[Prev][Next][Index][Thread]

Re: Ctop Measurement vs. Calculation

Hi Bart,

	A coil's resonant frequency is affected by the surroundings, primary, and
all the physical dimensions of the coil as well as the secondary's
inductance.  The capacitances of just a sphere or toroid are correct but
when you place them on top of a coil, the electrostatic fields of the
terminal and coil combine in a complex way that cannot be predicted easily.  

The program E-Tesla5 can find the resonant frequency given all the physical
dimensions and the secondary inductance by massive finite element analysis.
 It can easily find Fo within 5%.  It is the only way I know to accurately
predict a secondary system's Fo frequency by calculation (although Robert
Jones may change that ;-)).  It is at:

http://users.better-dot-org/tfritz/site/programs/E-TESLA5.ZIP

It also outputs files that can do field plots in Excel so one can see how
the fields look around a given coil.  I ran your 12.5 x 44 inch 87.6mH coil
with the 16 inch sphere 55 inches(center) above the floor and got the
following from the program predicting 30.5pF at 97.4kHz.  I had to guess as
some of the dimensions but it still gets very close to what you measured.

======================
 E-TESLA  V5.11  April 6, 2000  Terry Fritz
  
17:44:25      05-22-2000
  
 Grid Size =  120 
 Scale Multiplier =  1 
 Terminated Coil
 Ceiling Distance =  150 
 Wall Distance =  75 
 Primary Height (Inner Turn) =  0 
 Primary Inner Diameter =  20 
 Primary  Outer Diameter =  30 
 Primary Height (Outer Turn) =  0 
 Secondary Base Height =  1 
 Secondary Diameter =  12.5 
 Secondary Length =  44 
 Secondary Inductance =  .0876 
 Terminal-1 Height (center) =  55 
 Terminal-1 Radius =  8 
 Terminal-1 Diameter (torroid only)=  0 
 Terminal-2 Height (center) =  55 
 Terminal-2 Radius =  0 
 Terminal-2 Diameter (torroid only)=  0 
 Top Voltage =  1 
  
  
 Pass    Ccalc (pF)          % Change            Fcalc (Hz)
  
 100     C= 1.609433          1509.433           F = 423868.9 
 200     C= 6.196862          285.0338           F = 216014.1 
 300     C= 11.15313          79.98034           F = 161016.2 
 400     C= 15.12293          35.59352           F = 138277.1 
.
.
.
 3100    C= 30.45542          .1032601           F = 97439.66 
 3200    C= 30.48271          8.960858E-02       F = 97396.03 
=====================

I ploted the fields in MathCad and posted the graphic at:

http://users.better-dot-org/tfritz/site/misc/Bart01.gif

Cheers,

	Terry



At 11:19 PM 5/21/00 -0500, you wrote: 
>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!)
>