Re: Tesla Coil Operation - was "Harmonics"

To: tesla-at-pupman-dot-com
Subject: Re: Tesla Coil Operation - was "Harmonics"
From: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> (by way of Terry Fritz <twf-at-verinet-dot-com>)
Date: Sat, 30 Jan 1999 22:15:07 -0700
Approved: twf-at-verinet-dot-com
Tesla List wrote:

>   Pendulums with magnets are also not an accurate anology because magnets
> are not mechanical. There is another reason. Magnets used in this way would
> not duplicate the same eleectrical function that is in the Tesla coil.
> Magmetism and electrostatics were known long before Faraday was born.

That analog is not good, I agree. 
It is more complex than a Tesla coil ;-)
 
>   I believe the Tesla coil is a complex electrical apparatus and it is not
> possible to duplicate its operation accurately using a mechanical analogy.
> The main problem is in duplicating the transfer of energy thru space from
> the primary to secondary coil. This involves electrical induction that was
> discovered by Faraday.

I must say that compared to almost any electronic circuit, the operation 
of a Tesla coil is very simple.
It is perfectly possible to build a circuit that works almost exactly as 
a Tesla coil, without a transformer. Just convert the primary-secondary
transformer to a "T" of inductors:
(L=inductance; M=mutual inductance)
      M
o---+   +---o         o---La---+---Lb---o
    |   |                      |  
    L1  L2       =             Lc
    |   |                      | 
0---+   +---0         o--------+--------o

The equivalence is: 
M=Lc; L1=La+Lc; L2=Lc+Lb
or:
Lc=M; La=L1-M; Lb=L2-M
The transformation is possible only if the three inductances result
nonnegative.
In a Tesla coil, M=k*sqrt(L1*L2), so certainly M<<L2. We can make La=0
to simplify the circuit. This requires L1=M, or k=sqrt(L1/L2). This
value for the coupling coefficient k is reasonable for a typical Tesla
coil. Adding the other elements of the original coil, we have the
circuit (exchange the gap with C1 if you prefer):
                    gap
        o--------+--o o--+---(L2-M)---0(terminal)
                 |       |          
power supply     C1      L1
                 |       |
        o--------+-------+------------0(ground)

This is essentially a Tesla coil with the bottom of the secondary
connected to the top of the primary and the bottom of the primary
grounded. This configuration may be problematic for the power
supply, that must be grounded (a normal NST cannot be used), but
it works exactly as the conventional circuit (with slightly different
unimportant transmission line effects). The primary and
secondary circuits can be far away from each other (a simplified
magnifier?), or the primary coil can be mounted orthogonal to the 
secondary to minimize coupling.
In old literature, this configuration is known as the Seibt circuit.
Look at these pictures:
http://www.coe.ufrj.br/~acmq/eln4382.jpg
http://www.coe.ufrj.br/~acmq/mk95943.jpg
Both show an induction coil used as power supply, a spark gap,
a primary capacitor (Leyden jars, splitted in the second picture),
an adjustable primary coil, and two secondary coils, tuned to
different frequencies. Just one resonates; see:
http://www.coe.ufrj.br/~acmq/ressona2.jpg

Of course, electromagnetic induction is still present in the inductors
themselves.

Antonio Carlos M. de Queiroz