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Re: Wire Length (fwd)
Original poster: Gerry Reynolds <greynolds@xxxxxxxxxx>
---------- Forwarded message ----------
Date: Thu, 21 Dec 2006 20:14:26 -0800
From: Barton B. Anderson <bartb@xxxxxxxxxxxxxxxx>
To: Tesla list <tesla@xxxxxxxxxx>
Subject: Re: Wire Length (fwd)
Hi Paul,
Excellent! Thanks for running the numbers. I should be able to perform
the measurements you discussed once the coil is ready. The comparison
between inner and outer grounded configurations noting the current
maximums are interesting, especially the rim grounded case where the
current rise to max is in the first few turns.
For the primary, I planned on using about 30 feet of copper ribbon,
about 2 turns. I was planning on the ribbon starting about 1" proximity
and to be wound in the same direction and on the same horizontal plane
of the secondary with 0.375" spacing between the 2 turns. So, just
imagine the ribbon as an extension of the secondary with the joint of
the two coils to be grounded. The ribbon itself is small but should be
sufficient. The ribbon dimensions are .007 x .375.
BTW, in Javatc I don't allow for the rim grounded situation (geometry
error). There are reasons for this but may not be needed with this
particular coil configuration (I'll have to check that out). I was able
to perform the model with Fantc however with no problems, however,
numbers are quite a bit off from your sim software. Ex; Lee came out to
7.5mH, 495kHz. This was using the highest resolution Fantc allows.
Take care,
Bart
Tesla list wrote:
>Original poster: Gerry Reynolds <greynolds@xxxxxxxxxx>
>
>
>
>---------- Forwarded message ----------
>Date: Thu, 21 Dec 2006 13:28:34 GMT
>From: Paul Nicholson <paul@xxxxxxxxxxxxxxxxxxx>
>To: tesla@xxxxxxxxxx
>Subject: Re: Wire Length (fwd)
>
>Bart wrote:
>
>
>
>>1.8125 = Radius 1
>>24.4375 = Radius 2
>>50 = Height 1
>>50 = Height 2
>>91 = Turns
>>18 = Wire Awg
>>
>>
>
>I ran this planar spiral through simulation software:-
>
>Mode frequencies - unloaded
>---------------------------
> Center ground Rim ground
>f1 388.6 kHz 464.2 kHz
>f3 1164 kHz 1236 kHz
>f5 1904 kHz 1972 kHz
>
>Low frequency (bulk) L and C
>----------------------------
>Ldc 4.205 mH
>Cdc 51.68 pF
>
>Equivalent L and C
>------------------
> Center ground Rim ground
>Lee @ f1 5.62 mH 9.99 mH
>Les @ f1 4.82 mH 6.18 mH
>
>Cee @ f1 40.5 pF 30.7 pF
>Ces @ f1 34.8 pF 19.0 pF
>
>V/I distributions
>-----------------
>(In these plots, the position given is the percentage turns from
> the cold end)
>
> Center ground:-
> http://www.abelian.demon.co.uk/tmp/baps-cg.f1.gif
> http://www.abelian.demon.co.uk/tmp/baps-cg.f3.gif
> http://www.abelian.demon.co.uk/tmp/baps-cg.f5.gif
>
> Rim ground:-
> http://www.abelian.demon.co.uk/tmp/baps-rg.f1.gif
> http://www.abelian.demon.co.uk/tmp/baps-rg.f3.gif
> http://www.abelian.demon.co.uk/tmp/baps-rg.f5.gif
>
>The f5 plots are looking a bit crumpled in places - limited
>spatial resolution of internal capacitance and small number
>of turns is the cause.
>
>In both configurations the highest voltage gradients per turn
>are occuring in the outer half of the winding.
>
>Bart, if you've settled on a primary design, I can try to
>predict the mode amplitudes and the time domain response.
>
>The effective series inductance at f1 (quarter wave resonance)
>in the rim-grounded configuration is almost 50% higher than the
>DC inductance. Look at the current distribution to see why: the
>current reaches a max at about 15% of the way into the coil,
>at which point the current is about twice the rim current.
>The induced voltage due to this extra current (brought about
>by internal C coupling between outer and inner parts of the
>winding) adds to the total voltage induced across the coil for
>a given rim current, ie the effective inductance is pushed up.
>
>If Bart can inject a measured current at f1 into the rim
>and simultaneously measure the center voltage, he should be
>able to confirm this effective inductance.
>
>Even more dramatic is the increase in the energy storage
>effective inductance (Lee) which is over twice the DC
>inductance!
>
>(The need for separate effective inductances to represent
>the induced voltage (Les) and stored energy (Lee) is one of
>the many subtleties arising from a non-uniform current
>distribution in a coil).
>
>Lee can be measured by a simultaneous measurement of input
>impedance (as seen looking into the rim) and Q factor.
>Then calculate
>
> Lee (measured) = (Q * Zin)/(2 * pi * Fres)
>
>This is a tricky pair of measurements to do accurately, but
>the sheer size of Lee compared to Ldc might enable Bart to
>demonstrate this point with the instruments he has available.
>
>See
>
> http://www.abelian.demon.co.uk/tssp/pn2511.html
>
>section 7 for definitions of these effective reactances.
>
>Let's compare the DC inductance with the (Wheeler, 1928)
>approximate formula posted by Shaun,
>
> (NR)^2
> L = -----------------
> 8R + 11W
>
>Here, W = 24.4375 - 1.8125 = 22.625 inches
> R = (24.4375 + 1.8125)/2 = 13.125 inches
>
>which gives L = 4.03 mH, an error of -4% compared with our
>more accurate calculation of 4.205 mH, so not bad at all.
>
>--
>Paul Nicholson
>--
>
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