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



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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