[Prev][Next][Index][Thread]
Re: Next step-> Magnifier
Finn Hammer wrote:
> About magnifier:
>
> I feel like taking on the challenge of building a magnifier system, 10kW
> pig and suitable rotary. In contrast to the classic TC, which is easy to
> make (anything goes, as long as it is in tune) the magnifier seems to me
> like a *black art*.
> Any help in establishing a fundamental understanding of its function
> would be much appreciated.
A model that can be useful for design purposes was proposed by me some
time ago (20/2/1998). The post caused a lot of discussion, but
measurements made by several members of the list showed that practice
and theory agree rather well. I repeat the key parts of the posts below,
with a few changes:
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.
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.
The resonance frequency is 1/(2*pi*sqrt(C1*L1)).
The relation C1*L1=C3*(L2'+L3) must hold.
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.
Using k'=M12'/sqrt(L1*L2'), the coupling coefficient of the magnifier
transformer, and obtaining the mutual inductance M12' from the
expression, we obtain the coupling coefficient of the equivalent Tesla
transformer:
k=k'*sqrt(L2'/(L2'+L3))
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.
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.
The model fails if there is significant capacitance across L2', what
creates an additional oscillatory mode. You can find in the archives
some discussions about this, without a clear conclusion yet.
Antonio Carlos M. de Queiroz