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Re: [TCML] Magnifier topics
We can think of the bottom Fig. as being the Spark Gap?
Correct me if wrong.
Joe in Texas
On Sun, 14 Feb 2010 10:48 +0000, "Paul Nicholson" <tcml88@xxxxxxxxxxx>
wrote:
> So far I think the only documented example of multiple resonant
> tuning of a TC is Antonio's 3:4:5 system described here,
>
> http://www.coe.ufrj.br/~acmq/tesla/mag345.html
>
> As a test of modelling software I set up a distributed model
> of this system. Plugging in the dimensions of all the coils,
> the 62pF 'transmission line' capacitance, and a guess at some
> of the topload dimensions, reproduces the behaviour quite well.
> I had to add an extra 2pF of top capacitance and I actually
> needed 70pF on the t-line compared with Antonio's 62pF, in
> order to get a reasonable tuning.
>
> Here is a comparison of lumped and distributed models, showing
> the impedance response seen looking into the gap:-
>
> http://abelian.org/tssp/acmq345a.gif
>
> The red curve is from a lumped model using the component
> values given by Antonio, plus a bit of resistance to simulate
> a plausible loss factor. The green curve is the distributed
> model, adjusted to match reasonably well by tweaking C2 and
> C3 as mentioned above.
>
> From Antonio's web page you can see that the lumped model
> gives a very good account and in this case the distributed
> model doesn't have anything much to add.
>
> Here is an animation of the resonator voltages (800 kbyte,
> 200 frames):
>
> http://www.abelian.netcom.co.uk/tssp/acmq345.anim.gif
>
> The 'resonator' in the top two graphs is the combined secondary
> and tertiary, with the dividing line marked at position 29.
>
> Output voltage reaches a peak at 6.6uS which is frame 132.
> If you can freeze it at that point, you see that there's
> only a little residual current in the secondary and hardly any
> secondary or transmission line voltage at all. Nor is there any
> tertiary current - all the bang energy that survives the losses
> is momentarily in the third coil's E-field. This animation
> has a 10kV firing voltage and the peak output is about 210kV
> (the lossless lumped model predicts 227kV).
>
> The step change in current between the top of the secondary
> and base of the tertiary is due to the current diverted into
> the added C2 - the 'transmission line' capacitance.
>
> You'll see some HF components excited in the secondary at
> the beginning of the bang. These don't couple well into the
> tertiary and are almost completely trapped in the secondary.
>
> It's fascinating to watch how the secondary coil drives the
> tertiary resonance, whipping it up to a peak. Getting the
> timing of that 'whiplash' correct is what multiple resonant
> tuning is all about. You can see from the animation that it
> really 'looks' right, but is not quite perfect because my model
> is still slightly out of tune.
>
> If more overtones where brought in and tuned correctly,
> it really would start to look like a whiplash at the peak,
> with (momentarily) all the resonator voltage rise occurring at
> the top end of the tertiary. Extra overtones can be tuned
> by hanging capacitance onto the resonator at key points,
> and/or splitting the resonator into yet more coils, each with
> suitable reactance. What you end up with in the limit is a
> pulse forming network involving stepped or graduated impedance
> transformation. This could be described as a 'wide band' or
> 'pulse' TC. It wouldn't be of any practical use because it
> would be lossy and the final segment of the resonator has
> to withstand the entire peak output voltage. However, the
> principle probably crops up here and there in pulse forming
> networks in power electronics.
>
> Note that the current distribution in both coils is almost
> uniform, especially so the secondary. This means that the
> effective inductance is very close to Ldc. Consequently the
> voltage distribution in each coil is almost a linear rise
> and this makes the Medhurst C valid for the equivalent shunt
> capacitance. This enables Antonio's lumped model based on Ldc
> and Medhurst to give such a good prediction of the resonant
> frequencies.
>
> Apart from those little HF ripples, the distributed model
> doesn't have a lot to add here, although it gives a nice
> picture of the resonator in action.
>
> There are three resonant modes (almost correctly tuned) in
> operation here. Separate animations of each:-
>
> 1/4 wave, 227kHz (232kHz measured, -0.4% error):
> http://www.abelian.netcom.co.uk/tssp/acmq345-1.anim.gif
>
> 3/4 wave, 303kHz (307kHz measured, -1.3% error):
> http://www.abelian.netcom.co.uk/tssp/acmq345-2.anim.gif
>
> 3/4 wave 383kHz (385kHz measured, -0.5% error):
> http://www.abelian.netcom.co.uk/tssp/acmq345-3.anim.gif
>
> and just for fun, the next higher resonance, which is not
> being tuned here,
>
> 5/4 wave 873kHz:
> http://www.abelian.netcom.co.uk/tssp/acmq345-4.anim.gif
>
> This overtone makes 500V available at the topload at 20k ohms
> reactive impedance.
>
> The errors of the distributed model (-0.4%, -1.3%, -0.5%)
> could be improved if we took the trouble to measure all the
> dimensions accurately and track down all the 'stray' wiring
> capacitances, etc, but the lumped model with errors of (1.8%,
> -1%, -1.3%) is already more than adequate for practical work.
>
> This 3:4:5 system really is a very good demonstration of
> multiple resonant tuning. The added C2 is large compared with
> the secondary coil's own shunt capacitance, which means that
> Ldc and Medhurst C are good to use. The tertiary coil is not
> quite so 'lumped' due to the relatively small topload but is
> still very well described. These conditions are likely to
> be present in most magnifiers and the well thought out set
> of design equations and programs that Antonio provides are
> completely justified for practical work.
>
> Hopefully the animations in this post will be helpful in
> visualising what the multiple resonant tuning is aiming for.
>
> The challenge for the coiler is as follows: you build the
> system according to the design equations and measure the three
> resonant frequencies. They will not initially be correct
> because the reactances can't be designed and built perfectly.
> They need to be adjusted to the desired ratios.
>
> Once the coils are wound, the system has three tuning variables
> to play with: topload height, added C2, and the primary tap.
> Or perhaps four if coupling can also be adjusted.
>
> Actually I think it is quite a problem to know which to adjust
> and by how much, in order to move the three frequencies into
> a correct alignment. Perhaps it is possible to define a
> tuning procedure? For example: C2 affects the 3rd frequency
> more than the others; coupling mostly affects the distance
> between 1st and 2nd (or is that 1st and 3rd); C3 affects the
> 1st frequency more than the other two;
>
> If one can allow that it is only the ratios of the frequencies
> that matter so that there are only two degrees of freedom,
> then in theory only two of the reactances need to be tunable.
> From considerations like these, can a tuning procedure be
> defined?
>
> There is no quenching in these models, so after 6.6uS the
> energy starts to transfer back to the primary. If anyone
> is interested, I can animate the response with quenching,
> and also with simulated discharges to ground from the topload.
>
> I'd like to post some more models of 3-coil systems, ones that
> aren't so lumped. There's some interesting physics to be found
> by looking at how the overtone mix, excited by the bang, changes
> when the secondary is split. I hope to show that it is not
> so much the higher k, but the extent to which the coupling is
> concentrated onto a smaller fraction of the overall resonator,
> that is responsible for higher overtone content.
>
> Dex wrote:
> > 1.Overall coupling in many magnifier systems
> > is in 0.2+ range.That means magnifier is
> > more efficient than a typical coil which
> > usually has problems when coupling is that
> > high.
>
> That's surely the simplest explanation for magnifier
> performance. Simply a fast energy transfer being more
> efficient.
>
> > 2.Voltage shape of the outputs are not completely
> > same even with the same overall coupling
> > (perhaps some effect to spark is possible due to
> > that difference)
>
> Another great possibility - the wave shape of the 3-coil is
> just better for developing a good breakout.
>
> I think 'accidental' multi-mode tuning must come further down
> the list of possibilities, and HF overtone heating effects at
> the bottom. Having spent much time studying coil overtones,
> I've still not found a use for them but I keep trying.
>
> --
> Paul Nicholson
> --
>
>
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