RE: Inductance of a conical coil

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Original poster: "John H. Couture by way of Terry Fritz <teslalist-at-qwest-dot-net>" <couturejh-at-mgte-dot-com>


Antonio -

I ran into this conical primary problem when i was developing the JHCTES
computer programs. I found that there was no difference in the inductance of
the spiral, solenoid or conical primaries provided you used the correct
parameters.

For example the JHCTES Ver 3.3 program uses the Wheeler spiral equation for
the spiral inductance. The program also uses the Wheeler solenoid equation
for the solenoid inductance. These two equations have been found to be
resonably accurate when compared to actual tests. You can use the JHCTES Ver
3.3 program to compare the primary in a flat spiral, conical, or solenoid
form.

If you go to the JHCTES Ver 3.3 on-line program you will find the default
example for a primary spiral has an inductance = 43.93 uh, 10 turns, 37 ft
length, 0.5 inch c/c spacing,  coupling =0.195 K.

You will get the same outputs as the spiral coil for a solenoid coil if you
click on the coil target and  make the avg radius = 7.0 inches, and the coil
height = 5.0 inches. Click "Caculate" and in the outputs Inductance = 43.93,
10 turns, 37 ft length, 0.5 inches c/c spacing, coupling = 0.197 K.

In other words there is always a solenoid coil that will be the equivalent
to a spiral coil with the same inductance, turns, length, spacing, and
coupling. This means there will always also be a conical coil with the same
inductance. That is the transistion from spiral to solenoid would include
the conical coil provided they have the proper parameters.

The numerator in both of the Wheeler equations is the same. The denominators
are  only slightly different. It is easy to allow for this difference in the
JHCTES program to get the primary inductances to be equal.

It all boils down to what you consider the parameters of the solenoid or
conical coils should be as an equivalent spiral coil.
It should be noted that for the conical coil the flat spiral is turned with
the center of the coil width as the axis. Therefore, the primary radius is
always the same for all three primary types.

I believe the spiral, solenoid, and conical coils all have the same
inductance provided they all have the same approximate  physical parameters.

John Couture

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


-----------Original Message-----
From: Tesla list [mailto:tesla-at-pupman-dot-com]
Sent: Saturday, February 22, 2003 10:22 PM
To: tesla-at-pupman-dot-com
Subject: Inductance of a conical coil


Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz
<teslalist-at-qwest-dot-net>" <acmq-at-compuland-dot-com.br>

Hi:

I was reviewing the archives looking for a good approximate
formula for the inductance of a conical coil. There was a
discussion years ago, but didn't come to a conclusion. That
formula that makes an average between the Wheeler approximations
for solenoids and flat coils is very poor. The Wheeler formula
for flat coils is also poor.
What would be the best formulas now?

By the way, I have added mutual inductance calculation to my
Teslasim design/simulation program.
http://www.coe.ufrj.br/~acmq/programs

Antonio Carlos M. de Queiroz