Secondary resonance freq

From:  Bert Hickman [SMTP:bert.hickman-at-aquila-dot-com]
Sent:  Tuesday, June 09, 1998 7:10 AM
To:  Tesla List
Subject:  Re: Secondary resonance freq

Tesla List wrote:
> ----------
> From:  Malcolm Watts [SMTP:MALCOLM-at-directorate.wnp.ac.nz]
> Sent:  Monday, June 08, 1998 12:20 AM
> To:  Tesla List
> Subject:  Re: Secondary resonance freq
> Hi Marco,
>             Very good question that deserves an answer:
> > From:  Marco Denicolai [SMTP:marco-at-vistacom.fi]
> > Sent:  Friday, June 05, 1998 1:11 AM
> > To:  tesla-at-pupman-dot-com
> > Subject:  Secondary resonance freq
> >
> > I measured yesterday the resonance frequencies of my secondary. It is a
> > 4.3" diameter PVC tube, winded for a length of 19.7" with AWG 26 wire.
> > I got the following results:
> >
> > 324 KHz
> > 813 KHz
> > 1475 KHz
> > 1766 KHz
> > 2053 KHz
> >
> > These without any top toroid or sphere. I used a function
> > generator (sine wave) and oscilloscope.
> >
> > I was waiting to measure the fundamental and all odd harmonics
> > (x3, x5, etc.) but can anybody explain to me how I have got the
> > above readings?
> To All: the following is an attempt at an intuitive picture of what
> is going on. Feel free to correct/flame etc. This is right at the
> edge of what I know.
>      I too have noted such odd spurii in experiments and this was
> with end feeding from a 7 Ohm resistive source.
>      Without a terminal you are right into free resonator territory.
> There is a less well defined boundary at the free end consisting of a
> bit more capacitance per turn than the bulk of the resonator than you
> get with a terminal stuck on the end. Other capacitances that would
> be swamped by a terminal if present are coming into play. You can see
> this effect also in bundle wound flyback transformer secondaries. It
> makes tuning a plasma globe supply using a driven oscillator an
> interesting experience. You can also see it in the analogue of an
> unbounded medium such as water in a lake. Ripples of many different
> frequencies can co-exist. NB - quartz crystals can also oscillate at
> many frequencies but I think most are harmonically related.
>      Perhaps I should defer to the RF experts on the list. I feel you
> have asked an excellent question which nobody seems to have addressed
> and I would be keen to hear more too.
> Malcolm

Marco, Malcolm, and all,

I've seen the same thing on base-driven resonator measurements. At the
time I attributed it to a measurement problem, and since I was only
concerned with the 1/4 wave response, put it on the back burner.
However, the recent posts by you and Marco got me to thinking about this
a a bit more. 

An open-ended resonator excited at 1/4-wave resonance will have a
voltage peak/current null at the far end, since the end is
open-circuited. If we now try to measure the 1/2 wave resonant frequeny
we'd expect to see a voltage null and a current maximum point at the far
end. However, this can only occur if the far end is hard grounded -
otherwise there's nowhere for the current to flow. Similarly, at higher
harmonic frequencies, the "internal" current maxima are not really
seeing hard grounds but are actually driving the remaining upper section
of the resonator. Perhaps this is why the higher frequency harmonics
don't directly conform to simple multiples of the 1/4 wave frequency...

-- Bert --