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Re: Arc length vs pwr
>>
>> If Cp is large enough so that the sec ckt can be treated as lumped
>> elements, then shouldn't we worry about the toroid acting as a
>> shorted turn, shunting the secondary inductor?
>>
Greg and Malcolm,
Awhile ago Mark R. posted some calculations showing the
coefficient of coupling between the primary and secondary for various
heights. At 8" the K was 0.068. So the toroid will not act as a
shorted secondary. I'll include Mark's post.
jim
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To: tesla-at-grendel.objinc-dot-com
From: MSR7-at-PO.CWRU.EDU (Mark S. Rzeszotarski, Ph.D.)
Subject: Primary Coil Topologies Part 2/2
Hello Coilers,
Here is the second part relating to tesla coil primary
geometries.
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 K, the coupling
coefficient between the primary and secondary. A companion posting
provides
insight into how the primary bathes the secondary.
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)= 26.25
Number of secondary coil turns = 860
Secondary coil wire diameter (inches)= .0285
Primary coil inductance in microhenries: 48.01
Secondary coil inductance in microhenries: 39720.50
Secondary coil capacitance in picofarads: 13.08
Position is secondary coil bottom turn position in inches
above bottom turn of primary coil
M = mutual inductance in microhenries
K = coupling coefficient
Position M K
.00 319.28 .231
1.00 276.84 .200
2.00 237.45 .172
3.00 202.73 .147
4.00 172.99 .125
5.00 147.86 .107
6.00 126.77 .092
7.00 109.12 .079
8.00 94.34 .068
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)= 26.25
Number of secondary coil turns = 860
Secondary coil wire diameter (inches)= .0285
Primary coil inductance in microhenries: 51.79
Secondary coil inductance in microhenries: 39720.50
Secondary coil capacitance in picofarads: 13.08
Position is secondary coil bottom turn position in inches
above bottom turn of primary coil
M = mutual inductance in microhenries
K = coupling coefficient
Position M K
.00 388.29 .271
1.00 347.99 .243
2.00 307.43 .214
3.00 268.97 .188
4.00 233.89 .163
5.00 202.68 .141
6.00 175.35 .122
7.00 151.70 .106
8.00 131.37 .092
Solenoidal Primary Coil Geometry
Primary coil diameter (inches)= 18.75
Number of primary coil turns = 9
Last turn elevation in inches = 6.75
Wire diameter (inches)= .3750
Solenoidal secondary diameter (inches)= 8.00
Secondary height (inches)= 26.25
Number of secondary coil turns = 860
Secondary coil wire diameter (inches)= .0285
Primary coil inductance in microhenries: 49.64
Secondary coil inductance in microhenries: 39754.23
Secondary coil capacitance in picofarads: 13.08
Position is secondary coil bottom turn position in inches
above bottom turn of primary coil
M = mutual inductance in microhenries
K = coupling coefficient
Position M K
.00 299.51 .213
1.00 278.66 .198
2.00 256.01 .182
3.00 232.21 .165
4.00 208.02 .148
5.00 184.23 .131
6.00 161.58 .115
7.00 140.65 .100
8.00 121.82 .087
Coupling Coefficient K Versus Secondary Coil Position
-
.24 | -
+
x -
| *
.19 | -
| *
| x -
| + x
| -
.13 | + x -
| x
| + *
| + *
| +
.06 | +
|
|
|
|
.00 |
+---------+---------+---------+---------+---------+---------+-
0 5 10 15 20 25
30
+=flat pancake, -=saucer, x=solenoid, *=overlapping data
Y-axis = Coupling coefficient (K)
X-axis = distance in inches from bottom turn of secondary coil
to bottom turn of primary coil
The solenoidal coil diameter was selected so that the primary
coil
inductance was approximately equal to that of a flat spiral, using the
same
number of turns, same wire size and same wire spacing.
Most people who use solenoidal primaries use a smaller diameter than
this,
which will increase coupling somewhat (often, too much).
The mutual inductance M is computed using the integration
formula of
Neumann, as described in Grover's text on inductance. The formula for
inductance for a saucer is based on an average between the inductance
of a
flat spiral and a solenoid, using appropriate geometric factors to
account
for the shape.
Conventional tesla coils use coupling coefficients between .05
and .20 or
so. Some of you high power folks use even higher K values, especially
if
you've got one or more of those high efficiency pulse discharge
capacitors.
I think Richard Hull's old Nemesis coil used a K=0.23 or so.
I am planning on a K=.18-.20, which implies positioning the
secondary coil about 1-2 inches above the primary, for a flat spiral
geometry.
Note that the saucer geometry is less critical with respect to
position. The inverted cone also provides higher coupling than a flat
spiral, which is not unexpected. However, the gain is small for a
large
diameter coil like this. Other considerations like strike distances
may
also impact your choice of geometries. For smaller diameter coils,
where
the total secondary inductance is much smaller, an inverted cone or
solenoidal geometry becomes more useful if critical coupling is to be
attained.
Comments?
Regards,
Mark S. Rzeszotarski, Ph.D.