Re: [TCML] toroids instead of spheres - why?

[Jim Lux <jimlux@xxxxxxxxxxxxx>]

On 8/22/13 4:48 AM, Scott Bogard wrote:
> I'm not sure which document you are referencing, but if I am not mistaken,
> a toroid typically has a larger capacitance for a given breakdown voltage
> does it not?  IT also has far superior top turns shielding characteristics
> which is why we use them so much; I believe this has to do with the E-field
> shape though and not the capacitance.

Yes, toroids will give a more "uniform" field along the secondary.  An 
infinite flat plate would be ideal, of course, but a toroid is a nice 
way to get an edge on the flat plate while keeping the field at the edge 
high enough that breakdown doesn't occur too soon, allowing more charge 
to be stored.  You could have a Rogowski type profile on the bottom of a 
sort of hemispherical electrode.  That's a flat plate that has a rolled 
edge, where the field is greatest in the flat plate part and gradually 
decreases.

http://home.earthlink.net/~jimlux/hv/rogowski.htm


However, for a given diameter, a sphere has larger capacitance than a 
toroid.
C(pF) for sphere is 4*pi*8.85*radius in meters.
An approximate formula from Bert Pool for a toroid (sorry for the change 
in units to inches) is
C(pf) = (1 + (.2781 - d2 / d1)) x 2.8 x sqrt ( pi( ( d1 - d2 ) ( d2 / 2 
)) / 2)

d1 = outside diameter of toroid in inches
d2 = diameter of cross section (cord) in inches

Some practical numbers.. a 36" diameter sphere has a C of about 50pF, a 
36" diameter toroid with 18" "tubes" has 35 pF capacitance. With 8" 
tubes (and a 20" disk in the middle) about 39 pF

>
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