[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: A new Tesla coil and k measurements



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

Tesla list wrote:
 >
 > Original poster: "Paul Nicholson by way of Terry Fritz 
<teslalist-at-qwest-dot-net>" <paul-at-abelian.demon.co.uk>

 > Yes.  You can always just compute the self L with the same routine
 > that does the mutual.  When you come to need the self L of each
 > element, resort to a formula for the approximately straight line
 > segments.  Perhaps if you have enough elements, you can just leave
 > out the self L of each, for only a small error.  The alternative
 > of using a bundle of filaments is non-trivial.

This gives a value close to the expected, but theoretically
incorrect, as the inductance of a filamental coil is infinite.
Returning to the origins, I was looking at Maxwell's book,
and found item 693:

"In calculating the coefficient of self-induction of a coil of
uniform section, the radius of curvature being great compared
with the dimensions of the transverse section, we first determine
the geometrical mean of the distances of every pair of points
of the section by the method already described, and then we
calculate the coefficient of mutual induction between two linear
conductors of the given form, placed at this distance apart."

In the same page, the required distance for a round wire transporting
uniform current is given as a*exp(-0.25) = 0.77888*a, where a is the
radius of the wire. There is also an expression for current in a
ring around the wire, that seems a good way to take skin effect
into account.
I tested this method with some coils, and the obtained values look
very good. It's only necessary to define two identical coils with their
bases at this distance, vertically, and compute their mutual inductance
by Neumann's formula. Looks even simple enough for an exact analytical
solution. If the loops are approximated as closed circles, the same book
gives the closed-form solution in item 701. Looks useful for secondary
coils, where the numerical integration is impractical and the loops
are closely circular.
I am implementing an accelerated version for solenoids, where the
identical loops allow great simplifications. Unfortunately, the
simplifications don't appear for flat or conical spirals.
Ex:
The coil that I use as primary in my transformerless Tesla coil:
http://www.coe.ufrj.br/~acmq/tesla/mres5l1.jpg
34 turns, height=0.121, radius=0.0455, wire diameter=0.0015
Vertical displacement: 0.0005841
Inductance:
Measured: 60.0 uH (including wiring)
Wheeler:  58.34 uH
Maxwell:  58.43 uH (Neumann, Euler method With 800 segments per turn)
Fantc:    57.95 uH
Using Maxwell's method in Fantc: 57.95 uH
Acmi:     57.87 uH
Using Maxwell's method in Acmi: 56.53 uH

Antonio Carlos M. de Queiroz