Deep in idle thought this weekend, I thought I would evaluate how a series resonant output would work for an induction heater. Ya, I've already got my IGBT half bridge, this is just hypothetical.
The problem is, all the work coil current flows through your inverter, but you at least get the concession that the capacitor neutralizes the inductor's reactance (at resonance), saving you some volts.
I figure, for a capacity similar to what I've already got going, I'd want around 400A capacity. For 100kVA in the tank, that's around 250VAC across the capacitors. At a typical Q = 5 (a reasonable loading, hm, 20kW too!), the inverter needs to run 50Vrms or so, fundamental. A full duty cycle square wave then is around 55V, call it +/-60V supply. So, this calls for transistors rated for at least 120V, and with all this current, MOSFETs are probably needed for the lower voltage drop.
A browse on Digikey shows about 14A/$ tops, in the 200Vds bracket. That's around $60, for 20 transistors, not unreasonable considering. A bit more than what I paid for the IGBTs, and for 10kW at that.
Supply sucks though. Anyone want to rewind a pole pig transformer? LOL! Another switching supply would probably be needed to drop 240VAC, or perhaps
3 phase power, down to the +/-60V needed. Some heavy strapping would be needed to hook up the 160A power supply. In the spirit of reuse, a largish size inverter TIG unit might be rewired for power supply, or better.
Wiring, though. How exactly would you go about wiring up something like this? Low inductance transmission line approach for sure, but geez, even for a 1 ohm line, if you've got 400A strolling through that bastard, let it go and it's up at 400V, correct? What's the typical impedance for a flat transmission line (plane, rather) geometry, anyways?
Or does impedance really matter any, since the pulse is shorter than the transmission line? (Figure tr = tf = 200ns or so and transmission line maybe 6", 12" tops.) On the other hand, is the velocity factor of such a transmission plane much lower than 0.67?
Tim
-- Deep Fryer: a very philosophical monk. Website:
Well, you can use the series-parallel configuration that I went with, but that's not pure series resonant, either, which was the point of this thought process.
Nah. What's your usual operating frequency? What's the inductance
10-30kHz depending on L and C. Figure L in the 4-20uH range, depending on how much you're trying to heat. Q = 30 to 70, lower around the 10kHz range.
Whyzat? TL is mostly what Terry was going on about as far as reducing inductance in the bridge wiring.
Tim
-- Deep Fryer: a very philosophical monk. Website:
I prefer to first establish the resonant circuit, using optimum components, and separately provide external AC power to replace the resonant circuit's low-Q losses. More on this below.
OK, let's take 10uH and 20kHz, which would resonate with 6.3uF and have j1.25 ohms of reactance. Connect the L and C together.
With 400A peak circulating in the resonant circuit, you'll also have sqrt(L/C) = 500V peak voltage. The stored energy is 0.8J per cycle and at 20kHz corresponds to a 16kW peak power level. For Q=5 you'll need to provide about 0.5 3.2kW = 1.6kW rms to replace the lost energy. Your heating power would be 1.6kW, less the coil + cap losses, etc. (I'd think you should aim at under 10-milliohms of total coil, wire and cap esr.)
There are lots of ways to couple in the energy. Let's break your 6.3uF into two parts, say 8.4uF in series with 25uF, so the bottom 25uF only sees 500*6.3/25 = 126 volts peak. Your job is to drive that node with 3.2kW peak = 25 amps peak. An inductor from a MOSFET H-bridge can nicely handle the task.
Do you see how much more attractive 126V and 25A is than dealing with the raw 400A and 500V? Running 400A through the switch would be painful and inevitably very wasteful.
Reduce the inductance by all means, but at these low frequencies propagation speed isn't an issue: you're working with all lumped elements. You certainly do want to include parasitic elements in your analysis, such as skin-depth, proximity effect, etc.
Like I said, it's a pretty half-assed number (5-20), so I can't say I'm too compelled to use more than one cheek in telling you about it. ;)
For instance, here I'll just relate what I have wired now.
7 turns of 1/4" copper tubing wound 3.25" i.d., 3.5" tall, comes to 3uH and has a Q = 58 at 20kHz. (I'm getting these values from COIL.EXE (by Brian Beezley), it's quite accurate.) 3uH resonates with 20uF at 20kHz, with reactance = 0.377 ohms and resistance = 0.0065 ohms. 400A rms is then 150V rms and thus 60kVAr.
With cap and hookup, total tank Q should be around 50, eh? (Drool, polypropylene...)
The series matching inductor subtracts a few microfarads, causing resonance to rise to something like 23kHz. I've measured the inductances and resonant frequency and it all comes to within 10% of expectations, which is as good as I can measure. So the theory seems to fit reality. Anyways.
My current load is a 1.5" o.d., 2" tall graphite crucible. The cross sectional area ratio (roughly the coupling factor) is 0.213. That means there is some value of resistance coupled to the coil that sucks maybe 1/5th the tank's circulating VAr. This completely and utterly ignores bEMF, which is maximal for aluminum, copper and silver, which tend to just sit there, wanting to push a vertical orientation, while the inverter buzzes on, while titanium and graphite heat nicely, and insulators (higher resistivity still) obviously don't heat at all. I should sit down and calculate bEMF and stuff some day.
Anyways again, the typical parameters for resonance with this load is something like:
+V = 100V. I = 10A (average), so P = 1kW or so. (About as much as I can pull from the
120V 15A outlet at the bench. Oh how the lights dim.) Tank = (trying to remember what it was!) maybe 250Vp-p = 88Vrms = 230Arms, so 20kVAr, so Q ~= 20. Inverter current: suprisingly sinusoidal; about 10A peak.
As this setup goes, that's a reasonable load. Much heavier (say, using a similar dimensioned steel pipe section) and tank voltage is loaded too much at resonance, demanding a smaller Lmatch (to couple more real power) or more capacitance and lower frequency (to raise amps, raising VA). Neither is really an option unless switching components to suit load is part of your design criteria (gack, 50A+ switches).
Q = 10 might be the lowest practical then. *Shrug* Wouldn't hurt to design to Q = 5 at any rate. The characteristics may be different, also, allowing a different curve of loading vs. heating. That's the other point I'm interested in.
Well, I count (400 / sqrt(2)) * (500 / sqrt(2)) = (400*500)/2 = 100kVAr, and so Q=5 power should be 100/5 = 20kW.
Clearly you're taking energy times frequency, and I don't see anything offhand wrong about that, but I don't know anything offhand wrong about using VAr to estimate, either..??? I mean, VA isn't nonsense, it's used for a lot of purposes. It can't be outright wrong to express tank energy in total VA. Likewise, the loss should be VAr / Q = VA(real), and real VA are just watts, and that's how the Q-factor works, right? At best, I could convince myself that voltage and current are individually related to Q, so VA is related to real power by Q^2, but if it were, we'd get the exact same answer, not 1.6kW vs. 4kW (100kVA/Q^2) vs. 20kW (100kVA/Q).
Clearly a figure too low, if the desired result is 10kW (or more), so needs more volts or amps (or something is screwey with one of our estimates).
Not a problem, the hardware store tubing has me covered. :-)
- Not necessarily practical though. High current, high value, low voltage capacitors aren't easy to come by (unless you have a magic source, which I would hope you wouldn't mind sharing :). Medium current, medium voltage, low value capacitors (like the 200 pcs 2.3A, 250Vrms, 0.1uF caps I got for $60) aren't unreasonable, if unwieldy to assemble.
Well yeah, but for only 1.6kW. That's 100A peak (and as much voltage) for
16kW.
Well yeah, but I'm not dealing with the raw 400A and 500V, I stated that in the first post -- the cap neutralizes the reactive volts, leaving you with "real" volts to handle. 400A is definetly ugly though, which is one of the things I wanted to discuss in this thread (I didn't state it very explicitly) -- how *do* you switch 400A (or more, for that matter) in a couple hundred nanoseconds, without smoking all your silicon?
Yep.
Tim
-- Deep Fryer: a very philosophical monk. Website:
Seems to me that, at these power levels, any power supply is serious overhead. Why not work directly off the rectified AC line voltage, and start the design from there?
The best way to drive the resonant circuit is with a current source. But you want your MOSFETs to act as switches, so the current source needs to be on the power-supply side. This is usually implemented by with a series inductor. The inductance would be much more than 10uH * 25/6.3, say 1mH. The current is set by the supply voltage, load and tuning frequency, and would be 25A in our example.
That's a pretty serious inductor, especially if you want it to also have very low loss.
As attractive as this looks, it has a big engineering problem, tuning. A common solution is to provide a servo-controlled oscillator frequency, using voltage and current sensors to sense any out-of-tune phase shift.
Yeah, that's the other reason it's more of a thought exercise -- even 160V, let alone 320V or more is too much for water cooled coils made of tubing, I mean because you need so many more turns to make up for the higher supply voltage and lower inverter (thus tank) current.
This is also one of the problems with building a straight up tube power oscillator: you get kilovolts at an amp or two right off the plate. Kilohms, not ohms, so you need, say, a hundred turns of hookup wire for the coil. Damned if you can cool that as easily as 1/4" or 3/8" copper tubing. You can still use tubing and just go for high-assed frequency, but it's crap for melting a chunk of metal. (Good for case hardening though.) So you can use a transformer, but that adds more EM parts handling the high power, and adds some phase shift, potentially messing up your self excitation simplicity.
And hence I went with the L-matched tank coil in my project.
Tim
-- Deep Fryer: a very philosophical monk. Website:
Ya, that's another thing my L-match network has going for it: a mere 50uH or so, 50A rating tops, easy enough to do on ferrite with some hefty wire.
BTDT of course, as I have already have a phase detector and error amplifier. Which reminds me, got any ways of detecting the phase of zero volts? My phase detector gets stuck on when there's effectively no resonant voltage, because the comparator that's supposed to clip the tank's sine wave into a clean square just doesn't have enough signal input. Adding in a dash of inverter output just makes things worse (false peaks and a discontinuous transfer function, ack!).
Hum... missing pulse detector? That might do it.. I may have to sit down with more paper and figure that one out...
Tim
-- Deep Fryer: a very philosophical monk. Website:
Win is of course dead right. I referred to transmission lines for several reasons:
- parallel plates are about the easiest way to get real low inductance, which is what you really need.
- as you increase width, AC and DC resistance decrease, as does inductance. yay.
- it really is a transmission line - although for any practical case, we can analyse it as lumped elements. But TLs get you thinking about fields, which is exactly what you need to think about from an EMI perspective (and with power stuff, self-susceptibility is a major problem)
- R,W,vD have the formula for the inductance of a parallel-plate TL, so we dont have to work it out
but the key aspect is minimising the inductance. at which point you end up with broad flat plates, closely spaced, and bucketloads of caps rather than a few monstrous ones.
So basically, at high currents and relatively slow (200ns) edges, the TL reduces to two plates in any kind of space such that the dielectric constant matters roughly nil? (Besides absurd values putting impedance on par with the circuit, and possibly, slowing down the wave speed to values that matter.)
Tim
-- Deep Fryer: a very philosophical monk. Website:
its the slow edges rather than the high currents that mean we dont care about its TL (AKA distributed circuit) behaviour, and instead can model it as lumped L,C.
the geometry of parallel plates is what gives us the nice low inductance per unit length.
the dielectric constant wont affect the inductance, just the capacitance
- and hence velocity, impedance etc, none of which we really care about. From the perspective of a DC bus, more capacitance (close plates) is a good thing. Witness John Larkins various comments on decoupling caps with multi-layer PCBs in a few earlier threads.
a 200ns edge looks like about 1.6MHz, and if we assume about 67% c, thats a wavelength of 126m, so anything less than 6.3m can be treated as a lumped circuit.
with those sorts of numbers, who cares what the velocity really is.
you can calculate for yourself what sort of Er (many hundreds if not thousands) you need for your circuit to start requiring distributed-parameter analysis. FR4 is about 4.
I've seen PCB material with Er = 300. very expensive.
Yes, that's right and what I normally use; I wrongly expected E~ * f to give the same answer... I'll have to redo my sums.
I don't have time now to respond to your long post, but it's got good stuff to consider and I will. But let me say, you'd do well to consider my suggestion of separating the resonating elements from the driving elements. Yes, you can switch 400A with used industrial IGBT modules obtained at low cost on eBay
Idiots on Google Groups reply to their own message to move it back to the top of the list, but it just annoys real Usenet users where it just proves that they don't understand how Usenet works.
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Service to my country? Been there, Done that, and I\'ve got my DD214 to
prove it.
Member of DAV #85.
Michael A. Terrell
Central Florida
Yes, there were some hanging ends and I was wondering if you forgot about this thread or have been busy with work. Or you just don't care...
Undoubtedly, but the new post inevitably highlights the thread, whether organized by latest-post or tree layout, so Usenet or not, it is effective. Heh, hey, it worked on you. ;o)
Tim
-- Deep Fryer: a very philosophical monk. Website:
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