Primary AC resistance measurements

It has been observed that the innermost turns of primary coils will run noticeably warmer than outer turns. The consensus on the Pupman Tesla List is that this is due to the proximity effect, raising the AC resistance of the inner turns, due to the stronger magnetic fields present there. I was wondering if these losses could be minimized by a suitable choice of conductor. Litz wire and ribbon come to mind, but I've never seen any hard data comparing various primary conductors.

I was fortunate to have access at work to an HP4194 impedance/gain-phase analyzer, pictured below, that can analyze AC resistance and inductance over a range of frequencies. The photo shows the curves for inductance (essentially flat) and AC resistance (sloping upwards) for the 14 gauge close-wound coil. The cursor dots are at 600 KHz. All coils were hand-held during the test, not on the concrete floor as pictured.

I constructed nine test primary inductors, most built with similar geometry and inductance, but using different conductors. The conductors I chose were:

Except as noted, all were identically wound as flat spirals, inside radius = 4.0", turn-turn spacing = 0.5", number of turns = 13. I tweaked the actual number of turns to achieve a nominal inductance of 67 uH on all coils.

Measured data, all resistances in milliohms. In order of ascending DC resistance:

	R_dc	R_ac 40 KHz	R_ac 80 KHz	R_ac 100 KHz	R_ac 200 KHz	R_ac 400 KHz	R_ac 800 KHz
Cu Ribbon, .030 thk	13.3*	150	204	212	336	495	707
#7 Litz Wire	21.7	113	156	185	367	841	1830
Cu Tubing, 2-layer	28.0*	166	238	253	376	529	1027
Cu Tubing, 1-layer	33.7*	148	192	209	294	431	547
0.1" Al wire	51.2*	208	289	297	445	670	1500
#10 stranded	53.3	209	303	320	520	847	1620
#14 solid close-wound	89.8	220	311	327	471	707	1040
#14 solid 2-layer space	109.5	222	313	322	476	713	1590
#14 solid space-wound	128.5	257	362	388	552	760	1060
Cu Ribbon, .008 thk	132.5	283	320	345	410	573	863

* Indicates that coil termination wires were not included in R_dc measurements, but were included in R_ac measurements.

That the Litz wire was only marginally lower in resistance than the copper tubing at low frequencies, and showed the highest resistance at high frequencies was a real surprise! Yes, I am sure that this is in fact Litz wire with individually insulated strands, and that all strands at both ends were stripped and tinned together. I re-tinned one of the ends and took a second set of measurements several weeks later with the same results. I was expecting that the Litz would be far superior to the everything else, and that the inner turns of a complete primary inductor could be wound with Litz. This might put the best conductor where the losses are highest and still allow easy tapping of the outer turns, but it turns out that copper tubing is pretty hard to beat, from cost, convenience, and performance points of view.

I later found some great information on Litz wire on Cooner Wire's web site, http://www.coonerwire.com/Products/Litz/DesignD_2.html. Their chart recommends strand wire gauges as a function of the intended operating frequency. It indicates that my 30 gauge strands would be appropriate for 1-10KHz, although my data shows deteriorating AC resistance just above 100 KHz. But I think we’re in the ballpark. So I think the problem is not Litz wire in general, but rather the relatively coarse strands of my particular Litz wire. If my Litz wire were made of #38 strands as the vendor had indicated, things would probably have measured very differently. Even so, for up to 100KHz, my #30-stranded Litz was the best performer of all tested conductors.

The thin copper ribbon that I used was some very thin (.008") 1/2" wide straps, 18" long, many pieces soldered together. The outermost 3/4 turn was made of a double layer of 1/2" wide copper foil tape (thinner still), as I was short a couple of strap segments. It may be that the skin (effect) depth is greater than its thickness, so the performance may be limited by its relative thinness. I believe that it fared as well as it did by virtue of the fact that the adjacent-conductor spacing is nearly the full 1/2", reducing the proximity effect.

I was surprised that the space-wound #14 coil had a higher AC resistance than the close-wound coil. I was expecting that the close-wound coil would suffer greater from the proximity effect and have a higher AC resistance, but wrong! The close-wound coil used fewer feet of wire and so had a comparably lower DC resistance, and the AC resistance was roughly the same degree lower than the space-wound coil. This suggests that one should space the primary turns as close as is practical.

The 1-layer copper tubing vs. 2-layer copper tubing measurements really surprised me. The two-layer coil used slightly less tubing so had a comparably lower DC resistance, but all AC resistances were higher - about 120% in most cases, and much higher at 800KHz. Also, the measured inductance of the two-layer coil was the nominal 65uH through 200KHz, but rose to 66.7uH @ 400KHz, and to 74.5uH @ 800KHz. All single-layer coil inductance measurements were flat across all frequencies. The thing that was different for the two-layer coil is that both top and bottom coils were 11 turns, tapped at 7 turns, so there were four unused turns at each end of the coil. It would have been interesting to have tested a true 7-turn & 7-turn two-layer coil but I wasn't eager to slice up my primary.

To determine whether the unused turns were responsible for the poor performance, I constructed a 2-layer coil of #14 solid wire, but with no unused turns. At 200 KHz and below, the 2-layer coil had a very similar resistance to its 1-layer counterpart, but beginning at 400KHz, the 2-layer AC resistance really began to soar, just as with the 2-layer tubing coil. The inductance of the 2-layer coil did increase from 66.5 uH (at all frequencies to 400 KHz) to 68.1 uH at 800 KHz. But the puzzling thing is that with the 1/4" tubing, the 1-layer coil had the lower resistance (over all frequencies), while with the #14, the 2-layer coil had the lower resistance (until somewhere above 400 KHz). Not sure what to conclude...

The .03"x1" copper ribbon had the lowest DC resistance of all test coils and I would have expected it to have the lowest AC resistance by virtue of its greatest spacing between turns. But instead, its AC resistance was just slightly higher than the 1-layer copper tubing coil, across all frequencies. Two thoughts come to mind: The tubing was recently steel-wooled to a bright finish, whereas the ribbon had a dull brown patina. Perhaps the oxidized surface where the skin effect currents flow is responsible for the higher resistance. Or more likely, the wider ribbon conductor promotes eddy currents and their losses, much like the way thinner Litz strands would have lower losses.

That the stranded #10 wire fared so poorly is no surprise. I often hear people suggesting the use of coaxial cable with a braided shield as a primary conductor, and I wanted to demonstrate that stranded conductors are a poor choice, despite having a low DC resistance.

The Aluminum wire fared reasonably well for most typical Tesla Coil frequencies. I often hear advice saying that aluminum wire is utterly unsuitable for use in a Tesla coil, due to the skin effect forcing the surface currents into the outer oxide layer. I think this is not so, at least for reasonable TC frequencies. Up through about 400KHz, the AC resistance stayed about 50% higher than that of the copper tubing. I would conclude that if the aluminum conductor were heavier (to equalize the DC resistance), that its performance would be comparable to the copper tubing, up to 400KHz. Of course, there are other very good reasons to select a copper primary over an aluminum one - the ease of soldering/splicing copper tubing, and the better integrity of a clipped-on connection to a copper conductor.

Some questions were raised in my earlier testing about whether unused outer turns resulted in measurements indicating greater losses. When I tested the aluminum primary, I also made two additional measurements. I constructed a 5-turn coil of #10 wire with the same OD as the aluminum primary. Without the extra 5 turns, the coil is the nominal 67uH. If the 5 turns were added, more or less on top of the outermost turn of the Al coil, the inductance rises to 150uH. I made one test with the 5-turn coil in place but with neither end connected. The other test had just one end of the 5-turn coil connected to the outermost turn of the Al coil, and the other end of the 5-turn coil unconnected. The table below is what I measured:

It does appear that the presence of unused outer turns results in slightly higher resistance at reasonable operating frequencies, and significantly higher resistance at very high frequencies.

1/4" copper tubing is a very good choice for primary coils. I'd recommend using the closest spacing possible. Do not under any circumstances use stranded or braided wire. Unresolved is if, and to what degree, unused outer turns and two-layer construction affect the AC resistance.

Also note that while this study gives definitive rankings to the AC resistance of various conductors and geometries, the actual impact to one's Tesla coil's performance was not addressed. It may be that spark gap losses are so far in excess of primary losses that the actual impact of conductor choice is negligible. Or quite possibly not.

Litz wire, copper tubing, #10 stranded, and 8 mil copper ribbon	The HP4194 impedance/gain-phase analyzer
1/4" Copper tubing, single layer	1/4" copper tubing, dual-layer
Litz wire	Solid #14 close-wound
#10 stranded wire	Solid #14 space-wound
.008" thick copper ribbon	.03" thick copper ribbon