TeslaDesignPage2
From Simreal
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’ (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
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:
Units = Inches Ambient Temp = 80°F ---------------------------------------------------- Surrounding Inputs: ---------------------------------------------------- 0 = Ground Plane Radius (we are operating in outer space) 0 = Wall Radius 0 = Ceiling Height ---------------------------------------------------- Secondary Coil Inputs: ---------------------------------------------------- Current Profile = G.PROFILE_LOADED 5.375 = Radius 1 5.375 = Radius 2 18 = Height 1 61 = Height 2 1000 = Turns 18 = Wire Awg ---------------------------------------------------- Top Load Inputs: ---------------------------------------------------- Toroid #1: minor=4.5, major=40, height=70, topload Toroid #2: minor=4.5, major=36, height=66, topload
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 1.169”, 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!
[1] http://www.easternvoltageresearch.com/designfiles/paper_howto.pdf
[2] http://www.classictesla.com/java/javatc.html
[3] http://4hv.org/e107_files/public/1197099718_27_FT35619_scantesla810.zip
[4] http://4hv.org/e107_plugins/forum/forum_viewtopic.php?35619
[5] http://4hv.org/e107_files/public/1197094330_27_FT0_scanteslamoderncpu.zip
[6] http://www.easternvoltageresearch.com/
[7] http://www.ni.com/multisim/
[8] http://www.techlib.com/files/voltmult.pdf
[9] http://www.tb3.com/tesla/capacitors/capacitors.html
