Because I’m a glutton for punishment, I am designing a Tesla coil from scratch. I’ll be using the work of those that came before me of course, because while I like to do things the hard way, I’m not entirely insane. This installment of my build notes is the starting point in my thinking; from a desired arc length, I will work backwards through the design until I reach the wall plug. Then I’ll refine and construct the coil, and hope that it works!
At first, I thought it would be useful to simply bring up the relevant theory, maybe run some calculations, throw up some graphs, make a SPICE model, and then the various parameters might be made obvious. As it turns out, there are quite a few models of operation for the Tesla coil; piecewise, you can assemble an amazing mathematical model of the entire thing (though poking around in these models made my brain hurt). The trouble is that there appears to be a lack of agreement on exactly what is the _right_model.
Corum & Corum wrote a detailed paper to refute the simple lumped-component model in favor of a distributed-inductor model [1][2], thereby throwing the gauntlet down between the two primary camps: radio people and non-radio people. The radio people tend to see the Tesla coil secondary like an antennae (and there is good reason to do so). However, the Corum^2 paper had a nicely-worded rebuttal by Terry Fritz [3] and work by Ćosić et.al. seems to show that the simpler lumped model does in fact work fairly well [4], which bodes well for easier SPICE simulations.
These two models only matter when it comes time to find the correct operating frequency of the coil. On the one hand, the inductor (coil) + capacitor (topload) LC circuit has a characteristic resonance in the lumped model. On the other hand, the wire length of the secondary coil (in conjunction with mysterious speed-of-electricity-in-copper issues [5]) gives a characteristic quarter-wavelength frequency for optimal voltage amplification on the top end of the coil.
Some calculators (and coilers, I assume) simply punt and adjust the circuit so that the LC resonance simply matches the quarter-wave resonance and brush the whole argument under the carpet.
Theory, it seems, is not the place to start. What we do have, however, are a number of rules-of-thumb guides that define the working space of the average coiler, and a whole raft of electronics formulae that can be used to crunch out the details later.
There are many assumptions that I make right up front. Since I’m coiling to make pretty sparks for display purposes, I want to optimize for zap factor. Other choices could include stable high voltage for physics research, or a high-frequency plasma discharge with low noise characteristics to make a plasma speaker.
Given the purpose, you now get to choose a technology. I’m choosing the DRSSTC (dual-resonant solid-state Tesla coil pioneered by Jimmy Hynes, Steve Ward, and others, and kitted up by Daniel McCauley (which makes a really nice entry point to the field, thanks Dan!). Of course, you could also go with the traditional spark gap coil, vacuum-tube control, the so-called “online” configuration, and so on.
First Decision:
9 to 10 foot sparks using DRSSTC technology.
Okay, maybe I _am_ insane.
How much power will that take? D.C Cox of Resonant Research Labs has an extended mix version of John Freau’s spark-length-to-power formula [6]:
d = k’ * sqrt p
Where d is spark distance in inches, p is input power in watts (or VA as metered from the wall), and k’ is a “fudge factor” coefficient based on the secondary coil diameter:
Dia. k’
3-10” 0.85
11-16” 1.00
17-20” 1.30
21-36” 1.70
37-48” 2.0
But what should our secondary coil diameter be? In other guides, they say you can expect a spark length 2 to 3 times the height of the secondary coil (needs reference), and looking ahead a bit, we see that a diameter of about 1/4 the secondary height is reasonable.
Given a 9’ (108”) spark, that is 2 to 3 times longer than the secondary winding, we have a winding height of 36 to 54”, and with a height/diameter ratio of 4:1 that leaves us with a 9” to 12” diameter coil. Plugging that in to the k’ table, we can just pick something near 1.
p = (d/k’) ^ 2 = (108/1.0)^2 = about 12kVA
12kVA is a big chunk of power. From a 15A outlet running at about 115V RMS (though I’m not entirely sure my voltmeter is given me RMS here; a 125VAC peak-to-peak calculates out to about 90VAC RMS) for 1.7kVA (or 1.3kVA), we should be able to get 12kVA bursts from a capacitor bank if we only fire for 10% (giving some allowance for inefficiency). So it might be possible. Especially if I use a 20A circuit and not the lame 15A.
The RRL guide also indicates we need a toroid major diameter of 1.7 to 2.0 times the secondary’s diameter, with a minor to major diameter ratio of 3.8 to 5.0, which is eerily similar to the guidelines for the secondary coil aspect ratio.
For example, Daniel McCauley’s Eastern Voltage Research guide [7] gives aspect ratios for various smaller coil diameters:
Dia. h/d
<=4” 4.5:1 to 5:1
to 6” 4:1 to 4.5:1
>6” 3:1 to 4:1
Deep Fried Neon [8] gives similar advice, recommending secondary diameters for various powers, and then ratios from diameter:
Power Dia.
<500W 3” to 4”
to 1.5kW 4” to 6”
to 3kW 6” to 10”
>3kW 10”+
Dia. h/d
3” 6:1
4” 5:1
6” 4:1
8”+ 3:1 to 5:1
Given all this, where are we now?
9’ (108”) sparks
12kVA power
3:1 to 4:1 secondary aspect ratio
3’ to 4’ (36” to 48”) winding height
9” to 12” winding diameter
Various guides, such as Richard Quick’s archived discussion on Pupman [9] and TeslaMap’s guide [10], among others, indicate that 800 to 1,000 turns on the secondary are optimal (though when it comes down to actual coils in hand, I’ve seen winding counts of 2,000 and more). My Mini Brute has roughly 1,000 windings (I didn’t count; my next coiler is going to have a quadrature counter in it, that will be handy) and generally follows the guidelines for a 3:1 aspect ratio.
Picking a nice round number of n=1,000, we need a wire spacing of .036” to .048” (36 to 48 mils). This lands us right around 18gauge [19] (17..19ga; 18 is a common size though). 18ga is 40.3 mils, and Classic Tesla’s Turn Calculator [11] gives a single-layer enamel thickness of 1.5 mils. Taking into account some inefficiency in winding, and we have about a 43” heigh coil. At the aspect ratio chosen, we need about a 10” diameter form.
The easiest to find material to use for the form is PVC (polyvinyl chloride) or PE (polyethylene) water pipe. The _best_ material, electrically, is polystyrene or polypropylene; but we can make PVC or PE work, and coating it with epoxy or polyurethane helps improve its dielectric performance as well (or so say the guidelines).
Schedule 40 PVC is easily found in 3” and 4” diameters (with actual ODs of 3.5” and 4.5” due to obscure historical reasons). Harder to find is schedule 40 in 6”, 8”, 10”, and 12” trade diameters (OD of 6.625”, 8.625”, 10.75”, and 12.75”).
Whereas all ANSI “schedule” pipes are listed as having the same ODs [12], however I’ve discovered that “green” plumbing pipes are different (and, as best I can find, metric). This green-colored plumbing is apparently based on smooth-wall polyethylene, which is popular in Europe, but deeply confusing when purchased as (what I thought was) schedule 20 PVC, but which in fact did not conform to ANSI dimensions. So stay alert! It’s a jungle out there.
Assuming I can find it, I can use 10” trade PE sewer pipe, which has an actual outside diameter of 10.75”, a perfectly acceptable size according to all accounts. If I can’t find that, I might be able to modify a Sonotube, or start trolling the local plastics suppliers [13]. I’d love to use some of that transparent PVC, but the cost is a killer [14].
Of the many parameters that can be used to define the secondary coil, the guidelines in fact give us answers to most of them, and the rest can be easily calculated:
Form Diameter, Length, Wall thickness, Material, & Dielectric behavior
Wire Gauge / diameter, insulation thickness, and length
Coil Height, avg. Diameter, Winding count and spacing
Coil DC Resistance and AC Reactance, Inductance and Capacitance
Quarter-wave resonant frequency
Coil Q factor
Most of these values are constrained by the original desire for a 9’ spark, the availability of secondary form materials, and the rules of thumb listed above.
The design so far:
9’ (108”) sparks
12kVA power
4:1 secondary h/d aspect ratio
43” winding height
10.75” form diameter
18 gauge (0.0403” + 0.0015”) wire
1,000 windings
TeslaMap’s calculator [15] says that 43” of 18ga wire will give me 998 turns, using 2,800 feet of wire. Deep Fried Neon’s calculator [16] agrees, and gives me an inductance of 59.8mH and a self-capacitance of 18.3pF. Tesla Coil CAD 2.0 [17], with similar secondary values, gives me 950 turns, 2,670 feet of wire, 54.4mH, and 20.2pF, adding the interesting detail of a 92.11kHz quarter wave resonance (but did they take into account the slowdown of electricity in copper [5]?) and a need for a 34 to 35pF topload capacitor to make it resonate at this rate.
Note that 100kHz is a decent frequency to run at, well within IGBT limits when soft switched (though 50kHz would have been even more friendly, and the IGBTs do tend to be rated at 25kHz or less when hard switched).
The secondary circuit consists of a coil of wire, with a given inductance L and possibly quarter wave resonance lambda/4, plus a capacitor and discharge terminal, typically a sphere or toroid, with a capacitance C.
In theory, I want a topload toroid of approximately the same minor diameter as the secondary coil (10”), and with about the same aspect ratio to its major diameter (40”). Looking at what supplies are easy, and costs, that’s just not going to happen -- though it WOULD give me a nearly perfect effective topload capacitance of about 35pF according to the JavaTC calculator [18].
Instead of the $600 spun toroid of the correct dimensions, let’s try a simpler and cheaper one made from classic 4” trade diameter dryer vent (also about 4.5” actual OD).
A 40” toroid with 4.5” minor diameter gives (via JavaTC again) about 30pF effective capacitance on this coil; adding a second one below it with a 36” major diameter gives us the 33pF capacitance, which is close enough at this stage of design.
The tighter minor diameters will mean an easier breakout, with a lower potential maximum voltage, but it’s such an easy material to find it may be worth it. Anyway, toploads are the easiest part to swap out for experiments.
Secondary Design:
9’ (108”) sparks
12kVA power
4:1 secondary h/d aspect ratio
43” winding height on about a 48” form
10.75” form diameter
18 gauge (0.0403” + 0.0015”) wire
~1,000 windings
~54-55mH inductance
~20pF self capacitance
40” OD 4.5” aluminum duct toroid on top of another
36” OD 4.5” toroid
33-35pF topload capacitance
~92kHz quarter-wave and lump-model resonance
With this rough sketch in place, I could move on to the primary or bog myself down into mathematical and/or SPICE analysis... I’ve leaned on the various calculators pretty hard so far, and haven’t crunched the numbers myself yet... but right now... it’s dinner time!
References:
[1] http://www.ttr.com/corum/
[2] http://www.blazelabs.com/teslacoil.pdf
[3] http://www.pupman.com/listarchives/1999/October/msg00428.html
[4] http://www.tesla2006.org/presentations/other/The%20Analysis%20of%20Tesla%20Coil%20Apparatus.pdf
[5] http://en.wikipedia.org/wiki/Refractive_index
[6] http://www.classictesla.com/download/resonance_tips.pdf
[7] http://www.easternvoltageresearch.com/designfiles/paper_howto.pdf
[8] http://deepfriedneon.com/tesla_guide.html
[9] http://www.pupman.com/listarchives/1995/january/msg00139.html
[10] http://www.teslamap.com/guide.html
[11] http://www.classictesla.com/java/cst.html
[12] http://www.crestwoodtubulars.com/pipe_schedule.html
[13] http://www.regalplastics.net/
[14] http://www.clearpvcpipe.com/
[15] http://www.teslamap.com/download.html
[16] http://deepfriedneon.com/tesla_frame6.html
[17] http://www.richardsplace.net/tesladownload.htm
[18] http://www.classictesla.com/java/javatc.html
[19] http://www.interfacebus.com/Copper_Wire_AWG_SIze.html
http://www.classictesla.com/FormulasForTeslaCoils.pdf
http://www.classictesla.com/download/tc99.pdf
(cross posted to www.4hv.org)
Posted by Edwin at July 13, 2008 10:33 PM