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Registered Member #1305
Joined: Sat Feb 09 2008, 10:27PM
Location: IH35 & Parmer, more or less
Posts: 9
Step 1 (cross posted to my Wiki on simreal.com: )
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:

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’ (108â€) spark, that is 2 to 3 times longer than the secondary winding, we have a winding height of 36 to 54â€, 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 10â€+
9’ (108â€) sparks 12kVA power 3:1 to 4:1 secondary aspect ratio 3’ to 4’ (36†to 48â€) 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 6â€, 8â€, 10â€, and 12†trade diameters (OD of 6.625â€, 8.625â€, 10.75â€, and 12.75â€).
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 10.75â€, 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’ (108â€) sparks 12kVA power 4:1 secondary h/d aspect ratio 43†winding height 10.75†form diameter 18 gauge (0.0403†+ 0.0015â€) 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 (10â€), and with about the same aspect ratio to its major diameter (40â€). 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’ (108â€) 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†+ 0.0015â€) 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!
Registered Member #1034
Joined: Sat Sept 29 2007, 12:50PM
Location: Chillicothe, Ohio
Posts: 154
I don't know where you live but in the US larger diameters of PVC pipe can be found at pipe suppliers that sell to construction contractors. Actually they will sell to anybody but the larger PVC pipe comes in 20' lengths and it gets a little pricey.
I bought a 20' piece of 12" green pvc pipe for my latest coil project and I still have a 6' long piece left over. You can have it if you want to come down and get it.
Roger
(oops.. correction! the PVC actually come in 14' lengths )
Registered Member #1157
Joined: Thu Dec 06 2007, 12:11PM
Location: Houston, TX
Posts: 307
I35 and Parmer?
You live in Austin, TX, just over by Metric. In fact, I believe that that movie "Office Space" was filmed right where you live. Used to work at IXC over there for a while before I moved to Sprint and then finally to Houston, TX. With Austin being as "Under Construction" as it always is, you could head over to any number of new build neighborhoods and pick through their trash dumpsters or piles and find exactly what you need, as far as a green 6 or 8 inch PVC pipe.
I have yet to buy any PVC pipe for my coils, as I'm a cable guy and have access to all the construction areas.
What you get may be a little dinged up, but that is nothing that a little sanding and varnish won't cure.
Good to see another Texan. I'd also look up Joe DiPrima, from The Geek Group, he lives in Austin as well, and may be able to lend you a hand.
Registered Member #1305
Joined: Sat Feb 09 2008, 10:27PM
Location: IH35 & Parmer, more or less
Posts: 9
Yeah, I bought 20' (er, 14'? whichever) of 8" PVC last year for a project.. that hurt. Some plumbing supplier up near Pflugerville; I'll have to look 'em up again though and see how much damage a 10" section will do to my wallet.
As for Roger in Ohio (Ohio!) I'd love your spare 12" PVC, but that's a heck of a drive... and I don't think my friend is going to go back there to visit family anytime soon. Ah well.
As for cost? Cost is no object! Well, I'm not worrying about it yet at least; I expect to spend a couple grand or more on this.
Joe and Oliver of Arc Attack are great; no longer with Geek Group, I believe, but are still hanging out with the Dorkbot folks, and went to Burning Flipside this year too with their awesome coils. They do tend to be willing to help out, but the logistics of it can be tricky sometimes given everyone's schedules.
Registered Member #599
Joined: Thu Mar 22 2007, 07:40PM
Location: Northern Finland, Rovaniemi
Posts: 624
Ask for cardboard tubing. It is very cheap (at least where i live) and it can be used as sec. former without problems. Just bake all moisture out and varnish it properly :)
I was just looking for drain pipe in diameter of around 35cm. Cheapest PVC pipe was over 200euros (317$)
Then i found out about cardboard secondaries and i found local shop that can make almost anything from strong cardboard. I just bought cardboard tube 200cm long and 35cm in diameter and it was only 29euros (46$)
Registered Member #1305
Joined: Sat Feb 09 2008, 10:27PM
Location: IH35 & Parmer, more or less
Posts: 9
I've thought about cardboard, yes, in spite of its weaknesses -- the mention of the Sonotube above, for example; these concrete forms (of various makers) come in many sizes.
But how the heck am I going to bake a 10" to 12" diamter, four-foot long tube? Maybe my heat gun... I dunno. And with our evil Texas humidity... I'll probably just end up paying a fortune for plastic.
Registered Member #1305
Joined: Sat Feb 09 2008, 10:27PM
Location: IH35 & Parmer, more or less
Posts: 9
Okay Tesla fans, I’m back and more incoherent than ever!
An avid reader noted that my RMS calculations were completely wack, so it’s good to know I’ve not achieved perfection yet (wouldn’t want to get bored). I must have hallucinated the ‘scope readings at home, because when I checked the outlet here at the office the ‘scope gave me something like 380VP-P, which gets a lot closer to the 110-120VRMS I would expect from my city-supplied electron conduit.
In this thrilling episode, I look at the Primary LC circuit and the DC supply, completely ignoring the switching and feedback circuits that tie them together. I’m also skipping most of the SPICE bits for now; I’m not getting much love from my SPICE (but then, I’m still not a strong analog engineer; digital is more my speed).
Glancing over the previous exploration results, I see that we left off with these attributes for the secondary (I apologize for the redundancy):
9’ (108â€) 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†+ 0.0015â€) 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
I didn’t keep a lot of the intermediate notes and parameters that I developed when I was poking around with the secondary, so when I went to recreate it I ended up with a slightly different 95kHz resonance. Here are my JavaTC parameters of note:
Most of the primary decisions are made for me by convention and the need for the primary to resonate at or near the secondary resonance (slightly slower, typically, since the secondary slows down when it sparks out).
By convention the primary consists of 10 +/- 5 turns of heavy-duty copper or aluminum; the small turn count appears to be necessary to keep resistance down, to minimize losses as the resonant current flies through the roof.
Since I like the aesthetics of copper pipe, I’m thinking of using 3/8†soft water pipe, which is a step up from the 1/4†pipe I used in my smaller coil. Other material choices include ordinary stranded or solid wire, Litz wire, or even coils of flat metal sheet.
The last choice to make with the primary coil is the geometry. This can be a helical winding like the secondary, a flat spiral, or the truncated inverted cone that splits the difference between these two. A helical winding is easy to make and has a strong coupling but its proximity of the primary’s top winding to high-voltage areas in the secondary encourage flashover. A flat spiral reduces these unwanted sparks at the expense of less energy transfer. The inverted cone is just plain harder to make.
Since I’m a masochist, and I like the look of it, I’m going to try an inverted cone with a rise of 30º. Since this will be an experimental coil, I will also try to find a way to make the primary easily replaceable. The secondary should also be easy to swap out, with (I hope) easily adjustable height above the primary to make it easy to play with coupling.
The first winding on the primary will be 2.5†from the secondary (following the recommendations of Eastern Voltage Research [1] ) and will have a spacing equal to the pipe diameter.
Finally, I need to pick a primary capacitor value. I pulled the convenient and arbitrary 100nF out of thin air, for lack of a better idea.
This gives me:
--------------------------------------------------
-- Primary Coil Inputs: --------------------------------------------------
-- 7.875 = Radius 1 14.370 = Radius 2 18 = Height 1 21.75 = Height 2 6.2607 = Turns 0.375 = Wire Diameter 0.1 = Primary Cap (uF) 4 = Total Lead Length (ummm, yeah, here’s a number) 0.125 = Lead Diameter (8ga, let’s go for it)
Giving this a quick spin through JavaTC [2], telling it to optimize for 0.15 coupling (which an earlier run told me was recommended), I get:
J A V A T C version 11.8 - CONSOLIDATED OUTPUT Thu Jul 24 13:07:54 2008
Units = Inches Ambient Temp = 80°F (Texas is hot) ... --------------------------------------------------
-- Secondary Outputs: --------------------------------------------------
-- 95.33 kHz = Secondary Resonant Frequency 90 deg° = Angle of Secondary 43 inch = Length of Winding 23.3 inch = Turns Per Unit 0.0027 inch = Space Between Turns (edge to edge) 2814.3 ft = Length of Wire 4:1 = H/D Aspect Ratio 18.2907 Ohms = DC Resistance 35867 Ohms = Reactance at Resonance 13.84 lbs = Weight of Wire 59.881 mH = Les-Effective Series Inductance 62.76 mH = Lee-Equivalent Energy Inductance 60.947 mH = Ldc-Low Frequency Inductance 46.547 pF = Ces-Effective Shunt Capacitance 44.412 pF = Cee-Equivalent Energy Capacitance 74.799 pF = Cdc-Low Frequency Capacitance 9.25 mils = Skin Depth 35.726 pF = Topload Effective Capacitance 85.0637 Ohms = Effective AC Resistance 422 = Q
--------------------------------------------------
-- Primary Outputs: --------------------------------------------------
-- 95.32 kHz = Primary Resonant Frequency 0.01 % = Percent Detuned 30 deg° = Angle of Primary 31.77 ft = Length of Wire 2.4 mOhms = DC Resistance 0.375 inch = Average spacing between turns (edge to edge) 2.552 inch = Proximity between coils 0 inch = Recommended minimum proximity between coils 27.901 µH = Ldc-Low Frequency Inductance 0.09973 µF = Cap size needed with Primary L (reference) 0.084 µH = Lead Length Inductance 197.457 µH = Lm-Mutual Inductance 0.15 k = Coupling Coefficient 0.149 k = Recommended Coupling Coefficient 6.67 = Number of half cycles for energy transfer at K 34.48 µs = Time for total energy transfer (ideal quench time)
The tuning process has reset my number of turns to 6.1475 and the secondary-to-primary spacing from zero to 1.169â€, and adjusted the primary radius and height accordingly.
The 35 µs transfer time means that, at 10% duty cycle, I need about 350 µs dead time giving me a max interrupter frequency of about 2.5kHz. This will be a decent top frequency if I ever want to make this coil musical, if not a great one -- the human ear is said to work best between 20Hz and 20kHz, while the telephone (not known for its amazing fidelity) filters this down to 350Hz and about 3.5kHz.
All in all these initial analysis results are not too bad, though the charts of numbers make my eyes cross.
Moving these numbers into Scan Tesla [3][4][5], I run it a few... million... times to see if there is any hope at all for my coil to produce giant sparks. That, and I want to get some sense of the current/voltage I’ll have to handle in the primary so I can use that data to inform the control circuit designs.
Scan Tesla recommends a few tweaks including reducing the primary inductance a bit, raising the primary cap to 150nF, plus increasing coupling to 0.17. It also wants me to reduce the inductance of the secondary just a wee bit while cranking the capacitance to 80pF, a big jump. On top of all that it wants 170 µs of drive time. But, it promises, if I do that, I’ll 15’ arcs; if I can manage to keep the 60kV / 5.1kA primary from exploding first.
I need to withstand 6,000A at about 60kV? That’s going to arc out of the primary well before I reach those levels -- sounds like I’ll want corona dope on both coils. That, and a guardian angel. Maybe Scan Tesla is just pulling my chain, but let’s go with these values anyway. After all, the miniBrute [6] has caps rated at 6kV and runs in the 500-600A range, and I was expecting to run this Tesla at about 10x the rating of the mini. As terrifying as these numbers are to a logic-level engineer, they may also be right on the money.
The primary capacitor will of course have to be an MMC [9] and preliminary investigations indicate this will be an expensive component, far more money than I had anticipated. The temptation to use the (explicitly forbidden) CD 940C is powerful, since it looks like it would save a lot of money compared to the CD 942C series, but then again, exploding caps would add more excitement to my project than I need. I’ll have to spend some quality time in the various references linked to the MMC [9] discussion and with my various suppliers.
The other half of this step was a reality check on the DC power supply. I want it to draw 15A from the wall and be able to provide roughly 12kVA pulses to the primary (via the control system) at a 10% duty cycle.
I spent the last couple of evenings running MultiSim [7] SPICE simulations of a Cockcroft-Walton voltage multiplier in a high-current configuration [8] to see what I could see. With three stages (1mF internal caps and a 10mF output filter, numbers I chose mostly arbitrarily, but after testing a bunch of combinations) I can get 900V or so with about five seconds of charge (slow partly due to the current limiting on the input), and minimal droop on a 10% duty cycle run. Unfortunately, those caps are going to cost a bundle, though building them up as an MMC might help.
A hefty transformer at the front end could provide both isolation and a nice step-up to 220 from my wimpy 110, but those suckers (e.g. the Hammond 298GT) are not going to save me much money-wise. Alternatively, I could require a plug-in to a 220V dryer outlet... but that would limit my venues quite a bit.
I think I’ll just have to suck it up and buy a crate-load of capacitors.
Next up: control circuits and component selection!
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Tesla Design from Scratch
