Re: Noncoupled Flux in Capacitive Transformers

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

Original poster: "Jolyon Vater Cox by way of Terry Fritz <twftesla-at-qwest-dot-net>" <jolyon-at-vatercox.freeserve.co.uk>

Since it would appear that the terminal is charged by electrostatic
induction via the influence ring-would it be incorrect to presume that the
polarity of the terminal is the opposite of that on the ring?

Is it not possible to get a capacitive transformer to do the other thing
i.e. step-down voltage and step-up current flowing into C1 by way of the
large circulating current that theoretically flows in the C1-C2-L2 loop?

----- Original Message -----
From: "Tesla list" <tesla-at-pupman-dot-com>
To: <tesla-at-pupman-dot-com>
Sent: Saturday, September 14, 2002 3:21 AM
Subject: Re: Noncoupled Flux in Capacitive Transformers


> 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
>
>
>
>
>