# Flat vs. Cone Primary

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From:  terryf-at-verinet-dot-com [SMTP:terryf-at-verinet-dot-com]
Sent:  Sunday, June 21, 1998 10:22 PM
To:  tesla-at-pupman-dot-com
Subject:  Flat vs. Cone Primary

Hi All,

In an off-line discussion, we were talking about how much difference
there is between the coupling coefficient (K) for a flat and conical primary
coil.  I ran the numbers for my research coil as a flat spiral and a 30
degree cone.  The number of turns on the cone was reduced slightly to keep
the primary inductance the same in both cases.  The program used is a not
yet released beta version of MANDK.  My testing has shown this program to be
extraordinarily accurate for my coil.

The results are as follows:

FLAT SPRIRAL
--------------------------------------------------
Mutual Inductance Program V2.0
Copyright (c) 1998 by Mark S. Rzeszotarski, Ph.D.

Flat Spiral Primary Coil Geometry
Primary coil inside diameter (inches)=     12.000
Primary coil outside diameter (inches)=     23.340
Number of primary coil turns =     15.125
Wire diameter (inches)=      .2500

Solenoidal secondary diameter (inches)=    10.250
Secondary height (inches)=     30.000
Number of secondary coil turns =  1000.000
Secondary coil wire diameter (inches)=      .0200

Calculational results are as follows:
Primary coil inductance in microhenries:          131.76
Secondary coil inductance in microhenries:        76278.20
Secondary coil distributed capacitance in picofarads:     15.69
(Medhurst formula, assumes one end of secondary is grounded)

Position is the secondary coil bottom wire position in inches
above the bottom wire of the primary coil.
A negative value means the bottom wire of the
secondary is below the bottom wire of the primary.
A positive value means that the bottom wire of the
secondary is above the bottom wire of the primary coil.
M = Computed mutual inductance in microhenries
K = Computed Coefficient of Coupling
Position           M                K
.00          635.96            .201
.50          589.31            .186
1.00          544.25            .172
1.50          501.75            .158
2.00          462.21            .146
2.50          425.71            .134
3.00          392.18            .124
3.50          361.48            .114
4.00          333.42            .105
4.50          307.80            .097
5.00          284.44            .090
5.50          263.13            .083
6.00          243.69            .077
6.50          225.95            .071
7.00          209.76            .066
7.50          194.97            .062
8.00          181.45            .057
8.50          169.08            .053
9.00          157.74            .050
9.50          147.35            .046
10.00          137.80            .043
10.50          129.03            .041
11.00          120.96            .038
11.50          113.53            .036
12.00          106.67            .034
12.50          100.34            .032
13.00           94.49            .030
13.50           89.08            .028
14.00           84.06            .027
14.50           79.40            .025
15.00           75.08            .024
--------------------------------------------------

30 DEGREE CONE
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Mutual Inductance Program V2.0
Copyright (c) 1998 by Mark S. Rzeszotarski, Ph.D.

Inverted Cone Primary Coil Geometry
Primary coil inside diameter (inches)=     12.000
Primary coil outside diameter (inches)=     22.785
Number of primary coil turns =     14.380
Last turn elevation in inches =      2.696
Wire diameter (inches)=      .2500

Solenoidal secondary diameter (inches)=    10.250
Secondary height (inches)=     30.000
Number of secondary coil turns =  1000.000
Secondary coil wire diameter (inches)=      .0200

Calculational results are as follows:
Primary coil inductance in microhenries:          131.73
Secondary coil inductance in microhenries:        76278.20
Secondary coil distributed capacitance in picofarads:     15.69
(Medhurst formula, assumes one end of secondary is grounded)

Position is the secondary coil bottom wire position in inches
above the bottom wire of the primary coil.
A negative value means the bottom wire of the
secondary is below the bottom wire of the primary.
A positive value means that the bottom wire of the
secondary is above the bottom wire of the primary coil.
M = Computed mutual inductance in microhenries
K = Computed Coefficient of Coupling
Position           M                K
.00          704.76            .222
.50          661.07            .209
1.00          617.07            .195
1.50          574.00            .181
2.00          532.63            .168
2.50          493.37            .156
3.00          456.47            .144
3.50          422.01            .133
4.00          390.00            .123
4.50          360.39            .114
5.00          333.08            .105
5.50          307.96            .097
6.00          284.90            .090
6.50          263.75            .083
7.00          244.36            .077
7.50          226.61            .071
8.00          210.35            .066
8.50          195.46            .062
9.00          181.82            .057
9.50          169.32            .053
10.00          157.86            .050
10.50          147.34            .046
11.00          137.67            .043
11.50          128.79            .041
12.00          120.62            .038
12.50          113.09            .036
13.00          106.15            .033
13.50           99.74            .031
14.00           93.83            .030
14.50           88.35            .028
15.00           83.28            .026
--------------------------------------------------

Terry Fritz

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