Air-Core Transformers with applications in Tesla Coil design - diyAudio
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Old 21st March 2010, 09:27 PM   #1
thadman is offline thadman  United States
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Default Air-Core Transformers with applications in Tesla Coil design

YouTube - Tesla Guitar demonstration

As you're probably aware, Tesla Coils are pretty ridiculous. I've done some research with regards to the underlying mechanisms and am interested in potentially building one.

It appears a fundamental component of the Tesla Coil is its transformer.

I'm interested in designing an Air-Core transformer. However, I'm not sure how to calculate the coupling coefficient (k) for a given geometry. Could anybody offer further insight on this?

If we are able to define the Q factor and resonant frequency (f0), would design be fairly straightforward? What other variables should an engineer consider? Temperature is obviously a factor. How close is the behavior of real world transformers compared to simulations?

Would it simply be a matter of winding two coils around an insulator (ie cardboard, plastic, etc)? At this point I'm just interested in creating an electrical resonator (electrical input / output) with a given resonant frequency and Q factor. Shouldn't I be able to easily measure its behavior with an Oscilloscope?

Intuitively I would assume the coupling coefficient affects the amount of leakage inductance. Would it have any effect on the resonant frequency or the Q factor? Would it be desirable to maximize the coupling coefficient? What geometries would achieve this?

Thanks,
Thadman
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Old 22nd March 2010, 01:01 AM   #2
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k is very, very roughly the ratio of cross sectional areas. For a tall secondary inside a short primary, it will be less (because the top end sees hardly any of the primary / the flux lines are not vertical).

You can test small signal performance quite easily with a sweep generator and oscilloscope, or spectrum analyzer, or network analyzer, or etc. With sufficiently weak coupling, you can tune the primary and secondary independently, and you'll see gain as two humps if they aren't tuned equally, flat-topped if adjecent, or one sharp peak if very close.

Q multiplication is a series-resonant thing. I don't really know how much use it is for a low-k transformer. The low k looks like a big series inductor, which can resonate with some of the parasitic capacitance; the remaining capacitance is parallel resonant with the secondary's self inductance. Thus, it looks something like an LLC network, which is series-parallel resonant. Add a parallel resonant primary and you've got at least five elements in the equivalent circuit.

Notice two things: one, the voltage will NEVER "ring up and increase without bound". Q is always finite and therefore the voltage for a given power input is well-defined. Two, when voltage reaches breakdown, Q goes to pot, so for all your small-signal tuning, it doesn't really mean much, because all those sparks are going to smear it out quite nicely.

I don't know how much value there is in low-k Q multiplication (in terms of attaining a voltage gain higher than N2/N1). It seems to me you'll get fine performance just blasting amps into a transformer. You can tune it if you want, and you probably should, since these turns ratios make for big reflected capacitance. By working with transformer action, you don't have to worry about tuning different components, and you can get much hotter sparks out by enforcing a constant-voltage characteristic (or by driving it series-resonant, you can safely limit inverter current while retaining the high-O/C-voltage characteristic).

As for air-core transformers, they're perfectly calculatable, if you don't mind doing an insane amount of computation. Using a suitable model in an E&M simulator, you can get numerical results arbitrarily close to reality. Using a cheezy model, you can get "close enough" results. Using a circuit model, you can get similar results, making whatever assumptions of topology you like. In "close enough" terms, you can get excellent results from a lumped-constant model consisting of the secondary's parallel RLC equivalent, the series leakage inductance, and the primary's RLC equivalent, plus whatever you're driving it with (constant voltage, resonant, coupled, etc.?).

Tim
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Old 29th November 2010, 02:56 PM   #3
ontoaba is offline ontoaba  Indonesia
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The magnetic field is only around primary, but it is creating electromagnetic field that transfered and trapped at secondary. It is wireless power transfer that he applied to radio.
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