# TC Theory

```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

```