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Re: Help with this equation!
Subject: Re: Help with this equation!
Date: Sat, 31 May 1997 13:43:53 -0700
From: "Rick L. Kirby" <rkirby-at-earthlink-dot-net>
To: Tesla List <tesla-at-pupman-dot-com>
References:
1
Tesla List wrote:
>
> Subject: Help with this equation!
> Date: Mon, 26 May 1997 21:37:07 -0400
> From: Tom Heiber <theiber-at-lonet.ca>
> Organization: Power Surge
> To: tesla-at-pupman-dot-com
>
> This is an equation I got from Bert Pool's file.
>
>
>
=======================================================================
> EQUATION 10: CAPACITANCE OF A TOROID
> ___________________
> / 2
> C =(1+ (0.2781 - d2/d1)) x 2.8 x / 2 pi (d1-d2)(d2/2)
> / -------------------
> \/ 4 pi
>
> C = capacitance in picofarads (+- 5% )
> d1 = outside diameter of toroid in inches
> d2 = diameter of cross section (cord) of toroid in inches
>
> Equation courtesy of Bert Pool
>
>
=======================================================================
>
> CAN ANYONE help me solve for D1 as in D1=........
> I have been trying to do this without any results (I suck at math)
>
> Thank You
>
> Tom Heiber
Tom
I like to make look up tables with a spread sheet for problems
like this. I will include the table I made last year using this same
equation you have above you might find it useful.
The table was too wide so I had to divide it into. The first
section is the left half and the second section is the right half.
[section 1 of table 1]
To use this table choose a dia for (d2) across the top of the table
from 1"-12". Then looking down the left side choose a dia for (d1)
from 6"-60". then look to the intersection of this row and column to
find the calculated (pf) a toroid with those diminsions.
1 2 3 4 5 6 7 8 9 10 11 12
6 6.2 6.6 5.8 4.3 2.5 na na na na na na na
7 6.9 7.8 7.3 6.1 4.4 2.6 na na na na na na
8 7.6 8.8 8.7 7.7 6.3 4.5 2.6 na na na na na
9 8.2 9.8 9.9 9.3 8.0 6.4 4.6 2.7 na na na na
10 8.8 10.7 11.1 10.7 9.7 8.2 6.6 4.7 2.8 na na na
11 9.3 11.5 12.2 12.0 11.2 10.0 8.4 6.7 4.8 2.9 na na
12 9.8 12.3 13.3 13.3 12.6 11.6 10.2 8.6 6.8 4.9 3.0 na
13 10.3 13.1 14.2 14.4 14.0 13.1 11.9 10.4 8.7 6.9 5.0 3.1
14 10.8 13.8 15.2 15.6 15.3 14.6 13.5 12.1 10.6 8.8 7.0 5.1
15 11.2 14.5 16.1 16.6 16.6 16.0 15.1 13.8 12.4 10.7 9.0 7.1
16 11.7 15.1 16.9 17.7 17.8 17.4 16.6 15.4 14.1 12.6 10.9 9.1
17 12.1 15.8 17.7 18.7 18.9 18.7 18.0 17.0 15.8 14.3 12.7 11.0
18 12.5 16.4 18.5 19.6 20.0 19.9 19.4 18.5 17.4 16.0 14.5 12.9
19 12.9 17.0 19.3 20.5 21.1 21.1 20.7 20.0 18.9 17.7 16.3 14.7
20 13.3 17.5 20.0 21.4 22.1 22.2 22.0 21.3 20.4 19.3 18.0 16.5
21 13.7 18.1 20.7 22.3 23.1 23.4 23.2 22.7 21.9 20.9 19.6 18.2
22 14.0 18.6 21.4 23.1 24.0 24.4 24.4 24.0 23.3 22.4 21.2 19.9
23 14.4 19.2 22.1 23.9 25.0 25.5 25.6 25.3 24.7 23.9 22.8 21.6
24 14.7 19.7 22.7 24.7 25.9 26.5 26.7 26.5 26.0 25.3 24.3 23.2
25 15.1 20.2 23.3 25.4 26.8 27.5 27.8 27.7 27.3 26.7 25.8 24.7
26 15.4 20.7 24.0 26.2 27.6 28.5 28.9 28.9 28.6 28.0 27.3 26.3
27 15.7 21.1 24.6 26.9 28.4 29.4 29.9 30.0 29.8 29.4 28.7 27.8
28 16.0 21.6 25.2 27.6 29.3 30.3 30.9 31.1 31.0 30.7 30.0 29.2
29 16.3 22.0 25.7 28.3 30.1 31.2 31.9 32.2 32.2 31.9 31.4 30.6
30 16.6 22.5 26.3 29.0 30.8 32.1 32.9 33.3 33.4 33.2 32.7 32.0
31 16.9 22.9 26.9 29.6 31.6 33.0 33.8 34.3 34.5 34.4 34.0 33.4
32 17.2 23.4 27.4 30.3 32.3 33.8 34.8 35.3 35.6 35.5 35.2 34.7
33 17.5 23.8 27.9 30.9 33.1 34.6 35.7 36.3 36.7 36.7 36.5 36.0
34 17.8 24.2 28.5 31.5 33.8 35.4 36.6 37.3 37.7 37.8 37.7 37.3
35 18.1 24.6 29.0 32.2 34.5 36.2 37.5 38.3 38.8 38.9 38.9 38.6
36 18.4 25.0 29.5 32.8 35.2 37.0 38.3 39.2 39.8 40.0 40.0 39.8
37 18.6 25.4 30.0 33.4 35.9 37.8 39.2 40.1 40.8 41.1 41.2 41.0
38 18.9 25.8 30.5 33.9 36.5 38.5 40.0 41.0 41.7 42.1 42.3 42.2
39 19.2 26.2 31.0 34.5 37.2 39.3 40.8 41.9 42.7 43.2 43.4 43.3
40 19.4 26.6 31.5 35.1 37.9 40.0 41.6 42.8 43.6 44.2 44.5 44.5
41 19.7 26.9 31.9 35.6 38.5 40.7 42.4 43.7 44.6 45.2 45.5 45.6
42 19.9 27.3 32.4 36.2 39.1 41.4 43.2 44.5 45.5 46.2 46.6 46.7
43 20.2 27.7 32.8 36.7 39.7 42.1 43.9 45.3 46.4 47.1 47.6 47.8
44 20.4 28.0 33.3 37.3 40.4 42.8 44.7 46.2 47.3 48.1 48.6 48.9
45 20.7 28.4 33.7 37.8 41.0 43.5 45.4 47.0 48.2 49.0 49.6 49.9
46 20.9 28.7 34.2 38.3 41.5 44.1 46.2 47.8 49.0 49.9 50.6 51.0
47 21.2 29.1 34.6 38.8 42.1 44.8 46.9 48.6 49.9 50.8 51.6 52.0
48 21.4 29.4 35.0 39.3 42.7 45.4 47.6 49.3 50.7 51.7 52.5 53.0
49 21.6 29.8 35.5 39.8 43.3 46.1 48.3 50.1 51.5 52.6 53.5 54.0
50 21.9 30.1 35.9 40.3 43.9 46.7 49.0 50.9 52.3 53.5 54.4 55.0
51 22.1 30.4 36.3 40.8 44.4 47.3 49.7 51.6 53.1 54.4 55.3 56.0
52 22.3 30.8 36.7 41.3 45.0 47.9 50.4 52.3 53.9 55.2 56.2 56.9
53 22.5 31.1 37.1 41.8 45.5 48.5 51.0 53.1 54.7 56.1 57.1 57.9
54 22.8 31.4 37.5 42.3 46.0 49.1 51.7 53.8 55.5 56.9 58.0 58.8
55 23.0 31.7 37.9 42.7 46.6 49.7 52.3 54.5 56.3 57.7 58.9 59.7
56 23.2 32.0 38.3 43.2 47.1 50.3 53.0 55.2 57.0 58.5 59.7 60.7
57 23.4 32.4 38.7 43.6 47.6 50.9 53.6 55.9 57.8 59.3 60.6 61.6
58 23.6 32.7 39.1 44.1 48.1 51.5 54.3 56.6 58.5 60.1 61.4 62.5
59 23.8 33.0 39.5 44.5 48.7 52.1 54.9 57.3 59.2 60.9 62.2 63.3
60 24.0 33.3 39.9 45.0 49.2 52.6 55.5 57.9 60.0 61.7 63.1 64.2
[section2 table 1]
Use this section same as above. It covers (d2's) from 13"-24"
with the same range of (d1's).
13 14 15 16 17 18 19 20 21 22 23 24
6 na na na na na na na na na na na na
7 na na na na na na na na na na na na
8 na na na na na na na na na na na na
9 na na na na na na na na na na na na
10 na na na na na na na na na na na na
11 na na na na na na na na na na na na
12 na na na na na na na na na na na na
13 na na na na na na na na na na na na
14 10.8 na na na na na na na na na na na
15 11.2 14.5 na na na na na na na na na na
16 11.7 15.1 16.9 na na na na na na na na na
17 12.1 15.8 17.7 18.7 na na na na na na na na
18 12.5 16.4 18.5 19.6 20.0 na na na na na na na
19 12.9 17.0 19.3 20.5 21.1 21.1 na na na na na na
20 13.3 17.5 20.0 21.4 22.1 22.2 22.0 na na na na na
21 13.7 18.1 20.7 22.3 23.1 23.4 23.2 22.7 na na na na
22 14.0 18.6 21.4 23.1 24.0 24.4 24.4 24.0 23.3 na na na
23 14.4 19.2 22.1 23.9 25.0 25.5 25.6 25.3 24.7 23.9 na na
24 14.7 19.7 22.7 24.7 25.9 26.5 26.7 26.5 26.0 25.3 24.3 na
25 15.1 20.2 23.3 25.4 26.8 27.5 27.8 27.7 27.3 26.7 25.8 24.7
26 15.4 20.7 24.0 26.2 27.6 28.5 28.9 28.9 28.6 28.0 27.3 26.3
27 15.7 21.1 24.6 26.9 28.4 29.4 29.9 30.0 29.8 29.4 28.7 27.8
28 16.0 21.6 25.2 27.6 29.3 30.3 30.9 31.1 31.0 30.7 30.0 29.2
29 16.3 22.0 25.7 28.3 30.1 31.2 31.9 32.2 32.2 31.9 31.4 30.6
30 16.6 22.5 26.3 29.0 30.8 32.1 32.9 33.3 33.4 33.2 32.7 32.0
31 16.9 22.9 26.9 29.6 31.6 33.0 33.8 34.3 34.5 34.4 34.0 33.4
32 17.2 23.4 27.4 30.3 32.3 33.8 34.8 35.3 35.6 35.5 35.2 34.7
33 17.5 23.8 27.9 30.9 33.1 34.6 35.7 36.3 36.7 36.7 36.5 36.0
34 17.8 24.2 28.5 31.5 33.8 35.4 36.6 37.3 37.7 37.8 37.7 37.3
35 18.1 24.6 29.0 32.2 34.5 36.2 37.5 38.3 38.8 38.9 38.9 38.6
36 18.4 25.0 29.5 32.8 35.2 37.0 38.3 39.2 39.8 40.0 40.0 39.8
37 18.6 25.4 30.0 33.4 35.9 37.8 39.2 40.1 40.8 41.1 41.2 41.0
38 18.9 25.8 30.5 33.9 36.5 38.5 40.0 41.0 41.7 42.1 42.3 42.2
39 19.2 26.2 31.0 34.5 37.2 39.3 40.8 41.9 42.7 43.2 43.4 43.3
40 19.4 26.6 31.5 35.1 37.9 40.0 41.6 42.8 43.6 44.2 44.5 44.5
41 19.7 26.9 31.9 35.6 38.5 40.7 42.4 43.7 44.6 45.2 45.5 45.6
42 19.9 27.3 32.4 36.2 39.1 41.4 43.2 44.5 45.5 46.2 46.6 46.7
43 20.2 27.7 32.8 36.7 39.7 42.1 43.9 45.3 46.4 47.1 47.6 47.8
44 20.4 28.0 33.3 37.3 40.4 42.8 44.7 46.2 47.3 48.1 48.6 48.9
45 20.7 28.4 33.7 37.8 41.0 43.5 45.4 47.0 48.2 49.0 49.6 49.9
46 20.9 28.7 34.2 38.3 41.5 44.1 46.2 47.8 49.0 49.9 50.6 51.0
47 21.2 29.1 34.6 38.8 42.1 44.8 46.9 48.6 49.9 50.8 51.6 52.0
48 21.4 29.4 35.0 39.3 42.7 45.4 47.6 49.3 50.7 51.7 52.5 53.0
49 21.6 29.8 35.5 39.8 43.3 46.1 48.3 50.1 51.5 52.6 53.5 54.0
50 21.9 30.1 35.9 40.3 43.9 46.7 49.0 50.9 52.3 53.5 54.4 55.0
51 22.1 30.4 36.3 40.8 44.4 47.3 49.7 51.6 53.1 54.4 55.3 56.0
52 22.3 30.8 36.7 41.3 45.0 47.9 50.4 52.3 53.9 55.2 56.2 56.9
53 22.5 31.1 37.1 41.8 45.5 48.5 51.0 53.1 54.7 56.1 57.1 57.9
54 22.8 31.4 37.5 42.3 46.0 49.1 51.7 53.8 55.5 56.9 58.0 58.8
55 23.0 31.7 37.9 42.7 46.6 49.7 52.3 54.5 56.3 57.7 58.9 59.7
56 23.2 32.0 38.3 43.2 47.1 50.3 53.0 55.2 57.0 58.5 59.7 60.7
57 23.4 32.4 38.7 43.6 47.6 50.9 53.6 55.9 57.8 59.3 60.6 61.6
58 23.6 32.7 39.1 44.1 48.1 51.5 54.3 56.6 58.5 60.1 61.4 62.5
59 23.8 33.0 39.5 44.5 48.7 52.1 54.9 57.3 59.2 60.9 62.2 63.3
60 24.0 33.3 39.9 45.0 49.2 52.6 55.5 57.9 60.0 61.7 63.1 64.2
Rick L. Kirby