Ctop Measurement vs. Calculation

• To: tesla-at-pupman-dot-com
• Subject: Ctop Measurement vs. Calculation
• From: "Barton B. Anderson" <tesla123-at-pacbell-dot-net> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)
• Date: Mon, 22 May 2000 07:56:52 -0600
• Approved: twftesla-at-uswest-dot-net
• Delivered-To: fixup-tesla-at-pupman-dot-com-at-fixme

Dr. R, Ed S., all, 

I was experimenting a little this weekend with a sphere top capacitance.
The sphere is 16" in diameter on top of my 12.5" x 44" secondary. D.C., I
was referencing a post you sent to the list a long time ago. You measured
the capacitance of a few spheres and toroids on an insulated column. Here's
the data you posted: 

7 inch dia sphere - - - - - - - - - 14pF 
14 inch dia sphere - - - - - - - -  22pF 
30 inch dia sphere - - - - - - - -  44pF 
40 inch dia sphere - - - - - - - -  60pF 

1.75 x 7 toroid - - - - - - - - - -  9pF 
8 x 3 toroid - - - - - - - - - - -  11pF 
12 x 3 toroid - - - - - - - - - - - 16pF 
14 x 4 toroid - - - - - - - - - - - 25pF 
24 x 6 toroid - - - - - - - - - - - 38pF 
34 x 8.5 toroid - - - - - - - - - - 50pF 
48 x 12 toroid - - - - - - - - - -  67pF 

The sphere I used is nowhere near the values above. My sphere (16") should
be near 24pF (comparing to your 14" sphere above). However, using a large
loop antenna and scope, I measured a near perfect 100kHz (the waveform was
beautifully locked on). It should have been about 79kHz (Ls = 87.6mH , Cs =
21.6pF). It appears Ctop was only 9pF. This is far from what I expected. I
expected some error from self distribution, but not this much. Sphere was
set directly on top of the coil and run without breakout long enough to
obtain measurements. I did this several times and got the same results
using both 0.02uF and 0.04uF tank cap sizes (retuning). 

Also, I was looking at the measurements above and calcing Sphere Ctop using
1.414 x diam. At 14", the error is 30% but gets close with the 30" and 40"
spheres. Is the equation incorrect? Is there a more accurate equation I'm
not aware of? 

The toroid calculated values were worse. Errored 16% to 37%. 

The calculation used was: 
CpF = ((1+(.2781-d2/d1))x2.8)*(sqrt(2pi^2(d1-d2)*(d2/2)/4pi)) 
d1 is the outer diameter of the toroid. 
d2 is the diameter of the cross section. 

If others have done similar tests, what were the results? 

Thanks in advance, 
Bart (happy to be coiling again!)

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