Max Indutance of a Solenoid

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Original poster: "Barton B. Anderson" <bartb@xxxxxxxxxxxxxxxx>

Hi All,

After looking at Gary's coil data from 7 years ago, Mike asked 
offline to look at max inductance of a solenoid coil. Sounded 
interesting so I did. If you have been on the list long enough, 
you've likely heard max inductance h/d ratios. The most commonly 
stated is maxL is when H=0.9R or H=0.45D. I ran some numbers to look 
at that. BTW, for those particular max inductance statements, a fixed 
wire length and a fixed wire pitch must be maintained.

Here is a pdf of the data I ran:
http://www.classictesla.com/download/max_L_table.pdf

The first table is a solenoid coil where the wire length is 
maintained and the wire pitch is maintained. This requires the radius 
and height to be varied as h/d is incremented (and in my table, by 
0.05 increments). What was found is that at low frequency (Ldc), 
H=0.45D is relatively true, but only for low frequency inductance. 
This has no bearing on a resonant transformer. At the resonant 
frequency of the transformer, Les is realized by the transformer. Les 
is the lumped value for the inductance at the transformers resonant 
frequency. It is easiest to view it as the "resonant frequency 
inductance". At high frequencies, the current is not distributed 
evenly along the coils length. The change in current within the 
windings causes the inductance. Because high frequencies cause 
different currents in one portion of the winding versus another 
portion of the winding, the total inductance at high frequency is 
different than the total inductance at low frequency.

In both cases of Ldc or Les, the actual geometry is ridiculous for a 
classic tesla coil application, but may be good for some other 
application. Just thought I'd share the table with the list.

The 2nd table shows what would occur if the wire length was fixed yet 
the pitch was allowed to increase with h/d. In this case, max 
inductance had an h/d of 2.5. Easier to look at with data than to 
actually build.

Take care,
Bart