Re: Inductance calculations

["Tesla list" <tesla-at-pupman-dot-com>]

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: "Barton B. Anderson by way of Terry Fritz 
<teslalist-at-qwest-dot-net>" <classictesla-at-netzero-dot-com>
 >
 > Hi Antonio,
 >
 > Ok, checking "Maxwell L" and "Elliptic fun" I get 45.96uH. I downloaded,
 > unzipped, and ran Steve Moshier's coil program. There certainly is
 > consistency between programs for the inductances identified. I ran each,
 > changing only heights to get a few rows of data ( r1r2=.5m, wd=.002m, t=5).
 >
 > ht      Fantc   Acmi    MandK  |  Inca     Moshier
 > 0.2m    39.35   39.32   39.44  |  45.96    46.38
 > 0.5m    25.87   25.84   25.93  |  35.29    35.74
 > 0.75m   20.45   20.43   20.50  |  31.11    31.60
 > 1.0m    16.96   16.93   16.99  |  28.48    29.04

With the version now in my site the numbers will be a bit different,
because I improved the precision of the elliptic functions:
46.43, 35.75, 31.57, 28.94
Even closer to Moshier, but our methods are very different.
Numerical integration with 5000 segments/turn gives:
46.41, 35.77, 31.64, 29.09
So, the formula used in the coil program appears to take the spiral
into account. Better than my rather dumb integrals that take forever
to finish. I will try the formula in Moshier's program with my elliptic
functions to see if they agree.

 > Maybe Paul can identify what is going on. Moshier's c-source is included
 > and appears well written and documented with referecences. I ran geometry 8
 > (Single-layer circular helical solenoid of round wire). coil.c points for
 > geo 8 points to "helsol" located in "formulae.c". There, Moshier references
 > Chester Snow '1952. I'm looking for papers on C. Snow but I'm not finding
 > much other than references. Somethings wrong on one side of the line or the
 > other if all are representing the same inductance inclusions.

The problem appears when the number of turns is small.
Testing a flat spiral, varying the external radius:
Internal radius = 0.50, wire diameter = 0.002, meters.

With 1 turn: Large difference.
r2    Wheller   Inca (el. fun.) Inca (numerical) Fantc
0.5   2.46 uH   4.11 uH         4.11 uH          4.11 uH
0.75  1.98 uH   5.31 uH         5.30 uH          1.96 uH
1     1.93 uH   6.55 uH         6.56 uH          1.89 uH
1.25  1.98 uH   7.81 uH         7.88 uH          1.95 uH

With 10 turns: Still significant difference.
r2    Wheller  Inca (el. fun.) Fantc
0.75  198 uH   210 uH          197 uH
1     193 uH   212 uH          189 uH
1.25  198 uH   226 uH          195 uH

With 100 turns: Close.
r2    Wheller  Inca (el. fun.) Fantc
0.75  19.8 mH   19.6 uH        19.6 mH
1     19.3 uH   19.0 uH        18.9 mH
1.25  19.8 uH   19.6 uH        19.5 mH

Some experimental measurements on coils with small number of turns
would be useful. A problem is that the problematic coils mut be large
to have easily measurable low-frequency inductances.

Antonio Carlos M. de Queiroz