Re: Tesla magnifiers (fwd)

["Tesla list" <tesla@xxxxxxxxxx>]

---------- Forwarded message ----------
Date: Sun, 16 Sep 2007 11:59:18 -0300
From: Antonio Carlos M. de Queiroz <acmdq@xxxxxxxxxx>
To: Tesla list <tesla@xxxxxxxxxx>
Subject: Re: Tesla magnifiers (fwd)

Tesla list wrote:
> ---------- Forwarded message ----------
> Date: Sat, 15 Sep 2007 21:33:29 +0000
> From: jhowson4@xxxxxxxxxxx
> To: tesla@xxxxxxxxxx
> Subject: Tesla magnifiers
>
> Hello all I am researching about the tesla magnifier for an AP physics
> paper at school and I read a bunch of sites about how it works and I am
> still really confused.  basically I think I understand that the primary
> should be of a low inductance and should have a high coupling with the
> secondary which should be of a slightly larger inductance, and that the
> point of that is to generate a high voltage through normal transformer
> action no resonance.  This is where I am lost how is the resonant
> frequency of the 3rd coil found.  
A magnifier with coils L1, L2, and L3, primary capacitor C1,
tertiary capacitance C3, and coupling coefficient k12 between L1
and L2 is equivalent to a two-coils system with:
C1'=C1
C2'=C3
L1'=L1
L2'=L2+L3
k12'=k12*sqrt(L2/(L2+L3))
This is easy to verify by using transformer equivalent circuits.
The system can then be designed as a conventional coil, following
the tuning relation:
C1*L1=C3*(L2+L3)
The inductances can be chosen as convenient.
If k12' is high (>0.2), it's important to use one of the values of
the coupling coefficient that result in complete energy transfer.
This rarely happens in Tesla coils used for spark production, however.

This works well as long as the capacitance C2 at the connection between
L2 and L3 is negligible.
If this capacitance is not negligible, it stores some energy that does
not go to the output. C2 can be "tuned out" with somewhat more complex
design formulas, that result in complete energy transfer from C1 to C3:
http://www.coe.ufrj.br/~acmq/tesla/magnifier.html

> Is it a sum of the secondary inductance
> and the 3rd coil inductance with the capacitance of the top-load.  
This is the correct relation, kept in the simplified and ideal design 
formulas. Note that, as in a
two-coils system, the capacitance of the topload includes the effect of 
the "self-capacitance" of
the third coil, that approximately adds to it.
> Or is
> it just the 3rd coil and its top-load giving the resonant frequency.  and
> how is this frequency produced.  Is the driver circuit frequency the same
> as the resonant frequency of the 3rd coil and it is just having the
> voltage increased by the secondary which is feeding the 3rd coil or what
The driver resonance frequency is the resonance frequency of the 
combination L2+L3 and C3.
The voltage that appears at the top of L2 is not related directly by 
"transformer action" to the other
voltages, unless the coupling coefficient k12 is very high, what is 
usually not feasible.
The magnifier is useful in energy conversion applications, because it 
allows very fast energy
transfer without excessive proximity between the primary circuit and the 
output terminal. For
spark production, the main advantage appears to be just the separation 
between the driver and
the output coil. The system can be designed in a way that allows C2 to 
be just the distributed
capacitance present at the connection between L2 and L3, but then the 
effect of C2 is already
small, and the simplest approximation can be used.

Antonio Carlos M. de Queiroz