Re: Practical Magnifier Design ? ?

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

Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> 

Tesla list wrote:

 > Original poster: "Mccauley, Daniel H" <daniel.h.mccauley-at-lmco-dot-com>

 > I've tried searching some of the pupman archives, but it seems the
 > server hasn't been working lately and I'm trying to order both of
 > Richard Hull's videos on Magnifier design also.  And I did find some
 > good theoretic information on magnifiers from Antonio Carlos M. de
 > Queiroz's webpage.

Impedance matching doesn't apply on the design of these
circuits. They behave basically as lossless LC circuits.
If some interpretation in this direction can be obtained from the
design equations, I didn't observe it yet.

The most essential relation is just the tuning:
L1*C1=(L2+L3)*C3
This is enough for a Tesla-coil-like operation.

Another, for a true magnifier, is that the ratio between L3 and L2
is tied to the coupling coefficient between L1 and L2.
k12=sqrt(L2/(L2+L3))
k12 depends on the mode.

There is another relation setting the ratio between C3 and C2,
that depends on the mode, but this can be adjusted easily if
the other conditions are met.

Good quenching is important if you go for one of the fast modes,
where the notches in the primary energy are very fast.

I have the design equations implemented in the programs Magsim
and Mrn6, available at http://www.coe.ufrj.br/~acmq/programs.
Start with a third coil and its topload L3-C3, and the input
capacitor C1 that you want to use. Choose then a mode k:l:m that
results in feasible values for L2, k12, and C2. The energy
transfer time is essentially determined by the second factor, "l",
that shall be as low as possible for high efficiency (the minimum is 2,
but this would be a difficult design).
With m>>"l" the system starts to behave as a normal Tesla coil, and
C2 decreases. Eventually a distributed C2 can be used, what
avoids the problem of building a high-voltage lumped capacitor.
The modes with m=k+1, l=k+2, that would be the most characteristic
for a magnifier, also result in reduced RMS output voltage, what
(something that requires more tests for verification) may be
prejudicial for the formation of streamers.
If you use a geometry as the one that I used for my experimental
magnifier (L1 flat, L2 solenoidal), the distributed part of C2 can
be approximately predicted as the sum of the Medhurst capacitances
of L2 and L3. Add a few pF for the "transmission line", that can be
actually used to adjust C2.

Another practical consideration may be what happens after the
primary gap quenches. The system L2-C2-L3-C3 continues
interconnected, and the output voltage is not a single decaying
sinusoid (my tool don't look at this, but a simulator can be used
to see what happens). With m>>l, this is not a problem.

In conclusion, I recommend the use of the exact lumped design,
but in a way that results in a distributed C2 capacitor.

Some days ago I was looking at the equations that I have posted
at that site (http://www.coe.ufrj.br/~acmq/tesla/magnifier.html)
and noticed a new tuning relation that may be useful:
The third coil resonates with its self-C+topload at the same
frequency of the primary circuit, when the secondary coil is
short-circuited. L3*C3=L1*(1-k12^2)*C1.

Antonio Carlos M. de Queiroz