-dot-com/~terryf/tesla/experiments/experiments.html

As the title suggests, it documents the issues you are interested in.

Is there resonant rise in a Tesla coil?  Sure there is! :-)  But it will be
so small you can barely see it even if you know were to look.  Before the
streamer begins, the system has low loss (relatively) and resonant effects
do help the voltage to rise a bit.  However, the effect is hardly worth
noting.  Once the arc streamer load begins, the Q drops and the transient
effects swamp the effect.  Theoretically, there is a little phase delay
between the top and bottom currents in the secondary but they are in the
range of three degrees.  Hardy worth worrying over.

Wire length is not a factor in Tesla coils as far as resonant rise or
anything like that is concerned.  The 1/4 wavelength has meaning if the
wire were a long straight line but, in our case, the wire is in a coil
where the sections of wire are magnetically coupled to each other.  A
current in the lower windings induces current in the upper windings within
nanoseconds.  You COULD use transmission line and 1/4 wave theory to
predict that but I is not of any practical value.  Just thinking of the
secondary as an inductor with a parallel capacitor will do everything we
ever need to do.  Assume the time delays and resonances are zero and your
calculations will match reality within a few percent.  Few people can even
measure to the level required to see the fine effects of this resonance and
time delays in real Tesla coils.

1/4 wave theory has been around for about 100 years so it will take awhile
to get over it. :-))

It is interesting to note that the secondary system has resonant
frequencies at Fo, 3Fo, 5Fo...  Which are "excited" by the fast pulse of
power applied to the secondary system.  The top terminal capacitance damps
these heavily but bare coils driven with a sine generator show them well.
This causes some distortion in the waveforms as seen in real scope captures
and in easily predicted by advanced models.  Again however, the effects are
hardly worth noting unless your are really into the FINE details of TC theory.

One can use models such as the Corums discuss in their papers (some
empirical equations they give provide inaccurate results) but you will
basically end up using heavy headed transmission line theory to model
pretty much a lumped inductor and capacitor.  Not worth the effort unless
you are REALLY interested in knowing the system to the extreme.  Computer
models provide much more accurate representations and are much easier to
understand and "play" with if you want to learn of such things.

Terry

At 08:51 AM 1/16/99 EST, you wrote:
>Hi Cabbott and all,
>
>Here are some thoughts about why I still say a transiently excited TC doesn´t
>experience a resonance rise.
>
>Lets say:
>-------------
>FRes = 100kHz
>The coupling is so that after 5 oszillations the gap stops conducting.
>To keep things simple we will also say this is first notch quench.
>As soon as the secondary coil starts giving off sparks the Q drops to about
>10-20.
>------------------
>
>Now lets have a look at the whole thing on a sort of time graph:
>
>T=0:
>This is the starting point.
>
>T=0-50us:
>Energy is transfered from the primary to the secondary. The gap stops
>conducting.
>
>T=50-150us:
>The coil "rings" and the secondary starts to emit sparks. (It transfers its
>stored energy into the sparks). If the secondary did not lose energy at this
>time, we wouldn´t be able to get any sparks, right?
>
>T=150µs-10ms:
>Nothing happens. The stored energy has been used up to create ion channels
and
>sparks, etc.
>
>T=10ms
>The cycle begins anew.
>
>Looking at it from a slightly different angle: During 9850µs (out of 10000µS
>total) NOTHING happens in the secondary. There is no voltage present.
>
>It should be possible to simulate this on a computer, although it might
not be
>an easy task doing so from scratch. Any simulater gurus out there, willing to
>try?
>
>If we now compare the "push the swing idea" to our Tesla coil, this would
mean
>we could collect and store a charge in the secondary COIL (in multiples of
the
>primary energy stored in the primary cap) every time the gap fires.
>
>This is NOT possible, because the secondary is absolutly dead in 98.5% of the
>time, which means any "phase information" gathered, would be lost. Plus it
>would violate the energy conservation law. Output Joules can never be greater
>than the input Joules. Any sort of transformer cannot MAKE power.
>
>A nice equation for Vout would look something like this:
>
>Ep = X * (Es+Et)
>
>Ep = 0.5*C*V^2 Energy in the primary cap
>Es = Energy in the secondary
>Et = Energy stored in the toroid
>X = Is an "efficiency" factor
>
>If the output where to experience a resonant rise the (Es+Et CAN NOT be
>greater than Ep !!) factor "X" would have to be greater than one ...........
>and I don´t believe this is possible. I think determining the "X" factor
would
>be very, very difficult. As a matter of fact I wouldn´t even be able to guess
>an approximation for this.
>
>If there is a flaw in my theory, please do point it out to me. Otherwise I
>will stick to my comment that a spark gap driven TC DOES NOT EXPERIENCE A
>RESONANCE RISE.
>
>Coiler greats from germany,
>Reinhard
>
>

```