Re: Noncoupled Flux in Capacitive Transformers

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz <twftesla-at-qwest-dot-net>" <acmq-at-compuland-dot-com.br>

Tesla list wrote:
> 
> Original poster: "Jolyon Vater Cox by way of Terry Fritz
<twftesla-at-qwest-dot-net>" <jolyon-at-vatercox.freeserve.co.uk>
> 
> with regard to ordinary loose-coupled tuned transformers  where the
> secondary winding L2 forms tuned circuit with the capacitor C1, it is
> possible for secondary circuit to be resonant
> yet "seen" from the primary viewpoint  the circuit is still inductive due to
> the leakage reactance of the primary.

Something like this?
       1:n         
o----+     +----+-----+
     | k<1 |    |     |
     L1    L2   C2    Z2
     |     |    |     |
o----+-----+----+-----+

If the secondary L2 is tuned by a capacitor C2 across it, at the
resonance
frequency w the impedance seen at the input side is:
Zin=Z2/((n/k)^2)+jw(1-k^2)L1

> to make the primary appear purely resistive at resonance  it is necessary to
> decrease C1 to increase capacitive reactance referred to the primary across
> the turns ratio in order to cancel the leakage reactance.

Ok, but this is not always possible. Calculation left as exercise...
It's simpler (to calculate) to insert a capacitor in series with L1,
with value C1=1/(w^2*(1-k^2)*L1).
 
> in a similar vein would it not be possible to use some of the inductive
> reactance of L1 to cancel the leakage capacitance of c1 and C2 in the
> instance of the capacitive transformer?

With L1 in series, yes. L1=1/(w^2*(C1+C2)) cancels the "leakage
capacitance" C1+C2 at the frequency w (that is also the resonance
frequency of C1 in series with C2 and L3).

        +-----+----o
        |     |
        C2    |
        |     |
 o--L1--+     L3
        |     |
        C1    |
        |     |
 o------+-----+----o
 
> Also -on the slightly separate (?) issue of electric flux some of this does
> "leak" through the capacitor C3 -if this were not so would there exist a
> perfect capacitive transformer- a sort of dual of the theoretical "ideal
> transformer" of magnetic design?

No. C3 (in parallel with L3 above) just changes the reactance of L3,
that
has to be changes to compensate for its presence. What is missing in a
capacitive transformer is the "mutual capacitance", that doesn't exist
physically. Without it, it's not possible to eliminate the "leakage
capacitance" from the transformer.
 
> So -referring to the capacitive transformer Tesla coil-if the induction ring
> could intercept all of the the electric flux between the ungrounded terminal
> of L2 and ground, would that not be an ideal capacitive transformer -and no
> more likely to exist in reality than an ideal magnetic one as some electric
> flux would inevitably escape- not that any load could be connected between
> the topload and ground of such a "transformer" in any case since the
> influence plane would  have to totally enclose the ungrounded terminal
> precluding such a connection.

This would just eliminate C3 from the system, reducing the system to
the form in the drawing above. The "transformer" would continue as a 
regular capacitive transformer.

Note that the tuning relations for the sinusoidal steady state
capacitive transformer are not exactly the correct relations for the 
"capacitive transformer Tesla coil". 
The correct relation is actually:
L1*(C1+C2*C3/(C2+C3)) = L2*(C3+C1*C2/(C1+C2))
Or, considering that C1>>C2 and C1>>C3:
L1*C1=L2*(C2+C3)

I added an update to the page describing the system, showing that the
capacitive transformer approximation really gives the correct voltage 
gain if I use more precise values, and adding the relation above:
http://www.coe.ufrj.br/~acmq/tesla/mres4ct.html

Antonio Carlos M. de Queiroz