Modeling a magnifier

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From:  Malcolm Watts [SMTP:MALCOLM-at-directorate.wnp.ac.nz]
Sent:  Sunday, February 22, 1998 4:22 PM
To:  Tesla List
Subject:  Re: Modeling a magnifier

Hi Antonio,
The odd comment:

> From:  Antonio Carlos M. de Queiroz [SMTP:acmq-at-compuland-dot-com.br]
> Sent:  Friday, February 20, 1998 4:41 PM
> To:  Tesla List
> Subject:  Modeling a magnifier
>
> Hi:
>
> I was studying how to model a Tesla magnifier, and would like to hear
>
> A conventional capacitor-discharge Tesla coil is composed by two resonator
> LC tanks tuned for the same frequency, with the coils magnetically coupled
> with a low coupling coefficient.
> The lumped model for a conventional Tesla coil after the firing of the
> spark gap, and before any breakout of sparks in the secondary, ignoring
> resistances, is:
>
> +-----+     +-----+
> |     | <k> |     |
> C1    L1    L2    C2
> |     |     |     |
> +-----+     +-----+
>
> k is the coupling coefficient, k=M12/sqrt(L1*L2).
> This model works as well as a transmission-line model. The two tanks
> resonate at the same frequency, and the effect of the coupling is to
> produce an "oscillation" in the oscillation, that appears modulated
> in amplitude (DSB) at both tanks, with the energy moving back and forth
> between the two tanks. Periodically, all the energy is in the secondary tank,
> and if the spark gap is quenched at one of these instants (better if at
> the first), the energy is trapped in the secondary, in the resulting high-
> voltage RF in C2 produces the effects that people like to see.

All the experiments I've conducted show that quench is heavily
dependent on getting rid of energy from the system. Again I ask: can
anyone show repeatably and conclusively that their gap/s can quench
first maximum under no-breakout secondary conditions? For me, seeing
would be believing it can be done.

> A Tesla magnifier has a transformer with higher coupling coefficient, and
> a separate "third coil" resonator mounted some distance away.
> The ideal lumped model for a magnifier would be:
>
> +-----+      +--L3-+
> |     | <k'> |     |
> C1    L1     L2'   C3
> |     |      |     |
> +-----+      +-----+
>
> k' is the coupling coefficient, k'=M12'/sqrt(L1*L2').
>
> This model is exactly equivalent to the model of the conventional coil,
> if M12=M12', k=M12'/sqrt(L1*(L2'+L3)), L2=L2'+L3, and C2=C3.
>
> As the energy transference only occurs efficiently if both tanks in the
> first circuit resonate at the same frequency, this must also happen
> in the second circuit, when everything is connected together.

Tesla also stated this in the Notes. However, he fell back on the
mode of operation where L1 is tightly coupled to L2 and rendered
resonance in L2 unnecessary. L1/L2 virtually become an ordinary
transformer at k = 0.4 to 0.6.

> The resonance frequency is 1/(2*pi*sqrt(C1*L1)).
> The relation C1*L1=C3*(L2'+L3) must hold.

That appears to be so for loose coupling between L1 and L2 although
in one test I saw a plethora of resonances which I think is due to
the discontinuity between L2 and L3.

> The maximum output voltage is VC3max=VC1max*sqrt(C1/C3)=
>                                     =VC1max*sqrt((L2'+L3)/L1)
> The higher coupling coefficient in the magnifier transformer is only a
> consequence of the splitting of the secondary coil. The actual coupling
> coefficient, considering the transformer and the third coil, is as low
> as in a conventional coil.

Can't agree with that. In fact, tight coupling is an artifact of coil
geometry and proximity. For a tight coupled driver system, one
ideally wants no mag coupling to L3. In effect, L1C1 transformed by
L2/L1 becomes a signal generator for driving L3.

> And this is more polemic:
> The dynamic behavior of the magnifier system is practically identical to the
> one of a conventional coil (with that model, exactly), and so there is no need
> for different operating frequencies and special spark gaps (as I see commented
> in several places).
> The advantages of the magnifier are that the high voltage terminal can
> be moved away from the primary circuit, and that a more compact and predictable
> primary circuit can be used.
>
> What do you think?
>
> Antonio Carlos M. de Queiroz
> http://www.coe.ufrj.br/~acmq

Something approaching a useful ideal would be a system that allows k
between L1 and L2 to be adjusted while the coil is running to get the
best primary minimum of activity for any gap system I would think.

Regards,
Malcolm

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