From: "Mark S. Rzeszotarski, Ph.D."
Date: Tue, 17 Oct 2000 12:31:19 -0500
Subject: Re: [TSSP] Re: Some resonator theory notes
Hello All:
At 12:18 AM 10/17/2000 +0100, Paul wrote:
>I've updated
>
> http://www.abelian.demon.co.uk/pn1310.ps
>
>Latest rev is 0.2d, some errors are fixed and a couple of extra
>sections have been added.
>
>You'll notice that the typical tesla V/I profiles from which some
>approximations are draw in sections 8 and 9 are the same
>linear-V/cosine-I profiles that are the subject of the present
>contradiction between theory and Terry's measurements, so the
>question of whether those sections can be applied to real
>tesla coils remains open.
>
>There are however several testable predictions in those two
>sections which we can put to the test.
I suggest you take a look at a couple simple examples to illustrate
the failure of the lumped element model with no topload coils. The idea is
embodied in the posting below. Basically, just stack two coils with
different winding densities on top of each other. If lumped rules apply,
the resonant frequency should be the same (It isn't.). You may want to
model this to have a look at Cdis.
Here's a posting I made to the list a long time ago:
Hello Terry and All,
Terry Fritz has been experimenting with coils wound with non-linear
winding pitch and observed that the distributed capacitance appears to vary
with pitch. Being skeptical of his experimental setup, etc., I did a series
of experiments last night which essentially verifies his findings.
Distributed capacitance does indeed vary if the winding pitch of the coil
varies.
I have a series of coils all closewound with enamel wire to a height
of 10.5 inches using 3.5 inch diameter acrylic forms. I stacked 2-4 of
these coils one on top of the other to simulate changing winding pitch along
the height of the coil. I will present the findings here for a stack of
three coils. The individual coil data is shown below:
Coil AWG L Fres Cdis T B
A 16 0.970 mH 2120 5.81 pF 0.75" 1.50"
B 21 3.046 mH 1210 5.68 pF 0.75" 1.25"
C 24 6.172 mH 855 5.61 pF 1.00" 1.00"
where:
AWG is the wire gauge for the closewound 3.5" x 10.5" coil
L is the inductance in millihenries (BK Precision 878 meter, 1%
accuracy)
Fres is the self-resonant frequency in kHz, measured using an HP
4193A vector
impedance meter, verified using an oscilloscope.
Cdis is the calculated distributed capacitance based on measured L
and Fres
T is the distance in inches from the top of the winding to
the top of the coil form.
B is the distance in inches from the bottom of the winding
to the bottom of the coil form.
Experiment #1 - stack coil A on top of B on top of C. Connect base of C to
signal generator through a transformer, with the other transformer lead
going to my good RF ground. The transformer is simply an iron powder toroid
with 150 turns on the primary, connected to the signal generator, and one
turn on the secondary, connected to RF ground and the base of the coil
assembly. It's purpose is to reduce the 50 ohm output impedance of my
signal generator considerably. It's frequency response is fairly flat up to
2.5 MHz or so. I measured resonance from 6 feet distance with a 'scope
probe with 12" wire antenna attached. A digital counter was used for
measuring frequency, and an HP vacuum tube oscillator was used to drive the
system. I also measured the coil assembly base impedance and phase response
using an HP 4193A vector impedance meter with the base of the coil connected
to the meter. The top of the coil was always left floating in space, and no
top toroid was employed. There is a gap between coils, and the connecting
lead between coils was spacewound in this region to even out the taper
between coils, since the base lead on each coil is approximately 3 feet
long. Coils were placed 24" above the concrete floor in my basement, at
least 6' from the test equipment.
Findings: L=10.46 mH Fres=408 kHz, Cdis=14.5 pF, Zbase=26.6 ohms at resonance.
Comments: L is greater than the sum of the individual inductances of the
coils since mutual inductance between the coils is present. All coils are
wound in the same direction. Cdis is the calculated distributed
capacitance, based on the measured L and Fres. Zbase was measured using the
HP 4193A. Note that the measured Cdis is somewhat less than the sum of the
Cdis values for the individual coils.
Experiment #2 - stack coil C on top of B on top of A. Connect the base of A
to the signal generator. Repeat the above measurements. Now the 16 AWG
coil is at the base, the 21 AWG is in the middle, and the 24 AWG is at the top.
Findings: L=10.55 mH Fres=578 kHz Cdis=7.19 pF Zbase=26.6 ohms at
resonance.
Comments: L varies from the previous value above because the coils are not
exactly centered on their coil formers (See measurements T and B above.)
Note that Zbase has not changed! In addition, the resonant frequency has
gone up considerably while at the same time Cdis has dropped to a value of
about 1.5 times the single coil value.
It appears that one can reduce Cdis substantially using a tapered
winding approach. By using large wire size or turns spacing near the
bottom, one can reduce the Cdis of the coil system. This is one of the
things that Tesla was trying to do at Colorado Springs. Since the output
voltage of a tesla coil is proportional to the square root of
Cprimary/Csecondary, any reduction in Cdis is perhaps useful. One can, for
example, use a larger Ctoroid to store more energy for those nice hot
sparks, etc. Of course, the electrostatic properties of the toroid itself
may also be altering the current distribution along the coil. The primary
coil coupling would also have to be adjusted, but that is generally no problem.
I expected Zbase to vary somewhat and was surprised to find it did
not. However, this is in the non-spark breakout mode, and base currents are
minimal. My guess is that Zbase will change a bit when the sparks start flying.
More to ponder...
Regards,
Mark S. Rzeszotarski, Ph.D., MetroHealth Medical Center,Radiology
Department, Cleveland OH 44109-1998
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.