The old TI (nee Unitrode) appnotes are pretty good. There are plenty of books on the subject, alas I don't have any recommendations handy... I'm largely self-taught on the matter.
For a more basic explanation of terms and use, I wrote a page years ago,
https://www.seventransistorlabs.com/tmoranwms/Elec_Magnetics.html#magnetwhich is still not too bad I think. I'm a bit less equivocal on the matter of inductor design, though, alas, explaining how will not "fit into the margins here"...
Regarding your points, in order--
1, 2. k is related to leakage inductance,
https://en.wikipedia.org/wiki/Leakage_inductanceMutual inductance as well, but that's almost only used for theory, you'd rarely use it in circuit.
3. Those are more or less wound multifilar, so we can approximate leakage as the length of the winding times the inductivity of the transmission line thus formed.
Transmission line transformer theory is very useful; at least, if you know transmission lines already.
It's not always a great derivation method -- multilayer windings aren't easy to describe as TLs. But the low-frequency equivalent is still useful, in terms of measuring and relating the parameters of the basic 2nd-order model,
https://www.seventransistorlabs.com/Images/XfmrEquiv.png(where T1 is a transformer with some turns ratio, and primary/secondary inductance)
Namely that Cp (or other C depending on connection) and LL are equivalent to a transmission line of Zo = sqrt(LL / Cp) and τ = pi sqrt(LL * Cp) / 2, or thereabouts.
Anyway, single layer windings, particularly with matching turns counts, so that wires are largely on top of each other for the whole length, do model quite nicely as TLs. Imagine parallel-wire TL, wound edgewise onto a bobbin -- that's a two layer (one layer per winding) 1:1 transformer. Doesn't matter if there's tape between layers, that just sets the spacing between the wire pair. (There is some effect from adjacent turns, when the winding pitch is small; and from the inner layer being shorter length. But these are somewhat lower order effects, and the TL equivalent is in the right ballpark.)
So, you still have to know the wire size, length, number of turns -- they may not tell you these, in which case you can reverse-design the transformer from what it looks like, assuming standard components (core shapes, materials, airgap..), and arrive at a reasonable guess.
Better still, you can sample a few and take 'em apart.
4. Good transformers, >0.98 I'd say. You'll find coupled inductors (particularly split-wound toroids -- popular with CMCs as well) that are a bit worse, but if it's much worse than say 0.95 or 0.9, they might just be something special purpose, like for resonant power conversion, or RF tuning. Pulse transformers may be in the >0.998 range.
To clarify -- CMCs (common mode chokes) are actually more like transformers than chokes. They're used in a somewhat different way (indeed,
sideways); the important part is high magnetizing impedance (hence,
choking off an AC current).
Transformers generally have high impedance, so that they have little effect on the circuit -- also it doesn't much matter what phase that impedance is, so they can be quite lossy (in terms of core loss versus magnetizing reactance), it's just that, the high impedance draws a small fraction of total signal current so you don't care so much.
Transformers, designed with significant (i.e., relatively low) magnetizing inductance, could be better described as coupled inductors. Mind, they're still sold as transformers: this is a conceptual distinction, not a marketing distinction.
And, inductance stores energy, so for a given flux, less inductance stores more energy.
Flux, is integral volts dt, as explained by the link; inductance is the ratio of flux to current. If inductance is lower, it means more current flow for a given flux, and thus more energy storage. It might seem counterintuitive when energy is usually given in terms of current: E = 0.5 L I^2 But this assumes the amount of flux is unlimited, so we can just keep packing more and more energy into an inductor by increasing the current or inductance. But the core size would go up extremely quickly. For a given core (material, size and shape), flux (in the core) is fixed, and all we can do is vary the air gap between core halves (if it's a cut core), and the number of turns (which converts core flux into in-circuit flux, i.e. in terms of terminal voltage; and core magnetization into circuit current). And there's nothing special about turns, you'd store the same energy for the same amp-turns -- just at different flux and current, as you vary the number of turns.
5, 6. Well, if nothing else, you measure it once, and calculate the equivalent -- this can be done with a test circuit, or often, in the switching circuit as well. Example, use these formulas,
https://www.seventransistorlabs.com/Calc/RLC.html#frqor the last section, to go from a resonant frequency and impedance, to L and C.
Specifically, for testing Lp or Ls, leave all windings open-circuit, and connect one winding as shown. The resulting measurement will include Rp or Rs (as a parallel equivalent), and core loss (typically shown as parallel equivalent as well). For an inductor, or coupled inductor (or flyback transformer, etc.), this should be of modest value, and relatively high Q. For a transformer, this should be a relatively high value, and the Q may be poor.
For testing LL, short all other windings, and repeat the measurement. You may want to (or need to) change R1 or C to keep the frequency and voltage ratio in reasonable ranges. Also, don't forget to include signal generator impedance: if you measure V1 and V2, simply use their ratio, and the explicit R1 between them; if you measure V1 open-circuit and V2 closed-circuit, add source resistance to R1.
For two-winding transformers, this gives you all the magnetic parameters; for multiwinding, you may want to continue testing other windings with respect to the others shorted. In general, the coupling factor is a matrix, giving the coefficient between each pair of windings. There are certain limitations on this (I don't know the general formula offhand), namely that if for example k12 = 0.5 and k23 = 0.5, then k13 >= 0.25 or something like that; and, a passive linear transformer will obey reciprocity, meaning the matrix is symmetrical (k12 = k21, etc.). It's
even rarer that manufacturers give any hint about this sort of info, so you're on your own for this I guess. I'm not sure if I've ever seen more than one winding's leakage specified.
As for pulsed operation, presumably you'll get some kind of ringdown:
Here's a typical flyback waveform. Referring to Ch3, at the far left, voltage is low (transistor is on) then jumps up suddenly (turn-off). There is some ringing. In this instant, the transistor turns off, the secondary side diode turns on, and that means the secondary is an AC-short circuit -- the diode and filter capacitor are a low impedance. So the primary side shows leakage inductance, and this resonates with transistor capacitance. LL is small and Coss is modest, hence the fast blip of ringing. Some time later, the flat peak rolls off, as the inductor discharges and the secondary side diode turns off. Now Coss acts in parallel with diode Cjo, and the transformer reflects magnetizing inductance only -- hence the slower ringdown.
This is a typical DCM (discontinuous current mode) waveform, i.e., inductor current goes to zero between cycles. In CCM, the free ringdown period is gone, as the transistor turns on during the top peak.
Note that it works reciprocally: when the transistor turns on, it presents a very low impedance to the primary, so the secondary impedance reflects leakage inductance. This rings with diode capacitance Cjo.
For all three cases, we can identify an inductance and capacitance, and therefore a resonant frequency and impedance.
To dampen these resonances, simply connect an R+C across it, where Rsnub = sqrt(L/C) and Csnub >= 2.5 C.
When LL isn't particularly nice, you'll find this dissipates way too much power; it's not a particularly efficient method, rather brute-force. It's also poor at controlling peak voltages: C needs to be even larger, and R somewhat smaller.
In some cases, you might have enough core loss to do the job already; this is often the case for the lowest quality powdered iron materials (typically mix #26, 52). These are... not recommended for DCM operation.
They can be okay in CCM, with a small ripple fraction (i.e., ripple current peak-to-peak being a small fraction of DC current). Basically what's good for maybe 10W in DCM, but can handle tons of DC current just fine, might be capable of 100W in CCM (I cover this in more detail here,
https://www.seventransistorlabs.com/Articles/Core_Loss.html ).
"7." I never liked the phrasing "magnetic field collapse" -- it implies something that's simply not representative. It implies asymmetry, it implies... uncontrolled transient response, say. The fact is, the inductor simply does whatever you tell it to. In a switching converter, its terminal voltage is always perfectly well defined, clamped between Vin, Vout or some combination thereof, and therefore its rate of current change, and charge or discharge time, is all perfectly well defined.
The least well defined part of all that, is when the impedance changes abruptly: switches turning on and off. And here still, we have well defined impedances, if we just take the time to look for them. Switches aren't ideal, they have resistance or capacitance; transformers aren't ideal, they have leakage, losses, capacitance and so on. In the waveform above, the voltage doesn't spike up, in 0ns, to \$\infty\$V, it's perfectly defined by the switch turn-off rate, node capacitance and transformer leakage. It is entirely our fault, as designers, if we choose to ignore these parameters, and don't take responsibility to control them, whether by design (e.g. transformer windup) or additions (snubbers and such).
Well, in characteristic style, I've ended up writing quite a bit more into this margin than I initially led on, huh? Good luck, in any case.
Tim
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