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Re: Winding vs Space-Charge Capacitance


From: 	Mark S. Rzeszotarski, Ph.D.[SMTP:msr7-at-po.cwru.edu]
Sent: 	Monday, November 03, 1997 4:54 AM
To: 	Tesla List
Subject: 	Re: Winding vs Space-Charge Capacitance

Hello Terry and All,
Terry said:   
>     Testing I have done on secondary coils with no top toroid suggests that
>the secondary inductor's capacitance is composed of two main capacitances in
>parallel.  The first capacitance is internal to the coil winding itself and
>is probably composed of turn-to-turn capacitance.  The second capacitance is
>a large space-charge region that is developed around the top end of the
>coil.  The first capacitance is in the order of 0.25 pF while the second
>capacitance is on the order of 6.3 pF.  
>
>Coil length 29.0 inches
>Diameter 4.25 inches
>1000 turns #30 wire
>Non-Linear (winding pitch proportional to cos(x))
>inductance 16.06 mH
>Fo 496.2 KHz (no top terminal)
>Rac ~108 ohms
>Q ~460
>
>Note: Rac and Q may be inaccurate (unproven test methods).
>
>If this is true than it would suggest a number of possibilities to optimize
>output voltage.  I am surprised that the turn-to-turn capacitance is so low.
>This is one of my non-linear wound coils but if the turn-to-turn capacitance
>is this low, I should be concentrating on field patterns and forget the
>internal capacitances.  I haven't cross-checked these results so I may have
>a measurement problem or something.  
>
>        Does anyone have any comments on these results or comments on the
>small turn-to-turn capacitances I seem to be seeing.

        First, your comment that the turn-to-turn capacitance is low seems
appropriate based on some measurements I took on a series of 3.5 inch
diameter by 10.5 inch length closewound coils, each wound with a different
gauge wire:
16 AWG  Fres=2103 kHz   Ls= 0.98 mH   Cdis=5.84 pF
21 AWG  Fres=1196 kHz   Ls= 3.05 mH   Cdis=5.81 pF
24 AWG  Fres= 835 kHz   Ls= 6.17 mH   Cdis=5.89 pF
28 AWG  Fres= 530 kHz   Ls=15.12 mH   Cdis=5.96 pF
        The distributed capacitance may be increasing very slightly as the
turns get closer together, but represents a small effect in these results.
        Your overall results are consistent with what I would expect to see
from a non-linear wound coil, based on measurements I took on the coils you
sent me and some other experiments I have done since then.  If the base of
the coil is attached to a good RF ground and the top of the coil is left
unconnected, then the potential between earth and any given turn can
increase as the elevation above the earth increases.  Assuming a sinusoidal
current and voltage distribution on the coil in steady state, then the turn
to turn voltage difference (I times R) will be greatest at the base, where
the current is high, and lowest at the top, where the current is a minimum.
However, your nonlinear space winding results in a large distance between
adjacent turns near the base of the coil (Your turn to turn spacing is more
than three wire diameters at the base of the coil.), so the overall
capacitance should be low in this region, since capacitance between two
conductors depends strongly on 1/r (or worse), as well as the dielectric and
the potential difference between the adjacent conductors.  Flipping the
nonlinear coil upside down so the closewound turns are in the high current
region significantly drops the resonant frequency, implying that capacitance
has increased.  This means that the distance factor may be the most
important, since the total coil former surface area is the same in both
cases.  The overall effect is small if the Rac of the wire is kept low in
the high current region near the base of the coil.  (BTW, I would expect to
observe a Rac of at least 240 ohms for this coil, probably a bit higher.)  
        The second part of distributed capacitance is the isotropic
component, which appears to be based more on the volume of surface covered
by the wire.  It is relatively independent of turns spacing and wire size
(See above results).  I have built toroids out of metal "Slinky" toys, which
consist of a coil of wire which can be formed into a torus.  The capacitance
of the toroid is about the same as that of a solid metal surface.  Some of
the big boys have built top capacitance based on a number of smaller
components like clustered spheres as well.  This more global electric field
shaping seems to be the important component.  As a result, I suspect the
coil surface area is most dominant, and is why Medhurst's capacitance
formula works well for linear-wound coils.

Flame on,
Mark S. Rzeszotarski, Ph.D.