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Modeling a magnifier




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From:  Antonio Carlos M. de Queiroz [SMTP:acmq-at-compuland-dot-com.br]
Sent:  Monday, February 23, 1998 3:43 AM
To:  Tesla List
Subject:  Re: Modeling a magnifier

Hi all:

I see that my affirmation that magnifiers and conventional coils work in
the same way, based on a simple model, caused -some- polemic.

Let me clarify a point (that I should have observed before...):
The models shows matematically that there is always a conventional coil
that works as a magnifier, and vice-versa.
This does not mean that the conventional coil that is equivalent to
the magnifier is practical, or works as a conventional coil usually does.
And vice-versa.

The main problem commented may be solved by looking more carefully at the
equivalence equations:

M12=M12'
k=M12'/sqrt(L1*(L2'+L3))
L2=L2'+L3
C2=C3

Using k'=M12'/sqrt(L1*L2'), the coupling coefficient of the magnifier
transformer, and obtaining the mutual inductance M12' from the expression,
we obtain:

k=k'*sqrt(L2'/(L2'+L3))

For example: If the inductance of the third coil (L3) is three times the 
inductance of the transformer secondary (L2') (reasonable?):

k=k'/2 

A magnifier with k'=0.6 would be equivalent to a conventional coil with
k=0.3, what still requires very fast quenching for optimal operation
(about 3 cycles of the resonant frequency), and could have serious insulation
problems. 

In the other direction, a conventional coil with low k would be equivalent
to a magnifier with low k', what is not the right idea.

And the "radio theory" works, as always.

Antonio Carlos M. de Queiroz
http://www.coe.ufrj.br/~acmq