Re: 2 questions on resonance

To: tesla-at-pupman-dot-com
Subject: Re: 2 questions on resonance
From: Gary Lau 07-Apr-1999 0901 <lau-at-hdecad.ENET.dec-dot-com> (by way of Terry Fritz <twf-at-verinet-dot-com>)
Date: Wed, 07 Apr 1999 18:18:27 -0600
Approved: twf-at-verinet-dot-com
>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

Good question.  I have always assumed this to be the case too.
Certainly if allowed to build over multiple cycles, the resulting voltage
will be highest when resonance is met, but I just ran some quick
simulations with differing capacitances and a 15KV/60mA NST and see some
surprising things that now make me question this "wisdom".

As expected, if allowed to run over multiple cycles, highest peak voltage
occurs with a 10.8nF cap (which is precisely mains-resonant at 60Hz).
But allowing the gap not to fire over multiple half-cycles is something
that should never be allowed to occur, and therefore is irrelevant.

Now, if I assume the gap is sized to fire exactly once per half-cycle (as
if a sync RSG or precisely gauged static gap were used) and only look at
the peak cap voltage after the first half-cycle, it gets interesting.
The highest cap voltage did not occur with the 10.8nF cap, but with one
something less than 4nF.  But this is not the whole story either.
Highest POWER occurs with highest (1/2 CV**2), assuming a constant gap
firing rate.  The highest POWER occured with between 25-30nF.

These numbers are a rough first pass, because I did not optimize the
phase of the gap firing to be consistent every mains half-cycle, as would
be the case if using a sync RSG.  Terry has pointed out that if one does
use a sync RSG, the optimum cap is 17-20nF, and this does take into
account adjusting the phase for consistent firing every half-cycle.  I
see this also if I tweak the simulation phase (somewhat tedious).

It will be interesting to run a similar simulation with the gap firing
multiple times per half-cycle, to see which cap size draws highest power.
Using static gaps, this is a more realistic scenario, as the voltages
seem to get out of hand if you only allow one big bang per half cycle.  It
also looks like when using sync RSG's, the caps had better be rated for a
higher voltage than with a static gap configuration, particularly when
using lower capacitance values.

Until then, I don't see any evidence of higher power being pulled through
the use of resonant charging.  Thank you Malcolm, for bringing this up.

Gary Lau
Waltham, MA USA