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Primary Coil Topologies Part 1/2
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To: tesla-at-grendel.objinc-dot-com
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Subject: Primary Coil Topologies Part 1/2
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From: MSR7-at-PO.CWRU.EDU (Mark S. Rzeszotarski, Ph.D.)
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Date: Fri, 15 Mar 1996 06:45:55 -0500
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>Received: from slc5.INS.CWRU.Edu (slc5.INS.CWRU.Edu [129.22.8.107]) by uucp-1.csn-dot-net (8.6.12/8.6.12) with ESMTP id EAA29470 for <tesla-at-grendel.objinc-dot-com>; Fri, 15 Mar 1996 04:46:17 -0700
Hello Coilers,
I though I would post the results of a couple computer simulations
of the interaction between the primary and secondary of a conventional tesla
coil to perhaps answer some questions, and certainly to raise some
discussion. The results are in two parts to reduce the clutter.
Tesla Primary Coil Simulation - Mark S. Rzeszotarski, Ph.D. - 3/15/96
In this posting, the results of a computer simulation of three primary coil
geometries are explored. The parameter of interest is M, the mutual
inductance between the primary and secondary. This determines how much
energy can be transferred from the primary to the secondary. This series of
examples and accompanying graph illustrate how the primary coil bathes the
secondary coil.
In this example, the secondary coil consists of an 8 inch diameter form,
but the secondary coil is only 1 inch tall. What we can observe from this
simulation is how a conventional tesla primary interacts with a secondary
coil at various locations along the length of the typical secondary, using
the small one inch coil as a delta-L piece of a larger coil in this model.
What you observe is that most of the energy is coupled into the
secondary near the bottom of the coil, which is preferred if we assume that
phase changes are occurring along our quarter wave helical resonator
secondary as one moves away from the grounded end. Ideally, we would like
to dump all of the energy in to the bottom turn of the secondary (similar to
the extra coil concept Tesla employed). However, we also want to provide
"appropriate" coupling so that maximum energy transfer occurs. To examine
the coupling between the primary and secondary, see the companion posting.
Three coil geometries are explored: flat spiral, inverted cone or saucer,
and solenoidal. Typical coil sizes are employed in this simulation to fire
a secondary with overall length of 26.25 inches using 21 AWG gauge wire,
operating at about 130-150 kHz with a .025 uF primary capacitance. The
primary coil is assumed to be wound with 3/8 inch copper tubing. (These
parameters happen to match a coil I am constructing.)
Flat Spiral Primary Coil Geometry
Primary coil inside diameter (inches)= 12.00
Primary coil outside diameter (inches)= 25.50
Number of primary coil turns = 9
Wire diameter (inches)= .3750
Solenoidal secondary diameter (inches)= 8.00
Secondary height (inches)= 1.00
Number of secondary coil turns = 33
Secondary coil wire diameter (inches)= .0285
Primary coil inductance in microhenries: 48.01
Secondary coil inductance in microhenries: 425.33
Secondary coil capacitance in picofarads: 17.78
Position is secondary coil bottom turn position in inches
above bottom turn of primary coil
M = mutual inductance in microhenries
Position M
.00 43.82
1.00 40.66
2.00 35.86
3.00 30.78
4.00 26.07
5.00 21.94
6.00 18.43
7.00 15.49
8.00 13.05
9.00 11.04
10.00 9.37
11.00 7.99
12.00 6.84
13.00 5.89
14.00 5.09
15.00 4.43
16.00 3.86
17.00 3.38
18.00 2.98
19.00 2.63
20.00 2.34
21.00 2.08
22.00 1.86
23.00 1.67
24.00 1.50
25.00 1.35
26.00 1.22
27.00 1.11
Saucer-Shaped Spiral Primary Coil Geometry
Primary coil inside diameter (inches)= 12.00
Primary coil outside diameter (inches)= 25.50
Number of primary coil turns = 9
Last turn elevation in inches = 4.75
Wire diameter (inches)= .3750
Solenoidal secondary diameter (inches)= 8.00
Secondary height (inches)= 1.00
Number of secondary coil turns = 33
Secondary coil wire diameter (inches)= .0285
Primary coil inductance in microhenries: 51.79
Secondary coil inductance in microhenries: 425.33
Secondary coil capacitance in picofarads: 17.78
Position is secondary coil bottom turn position in inches
above bottom turn of primary coil
M = mutual inductance in microhenries
Position M
.00 42.04
1.00 42.15
2.00 39.90
3.00 36.39
4.00 32.40
5.00 28.41
6.00 24.64
7.00 21.22
8.00 18.20
9.00 15.57
10.00 13.32
11.00 11.39
12.00 9.76
13.00 8.39
14.00 7.23
15.00 6.25
16.00 5.42
17.00 4.72
18.00 4.12
19.00 3.62
20.00 3.19
21.00 2.82
22.00 2.50
23.00 2.22
24.00 1.99
25.00 1.78
26.00 1.60
27.00 1.44
Solenoidal Primary Coil Geometry
Primary coil diameter (inches)= 18.75
Number of primary coil turns = 9
Coil Height in inches = 6.75
Wire diameter (inches)= .3750
Solenoidal secondary diameter (inches)= 8.00
Secondary height (inches)= 1.00
Number of secondary coil turns = 33
Secondary coil wire diameter (inches)= .0285
Primary coil inductance in microhenries: 49.64
Secondary coil inductance in microhenries: 426.62
Secondary coil capacitance in picofarads: 17.78
Position is secondary coil bottom turn position in inches
above bottom turn of primary coil
M = mutual inductance in microhenries
Position M
.00 22.25
1.00 23.92
2.00 24.96
3.00 25.25
4.00 24.76
5.00 23.53
6.00 21.73
7.00 19.56
8.00 17.24
9.00 14.96
10.00 12.85
11.00 10.97
12.00 9.34
13.00 7.95
14.00 6.78
15.00 5.79
16.00 4.97
17.00 4.28
18.00 3.70
19.00 3.21
20.00 2.80
21.00 2.45
22.00 2.16
23.00 1.91
24.00 1.69
25.00 1.50
26.00 1.34
27.00 1.20
Graph of Mutual Inductance Versus Secondary Coil Position
50.00 |
|
+
- -
39.47 | + -
| + -
|
| + -
| -
26.32 | x +
| x x x x -
x + x -
| + x *
| + *
13.16 | + *
| + + * *
| + + * *
| + + x * * -
| + + * x x x x x x x * -
.00 | + *
+---------+---------+---------+---------+---------+---------+-
0 5 10 15 20 25 30
+=flat pancake, -=saucer, x=solenoid, *=overlapping data
Y-axis = Mutual Inductance in microhenries
X-axis = distance in inches from bottom turn of primary coil
to bottom turn of secondary coil
The solenoidal mutual inductance is maximized when the 1 inch tall
secondary coil is centered in the 6.75 inch tall secondary. This is not
seen in a typical secondary coil, which is normally much longer than the
primary coil. See the companion posting for overall results for a
full-length secondary coil including coupling considerations.
The conclusion one can draw from this is that for a large diameter coil (8
inches is large?), there is only a little to be gained by using a saucer
geometry versus a flat spiral, in terms of bathing the secondary. (More on
this in the companion posting.) It does become much more important in the
case of a small diameter coil, where the total secondary inductance is quite
low, and sufficient coupling is more difficult to achieve.
Comments?
Regards,
Mark S. Rzeszotarski, Ph.D.