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Flat vs. Cone Primary




----------
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
--------------------------------------------------
 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