You'd think with a user name like this...

I'm honestly not very interested in high voltage or loud noises.  My motivation for this is more to see, basically, the impedance of ionized air.  I'm coming at this from the perspective that a TC is a coupling network.

Coupling from what, to what?  Well, an inverter obviously (for the SSTC case).  The load then, is whatever the secondary looks like.

[Real] resistance, and power flow, are fundamental here.  This can't work in a vacuum -- or, well, it could, but making high voltages inside a shielded box with low losses, doesn't really mean anything.  Most of the power would be reflected back towards the source (or if you tune it hard enough, it'll be absorbed by the load alright, as material heating rather than anything interesting*).  Ultimately we want to make showy sparks here, so we need to know how much power those sparks consume.

*There are superconducting resonators, used for linear accelerators.  These are spun and electropolished niobium, cooled to 2K, with Q factors in the 10^7 range (no, it's not infinite -- no superconductor is actually ideal at AC).  This is necessary because the particle beam has such a minuscule cross section -- its impedance is extremely high.  To get reasonable coupling from the exciter klystrons to the beam, you need a very nice network.

Anyway, without further ado, just a crappy cellphone video:


As a network, the impedance simply can't get very high -- even with thousands of turns of fine wire, it's only in the 10s of kohms.  So, high voltages will have to draw amperes, and even with high Q factors (hundreds), hundreds of watts are needed (CW).  Big sparks need even more, and to have any hope of doing that from a residential circuit, you have to pulse it, too.

So i'm not surprised how much use is made from industrial IGBTs!

Also as an impedance transformer, a ratio on the order of Q is reasonable, which explains VTTC direct drive (the low ~kohms is a suitable plate load), but isn't helpful for SSTCs, so a primary winding is used (which can be tuned for additional impedance matching options).  Even with a 1:1000 turns ratio though, we still need hundreds of volts drive.

So, I started with 900V FETs (ran at 400V in this shot).  I could just as well go with lower voltages and higher currents, and figure out the primary side matching (namely, series resonant with a coupling cap, giving a transformation ratio on the order of (Q N2/N1)^2).  With the downside that two circuits have to be tuned.

Although, that's not so effective at this frequency (1.9MHz) due to stray inductance in the bridge layout.  Again, impedance dictates what we can do: a ~30 ohm load isn't terrible at ~2MHz, but a sub-1 ohm load would crumple, at least without a lot more work than I can do on copper clad (i.e., DFN style transistors on multilayer board, pushing stray inductance under 5nH).

Anyway, secondary properties can be calculated e.g. here:
http://hamwaves.com/inductance/en/index.html
Plugging in D = 43mm, N= 376, l = 150mm, d = 0.3mm and f = 1.8MHz, I get Zc = 21kohms (this is a transmission line equivalent impedance, more or less the impedance of the resonator; notice it's close to X_L).  f_res = 2.76MHz is predicted for the self resonance (parallel mode), which is loaded by the ground plane and "top load" (foil tape) in the real build.  The equivalent parameters, 2.092mH and Q = 425, go with that capacitance (evidently ~3.35pF, reasonable enough).

Tim

I'm one of the "original" guys that was working on induction heating, around the mid to late 2000s.  An early, nearly complete design:
https://www.seventransistorlabs.com/tmoranwms/Elec_IndHeat6.html
(I should go through these and fix the YT embeds -- the vids are still up there, though I think they've decayed in quality as YT's re-encoded them over the years...)

https://www.seventransistorlabs.com/Images/Induction1104.jpg
The first complete 1kW induction heater kit, that I'm aware of.  I wrote plans for this, though they need some fixing up nowadays and I haven't gotten around to that yet.

https://www.seventransistorlabs.com/Images/Induction1201.jpg
And my 10kW prototype, which I had tested up to 5kW.  Then other activities took priority and I didn't have time to continue development.

Which led to...
https://www.seventransistorlabs.com/Images/Tallboy_HotStuff.jpg
I designed 5kW MOSFET modules, controls and all that, basically the whole system design for a brand new industrial series.  Pictured here is 30kW from six modules strung together.  The series spanned 5 to 50kW and 20 to 400kHz.  I also began work on updating the larger (floor standing) units, which were IGBT powered and spanned 3-50kHz and 150kW per module (stack as many as you like, though I think the largest assembled there was under 1MW).

Since then, I've been doing more general design work; my designs are in production from automotive to medical.  I pride myself on passing EMC within the first prototype.

Tim