magnetics design -- 60mJ energy impedance matching

Ah, sorry. I didn't realize your spec. was snipped.

ISTM you want to make 0.5W across 0.68 ohms, for 50mS.

To do that you need a pulse transformer that can make

0.6V @ 850mA across your 0.68 ohm ignitor, from a 300V pulse.

To make up for connection losses and such at the ignitor, we'll take a WAG and say you want V.sec=2V @ 2A, which allows for 0 to 1.6 ohms of hookup loss. Adjust those assumptions as you see fit.

That's a 150:1 turns-ratio on the transformer.

I.pri = I.sec/150 = 13mA, which drops just 1/4 volt across your 20-ohm firing line--transmission losses are minimal.

Critical damping to stop ringing? Why does that matter? The thing's going to ring regardless of the transformer design, but your 20 ohm hookup will damp it.

50mS is a half-cycle of 10Hz, which sounds a lot like rusty old iron territory to my rusty self.

For a physical reality check, you might consider how large a 220VAC to 2VAC wallwart would be.

If the pulse could be shorter, the core could be a lot smaller.

HTH, James Arthur

More quiet as well. :-)

Lower cost, ease of packing, flexibility, etc. If I were looking for anything truly suspicious, it would be 40 gauge or finer. 30 gauge is pretty obvious and, frankly, I'd like it more obvious by choosing visible colors for it. Red wire wrap wire, for example.

Jon

Yes. .5W * 50ms = 25mJ.

If an average, then SQRT(.5W/.68) is indeed about 850mA. Problem is, this won't be an average situation. This will be a pulse from a cap discharge. So the current will likely vary a bit unless I add a lot of extras to filter and shape it. Which I don't want to do.

Secondary of 2V, roughly, at 2A, roughly. Yes. But these are all averages and then inflated a bit.

The way I looked at this is to take a slightly different tack at it. I figured that what I want a turns ratio such that the volts across the secondary roughly equals the current across the secondary times the squib resistance. Since V_sec=V_pri/a and I_sec=I_pri*a and finally, V_squib=I_sec*R_squib, I got a=sqrt(V_pri/I_pri/R_squib), which gives me about 25:1 as a turns ratio.

I would normally think 150:1 is fine, except for a few problems I can guess at. I'll get to those.

Yes, except....

Yes, if the primary current were 13mA. But did you calculate the primary inductance to achieve that?? We're getting neigh into kH territory. And I've never seen one of those. Way overdamped, too.

I'd need to buy into copper commodity stocks, first. ;)

Well, I'm actually fine with ringing, as long as enough of the energy gets across within the required time period. I just used that as a rough approach. I could loosen up on that. But if it rings and the primary current is high enough (smaller primary inductance), then I'm facing losing most of the energy in the wire. Bad news.

Short time periods imply higher currents, since the Joules is a constant. I'd like to allow simple (idiot proof) wiring, which means whatever they have on hand (or in a pinch) to attach to the secondary.

I'm looking to keep the peak currents on the secondary in the area of about 10A. As you already figured, an average of 850mA is required to get the job done. So 10A is a roughly doable target. Much more than that and it may create other problems I'd like to avoid.

Jon

Probably should have written, kHy. Hopefully, it got across.

Jon

Starting over with some different assumptions:

Want power in resistor. Want to make resistor look bigger, in particular, arbitrarily bigger than the transmission line resistance (maybe by 10 times). Voltage is higher and current is lower, but how much doesn't matter.

So we'll use an ideal transformer. With infinite inductance, the resistor is reflected straight through. Offhand, if the line is 20 ohms, we want the squib to look like 200. But it's 0.68 ohms, so we need a 294:1 impedance ratio or 17:1 turns ratio.

99% of the power is dumped into the load in 2.3 RC, so for t =3D 50ms, tau =3D 22ms and C =3D 22ms/200 ohm =3D 109uF. Voltage is V =3D sqrt(2*E /= C) =3D sqrt(2*0.05J / 0.0001F) =3D 32V. So a 100uF, 35V cap will suffice here. Quite moderate voltage ratings here.

For the transformer not to look like anything, it needs to have an inductance maybe 10 times the nearest impedance, so a primary impedance of 2kohms or so (at whatever the operating frequency could be considered to be) would be prudent. If we ballpark it as 45Hz average (1/tau), then L =3D 7H pops out. That's not too horrible.

Peak current from the capacitor is around 32V / 200 ohms =3D 0.16A. RMS for most of the pulse is closer to 80mA or so. Small wire is fine.

Now you just need a core with enough winding space and permeability for 7H worth of ~32AWG wire.

More choices: you could add a CMOS chopper (an H bridge thing, maybe build it with high-Vgs MOSFETs so you can built it complementary without worrying about more charge pumps) and have it run (self excited?) at 1kHz let's say. Just let it buzz down until the cap is discharged (a couple cycles). A _stock_ 2k:8 ohm audio transformer would be more than enough on the other end!

For that matter, an audio transformer may already be enough. Worth a try. Shame on you for not going directly to the junk box and trying it! ;-)

Tim

Well, this is my first shot at attempting a magnetics design. And I enjoy taking the opportunity to learn theory.

Interesting thoughts about H-bridge chopping. Complicates what I'd imagined as simpler, but what the heck?! I'll play with the idea and see how it flies. I kind of like it. I'd still like to learn if my volume calculations are solid, but I can set that aside for another day, too.

Jon

I remember being taught the rule of thumb that core cross-sectional area times winding cross-sectional area was a useful metric for comparing power transformer designs. But I haven't done much power transformer stuff, so I haven't practiced much with the formulae.

Thank goodness someone else asked this question.

George Herold

You're making this too complicated--25mJ is 25mJ. The thermal mass surrounding the ignitor integrates it for you. The main limit I see is if you hit the squib too hard it'll disintegrate (har) before it can deliver its full thermal payload. How hard is "too hard"? Dunno.

What you've just said is that V.sec = the squib voltage. They're directly connected, so no argument there.

Since V_sec=V_pri/a and I_sec=I_pri*a and finally,

Well, I'm kinda rusty, but ISTM the primary is determined by the volt*seconds per turn your core allows.

One weber being a volt*second through one turn, and a Tesla being one weber/m^2,

given a 3x3cm cross section laminated iron core that can handle 1T,

300V * 50e-3 sec turns.pri = ------------------ = 16,700 turns 1T * (0.03m)^2

Then choose secondary turns to give the desired output voltage.

turns.sec = turns.pri/150 = 111 turns.

If you could detonate the squib with a shorter pulse you could use far fewer turns, plus fatter wire.

Your stated requirements--especially the 10Hz part--demand a hefty chunk of iron. Sending 400Hz AC down the line instead would make the transformer _much_ smaller, and the squib wouldn't care.

For fun, try simulating this chunky beast:

R1 SW1 / 20r .------/ -----/\\/\\/\\----. .----------. | C1 _)(_ | --- 1.5uF 120H _)(_ 5.5mH 0.68r --- V=320V _)(_ | | | | === === === ===

Cheers, James Arthur ~~~~~~~~~~~~~~~~~~~

Version 4 SHEET 1 880 680 WIRE -48 -48 -288 -48 WIRE -288 -32 -288 -48 WIRE 32 32 0 32 WIRE -288 64 -288 48 WIRE -48 64 -48 -48 WIRE 0 64 0 32 WIRE 32 64 32 32 WIRE -64 112 -128 112 WIRE 48 112 16 112 WIRE 144 112 128 112 WIRE 368 112 256 112 WIRE 368 128 368 112 WIRE -128 144 -128 112 WIRE -128 224 -128 208 WIRE 144 224 144 192 WIRE 256 224 256 192 WIRE 368 224 368 208 FLAG -288 64 0 FLAG 144 224 0 FLAG 256 224 0 FLAG 368 224 0 FLAG -128 224 0 FLAG 32 64 0 SYMBOL ind2 128 96 R0 WINDOW 0 -32 39 Left 0 WINDOW 3 -62 73 Left 0 SYMATTR InstName L1 SYMATTR Value 120H SYMATTR Type ind SYMATTR SpiceLine Rser=10 SYMBOL ind2 272 96 M0 WINDOW 0 -33 37 Left 0 WINDOW 3 -65 72 Left 0 SYMATTR InstName L2 SYMATTR Value 5.5mH SYMATTR Type ind SYMBOL res 352 112 R0 SYMATTR InstName R1 SYMATTR Value 0.68 SYMBOL voltage -288 -48 R0 WINDOW 0 -4 -25 Left 0 WINDOW 3 24 104 Invisible 0 WINDOW 123 0 0 Left 0 WINDOW 39 0 0 Left 0 SYMATTR InstName V1 SYMATTR Value PULSE(0 5 10mS 10uS 10uS 1S) SYMBOL res 32 96 M90 WINDOW 0 -39 58 VBottom 0 WINDOW 3 -36 59 VTop 0 SYMATTR InstName R2 SYMATTR Value 20 SYMBOL cap -144 144 R0 SYMATTR InstName C1 SYMATTR Value 1.5µF SYMBOL sw 32 112 R90 SYMATTR InstName S1 SYMATTR Value "" SYMATTR SpiceModel MySwitch TEXT 136 88 Left 0 !K L1 L2 .99 TEXT 104 272 Left 0 !.tran 0 250mS 0 5uS TEXT -280 312 Left 0 !.model MySwitch SW(Ron=0.1 Roff=10Meg Vt=1 Vh=0 Lser=10n Vser=.6) TEXT -336 160 Left 0 !.ic V(n002)=320

I had already considered it. It's in the neighborhood of 80uH each way. It gets tossed into the model I'm using as leakage inductance. My fault for not mentioning it, earlier. I apologize for that.

Jon

That's where the dissipation takes place (except for the wiring), yes.

The all-fire spec says >> allows for 0 to 1.6 ohms of hookup loss. Adjust those

Yeah.

Egads!! It's the 3cm x 3cm that I'm actually trying to AVOID!

Instead of the switch, I just use a .IC spice command to set the initial voltage on C1. But yes, nice curve and low primary current.

I'm just not wanting 3cm x 3cm, kilometers of copper wire, and a 120H primary! I'm looking for something that can be entirely placed in a pocket here.... and not noticed, that much. That 120H monstrosity makes me laugh, just thinking about it!

Another thing crosses my mind... firing a three-engine or dual engine rocket. In this case, the energy delivery would need to be faster, I think, than 50ms and sufficiently simultaneous. In that case, I think I may be forced to re-consider the idea of energy storage at the remote site (which doesn't injur the existing desire to avoid that in the single-engine case) and to use flash-lamps for simultaneity and _safety_. It's very highly unlikely they will be triggered without a fairly high voltage, which I can generate over a single conductor wire and ground stakes at each end, I think. I'll need to consider how to avoid static charges that can only develop very, very small currents, just to be dead sure, but that is simple enough. More to play with.

Jon

Yet another thing I need to go think about. On first blush, I read your use of "winding cross-sectional area" as being not too different from "core cross-sectional area" in the case of toroids that I was thinking about. But do you mean the cross-section of the wire in the first phrase? That doesn't sound right, but I have to ask. Because otherwise, if I'm winding around a torus, the winding cross section is about the same as the core cross section.

Can you clarify what was being taught?

Jon

That sounds promising, and like fun.

Of course, but, meanwhile, your specs demand it. Hopefully I've illustrated that, and why.

You actually could do it with about a fist-full of iron and copper; it's not a ridiculous approach, it's just way bigger than your goal.

Right. You either need to store energy at the rocket, safely somehow, or go to a.c. transmission down the firing wires. A

300V, 400Hz squarewave, transformed down to 1.5VAC, direct into the squib, for example.

The no-local-storage philosophy is excellent and preferred, I think.

Fun project.

Cheers, James Arthur

That's what my example calculated--the max flux density for a given core.

Flux density = total flux / cross sectional area

I took it a little farther & calculated turns per winding.

Cheers, James Arthur

Pardon my lack of clarity.

While the core area sets the amount of flux that can be linked by any one turn of wire, the cross-section through which one can thread wires (however many) is also important.

The cross-sectional area of a single wire controls the copper loss and sets limits on current levels. BUT the cross-section available through which to send all the wires in the winding sets a limit on the transformer design realted to the power handling capacity.

For a given winding window, you can put a few large diameter wires (low voltage, high current) or lots of small diameter wires (high voltage, low current) or anything in between. But the available window limits the Volt-Amp product of the winding.

That is as fundamental a limit on the design as the limit imposed by core cross-section.

Is this any clearer? If not, ask away, and I will endeavour to pull my explanations out of the mud.

It's a bit better than a rule of thumb. It comes from the following:

V = N*d(phi)/d(t) so that V*t = N*phi (volt*seconds). But phi = B*Ac making V*t = N*B*Ac.

B is in Tesla, Ac is core area in square meters, N is turns of wire.

A given core has a core area Ac and a window area Aw. The number of turns you can put on that core is a function of Aw and the wire diameter (d) so that N = Aw/(d*d). The primary uses half of this and the secondary uses the other half. So you have Np = Aw/(2*d*d). Wire doesn't always stack perfectly and you might use wire with heavier insulation and you might wind the wire loosely, and so on. So, there is a fudge factor associated with the number of turns you can put on a core. Try .8 for estimation purposes so that Np = .8*Aw/(2*d*d).

So now you have V*t = .8*Aw*B*Ac/(2*d*d). Insert the maximum B from the core curves or data, insert your wire diameter, calculate your V*t, and you will have the AwAc product.

Referring to your earlier schematic:

The .67 ohm load reflects to the primary as 25*25*.67 or 418 ohms. Adding in the 20 ohms shown gives 438 ohms load on the capacitor. The V*t will be the integral of the usual time constant which I calculate to be 300*R*C = .197. If the core is iron, B can be up to maybe 10kGauss or 1 tesla. I think you said the wire is 30 AWG so the diameter is about .00028 meters in diameter.

Unless I've done something wrong, this give an AwAc product of 38.6e-9. So, your core should have about 2 square centimeters of iron area with an equal amount of window area depending on your choice of geometries.

It's been many years since I've gone through this, so please cut me some slack if I've made any glaring mistakes. Anyway, you get the idea.

Cheers, John

Oh, no. I have a hard time imagining anything clearer! It's so clear, in fact, that I think I actually understand some more of what I've been reading!!

Thanks very much, Jon

Thanks very much for the thoughts. I need to go through these, together with the other materials I have around (Unitrode magnetics book and some basic teaching materials, mostly, and zero experience) and make sure I follow well. (I'm definitely NOT going back to Maxwell equations, closed but arbitrary 3D surface integrals for magnetic fields, electric fields from point source electrons, etc. At least not today!) But one point is that I'm NOT necessarily using 30 gauge for winding. That's what I'm using to get the 100' out to the rocket site. The primary winding wire can be adjusted as appropriate. Same for the secondary. I just hated the volume results I was getting.

Anyway, much appreciated. I _will_ take advantage of the generous offer here and see where it takes me.

Jon