About the BH Curve screet shot The first image below is of the voltage ( Y axis) versus current (X-axis) in the primary winding of the saturating transormer.
I can see that current should equate to field H. But I wonder if there are any difficulties when equating voltage to flux density because (I am assuming) voltage is itself dependent upon inductance. It seems that real world inductances do have some frequency dependence (of actual inductance value in Henries that is).
In a textbook BH curve, I think there is no restriction upon the rate at which the field changes, it's just field vs flux.
Voltage is the time derivative of flux. So the top and bottom slopes, you need to imagine integrating them; going clockwise from bottom left, instead of jumping up then sloping down, imagine it moving diagonally up-right, then slowing down to nearly flat; which sounds a lot more like the usual B-H hysteresis curve you see.
This loop is dependent on frequency. If voltage remains constant, then width shrinks as frequency goes up (and saturation quickly becomes less severe); if width remains constant, then voltage goes up.
The B-H curve also depends on frequency, gaining more or less hysteresis (or the equivalent thereof) and changing its average slope. This is equivalent to the small-signal parameters changing with frequency, typically mu' dropping and mu'' peaking around some cutoff frequency. The loop area corresponds to mu'', while the slope corresponds to mu'.
Typically it's measured at lower frequencies, where mu' is dominant, and mu'' is obviously present, but is mostly true hysteresis (area ~independent of frequency). (Note that mu'' is calculated as an inductance component, whose reactance depends on frequency; so a constant loss fraction looks like a steeply changing imaginary-inductance parameter: this is why mu'' drops asymptotically at low frequencies.)
Incidentally, why are flyback transformers always depicted with "opposite polarity dots" - is this contruction (with primary would the opposite way to secondary) essential for a flyback design?
Equally, are "same polarity windings" essential for a forward converter?
Interesting question, actually -- the answer often depends on EMC. As such, this may be more advanced than you were expecting, and on a more basic level (transformer flux and overall winding voltages/turns/etc.), no, it doesn't matter, just so long as the polarities are correct.
Consider a 1:1 transformer, primary and secondary are single layers on a cylindrical form, same size wire. This looks very much like a twin-lead transmission line, wound edge-wise, and the characteristic impedance will be around 100 ohms (assuming magnet wire and a couple layers of insulating tape between them). The instant the primary switches off, the secondary switches on, magnetizing current is transferred. If the start end of both windings is switched (primary transistor, secondary diode), and the far end of both is common (primary DC bus, secondary GND), then we have a current pulse applied to one end of this transmission line -- the primary was carrying Ipk and the secondary 0, and suddenly they've swapped, to 0 and -Ipk -- and this wave propagates down the transmission line (in the space between windings).
On the primary side, we observe a spike -- normally attributed to leakage inductance, which is really the LF equivalent of the TL's inductance. (Which, if we're using this at an impedance much lower than 100 ohms, is most likely the best way to express it. Like a 12V 1A (DC) converter, that'll be closer to 4A peak, so down to 12V/4A = 3 ohms at the switch node, well into the inductive range!)
On the secondary side, we observe the dI/dt being modest, complementary to the primary-side spike -- the voltage has to spike up to drive that current into the secondary. This is easier to see with the tee or pi equivalent of the transformer,
the series element(s) manifest as leakage, and going from zero to full current over some time, requires some voltage pulse, simply enough.
And between primary and secondary, that is, the common mode -- we see at one instant, primary DC bus and output GND are steady (on the winding finish ends), while a spike is happening on the switch nodes (winding starts). After that wavefront propagates through the windings (transmission line), it reflects off the finish end and bounces back and forth (again, if the switching impedance is very low, this bouncing manifests as inductance). Meanwhile, the common mode voltage is driven apart by half the step voltage -- we get a big injection of common mode noise here.
If we ~short out the common mode voltage with a capacitor between grounds (DC bus to secondary GND, or primary GND which is bypassed to DC bus with a much larger capacitor already), we can reduce the CM voltage, confining most of the imbalance (leakage inductance spike) to the switching nodes. Hence this is a first line of defense against common mode emissions.
If the windings were counter-wound, then the primary switching edge would couple directly to secondary GND, and the diode doesn't see anything until after one transmission line delay. This situation puts 100% switching edge into the common mode, which is much worse -- remember in the first case it was just the leakage inductance spike, much shorter than the full pulse.
Well, these are convenient approximations, mind -- typically the switching edges are 10s or 100s of ns, while the transmission lines are just a few ns. We aren't working with ideal wavefronts that ping back and forth, we're working with sloppy waveforms that work more with the LF equivalent properties of the transformer (LL and Cp). The actual tradeoff need not be quite as bad as these examples show.
But it also gives you some idea of how to optimize transformer design, both to reduce LL and Cp (to reduce losses), and to help reduce EMI. If we can interleave P and S across multiple parallel layers, we can effectively make multiple TLs in parallel, which therefore have a lower total Zo, closer to Zsw -- LL goes down, at the expense of Cp going up. (When Zsw is so much lower than Zo, the rise in Cp isn't nearly as important. Conversely, when Zsw is higher than Zo -- typically the case in low power or high voltage converters -- Cp is more important, and looser winding geometry can pay off.)
Or we can balance operation, keeping the DM switching in the DM -- we can note this is a DM-CM conversion problem, so by reducing that conversion factor, we reduce EMI proportionally. This is an advantage of the two-switch converter: both ends switch at the same time (give or take variation in propagation delays), one going up, one going down; leakage manifests on both at the same time and common mode is ideally zero. Even if it's not (the delays, or edge dV/dt rates, don't match perfectly), it's a hell of a lot easier to filter because the fundamental balances out; we really only have to filter the high frequency crap that didn't balance out.
If the winding ratios are very different, we might end up with a situation where the shorter winding practically acts as a ground plane, with respect to the other -- this is most explicit in the case of 1-turn foil windings against N-turn wire windings. Here, it doesn't matter as much what the short winding is doing, but we are very concerned about the N-turn winding. We might treat it as a balanced winding over ground plane, just ignoring for now the fact that the "ground plane" is itself at an average 1/2-switching-node voltage. So, if we use two switches, one at each end of that winding (primary 2-switch inverter, secondary just two diodes), we can balance out its transients (which may be quite substantial -- a 400V step, say, on a 100-ohm TL, is a lot of peak current (~4A) and ringing!), and then only have to filter out the shorter winding's switching waveform.
Or we can insert a shield layer, which has the same effect as a one-turn foil winding: it acts as a ground plane, except that once again because it has to be slitted, there's some voltage across it, but at least it's only one turn, not, a hundred or whatever. And if we're careful about how we wind and wire up the primary and secondary, we might still be able to cancel that out (namely, if the shield is grounded on one side of the bobbin, and the windings come out the other side -- this works for double-opening EE cores for example, we can position it effectively 1/2 turn away from the windings; not so much for, say, EP cores).
Tim
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