Re: 2 questions on resonance
Having read the various answers, I can perhaps help rationalize this:
> Original Poster: Bert Hickman <bert.hickman-at-aquila-dot-com>
> Tesla List wrote:
> > Original Poster: "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
> > Dear all,
> > After reading the responses on resonant rise, I would like
> > to ask why it is said that resonant charging allows one to suck more
> > power from a NST? I suggest that if that were true, one could set the
> > gap wider than for a non-resonant situation and still have the gap
> > fire at the 2Fmains rate. Any comments?
> > Malcolm
> Malcolm and all,
> One can! Probably the best analysis of this was done by Glasoe in "Pulse
> Generators", section 9.5 (AC Resonant Charging). Although the math is
> fairly tedious, the result is that the capacitor voltage can reach Pi/2
> or 1.57 times the peak of the applied sinusoidal voltage for the
> lossless case. This means the output can reach up to 2.22 times the RMS
> faceplate voltage (or 33 kV) for the lossless case. While Ohmic losses
> will reduce this a bit, this implies that a 15 kV transformer might
> stress the tank cap to over 30 kV. Upon oscillatory discharge, the
> dielectric will be stresses to 2X this value, or about 60 kV. This is
> another way of looking at why the tank cap's DC rating should be at
> least 3-4X the expected applied RMS voltage. And it can get worse... if
> the gap missfires and we catch the NEXT peak, the voltage could be Pi
> times the peak of the input sinusoidal voltage (approaching 66 kV!).
> Practically speaking, I believe this voltage multiplication effect
> occurs in my resonant charging system, since I'm running with 18 gaps
> (0.54") off a pair of 15-60's, and at full power the system is actually
> firing at between 3-4X per half cycle (albeit somewhat chaotically).
> -- Bert --
Taking this scenario first, one can see that after the gap goes out,
the transformer has a full half cycle of energy delivery available to
charge the cap enabling the cap to reach a voltage higher than
SQRT2.Vrms at the next peak. This brings power delivery close to the
faceplate VA rating. I wonder if this power factor correction shows
up in the primary waveforms negating the need for a PFC cap? Anyway,
the major disadvantage is the subjecting of the transformer secondary
to a voltage greater than its open circuit voltage.
With the larger capacitor mentioned by Gary and Terry, one must
also get some partial cap charging after dwell as the transformer
comes down off its peak but this time the larger capacitance taken
with a limited energy delivery capability (which I think always
exists) cannot cause Vcap to exceed the peak transformer voltage.
With the gap set wide enough in the first case, I think you will get
just as much energy in the cap as in the second, the disadvantage
being the much higher voltage the smaller cap has to reach to reach
the same energy storage. I still don't see any evidence that the
transformer can do better than its faceplate VA rating.
The big cap idea sounds like it should be a firm recommendation
for capacitor sizing rather than the now (apparently) dated notion of
going for an Xl=Xc match. There is some inherent protection for the
transformer built in by way of secondary voltage limiting per half
cycle as a bonus.