An Inductance Study
by David McNamee, August 12, 1999

In order to maximize the Q factor of a given coil, its inductance must be as high as possible for the size of the coil.  If a length of wire is wound on a suitable form the resulting coil will have a certain inductance value.  If the same piece of wire is wound on a form of different dimensions it will have a different value. There are formulas in the literature to predict these values, but often give only approximations, especially across a range of form factors (the form factor is the diameter/height ratio of the coil; some use height/diameter).  Some of these formulae indicate that a maximum inductance may be had at one particular form factor.

This experiment seeks to discover if a form factor exists which results in a maximum inductance value (Imax) for a given length of wire. Various diameter cardboard forms were wound with the same piece of wire and measured with a Wavetek inductance meter.  A second set of coils were wound on the same forms using a different wire size of different length and measured to determine if Imax is a scaling function or a property unique to each coil design.  The coils are single layer close-wound solenoids.  The results are recorded below.

Group 1 - #26 magnet wire

 Winding Diameter, in. Height, in. Inductance, uH D / H H / D 1.60 5.15 880 0.31 : 1 3.22 : 1 2.12 3.94 1061 0.54 : 1 1.86 :1 3.47 2.39 1309 1.45 : 1 0.69 : 1 4.77 1.72 1347 2.77 : 1 0.36 : 1 7.15 1.14 1261 6.27 : 1 0.16 : 1

Group 2 - #19 magnet wire

 Winding Diameter, in. Height, in. Inductance, uH D / H H / D 1.62 4.35 158 0.37 : 1 2.68 : 1 2.14 3.28 190 0.65 : 1 1.53 :1 3.48 2.00 225 1.74 : 1 0.57 : 1 4.79 1.46 225 3.28 : 1 0.30 : 1 7.17 1.00 197 7.17 : 1 0.14 : 1

These results, when plotted on a graph, show that a maximum occurs for both groups in the vicinity of 2:1 to 3:1 diameter to height ratio:

The curve is fairly flat in this region, indicating that a coil within this range will have the maximum inductance possible for that length of wire.  The curve also steepens and exaggerates as the total number of turns goes up.  Also of interest is the left side of the curve, where the inductance dives rather quickly as the coil becomes long and slender.  This validates the reasoning of Tesla coil builders, many of whom wind their secondaries as relatively fat coils in the 0.2 : 1 to 0.5 : 1 diameter/height range.  Though this does not give the highest inductance, it is a practical balance between the simultaneous need for high inductance and flashover resistance.

While a 2:1 - 3:1 diameter/height ratio may not be useful for the secondary in a traditional Tesla coil, it might be considered for the secondary of a Tesla Magnifier system, where low resistance, lower voltage requirements, high current, and coupling requirements can take advantage of Imax.