Flyback vs. Coupled inductors vs. Transformer?

Question

So I am in the process of making a high voltage power supply and after a failed attempt at using a modified MOT and difficulties finding a flyback transformer, also difficulties understanding how they work, I've come here. I am wondering if I can make my own "flyback" from a ferrite rod, since as far as I know, a flyback is coupled inductors? But then, if you check the image, how are primaries able to be wound on the other side of the transformer and create such high voltage? Is that simply inducing a current in the primary of the flyback which is affecting the secondary, but I suppose that wouldn't make sense? I just don't understand how the ferrite doesn't become saturated from such low windings on the primary, when being used as a transformer. An explanation of this would be very helpful because after hours and hours on the internet I have not gained any concrete knowledge about the workings of these things.

Answer 1

There are two main differences between the cores in a fly-back transformer and in a traditional power transformer.

1. The core in a fly-back transformer has a much higher reluctance. This can be achieved in a number of ways. One is to add an air-gap to a core. Another is to use a core with a "distributed air gap", and a third is to use core materials that have naturally high reluctance. A distributed air-gap arises when the core consists, for example, iron powder in a binder. The binder is not air, but it is called an air gap nonetheless.

An increase in reluctance allows a core to store more energy for the same inductance. However, for the same inductance, more turns will be required.

Energy storage is important for a fly-back transformer because energy is stored in the core and air-gap (in fact largely in the air-gap) for part of a cycle, and then released later in the cycle. However, in classical transformer action, the power drawn by the load on the secondary side is transferred immediately from primary side power supply.

2. The core in a fly-back transformer generally can work efficiently at might higher frequencies than a traditional power transformer. The cores of traditional power transformers are typically made with silicon steel laminations. They work well for mains frequency applications, but become very lossy at higher frequencies. Ferrite cores, on the other hand can be efficient will past beyond 1 MHz.

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A word about air-gaps. A ferrite rod is not an ideal core for either a traditional power transformer, or for a fly-back transformer. The air-gap in a rod is, for the most part, too big. The consequence of this is that it will take a great many turns to create the appropriate inductance. An air gap in the millimeter range is much more appropriate.

Answer 2

Math Keeps Me Busy's answer covers the magnetizing aspect (self inductance), so that leaves the topic of mutual inductance (leakage).

In general, we can express a nonideal transformer as a "wye" of inductors (and an ideal 1:1 transformer, if we still need to express isolation between the two sides):

^{simulate this circuit – Schematic created using CircuitLab}

Where L1 = Lp - M, L2 = M and L3 = Ls - M.

Or a "delta" configuration, equally well.

See: Coupled Inductors as Transformer | Analog/RF IntgCkts

Note that, for odd turns ratios, we get negative inductors. This is merely a representation, of course. But if we confine ourselves to a 1:1 turns ratio (putting an ideal 1:N transformer afterwards), then L1 + L3 become realistic values. Particularly when the coupling coefficient (\$k = \frac{M}{\sqrt{L_p L_s}}\$) is large (\$M\$ approaching \$\sqrt{L_p L_s}\$), we call their sum leakage inductance (LL), and L2 the magnetizing inductance (Lm). This doesn't stop working for small k of course, just that we are less interested in LL, or find it less useful for such cases (which are also less commonly used).

Geometrically, leakage is the flux not coupled between windings. There is flux surrounding each winding, and not only that, but each part of each wire in each winding as well. We can overlap a pair of windings to share some of that flux, and thus couple the inductors; to couple them significantly, they must occupy nearly the same space.

This does not change when a core is introduced. In fact, the core contributes additional flux, but this does not change the intrinsic flux in the space around each winding. The core makes it "easier" (takes less current) to store a certain total amount of flux; but the introduction of a core does not affect the flux outside of its boundary. (Well, it does, it's a bit more complicated than this; but typical situations can be decomposed into rough equivalents, and, the above is most true for the most common case.)

When we draw the diagram with windings on opposite sides of a core loop, we're doing just that: a diagram, a cartoon, and nothing else. Indeed, this is a terrible way to construct a transformer, generally speaking: it maximizes leakage (the space between windings).

Practical transformers put the windings on the same "leg" of the core, with the windings in layers, one on top of the other. When low leakage is required, they might indeed be interleaved even closer than this -- for example, using a twisted pair, which leaves merely the gap between wires as leakage (which is therefore proportional to the between-wires geometry, and their length; such transmission line transformers are particularly convenient for analysis, and high-bandwidth applications).

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Why does leakage matter? We take a slight diversion.

Consider the flyback converter. Notice it's a minor transformation of the boost converter:

^{simulate this circuit}

The secondary simply has a different DC reference voltage, but the "start" ends of both windings share a supernode (they connect to either side of an ideal voltage source) so the dynamics are unchanged.

Leakage in the transformer, is equivalent to an inductance between M1 and D1 (LL1 and LL2 as shown). Any current stored in this loop, represents energy that must be cycled through the converter (because the current is rising and falling), but which cannot be cycled into the output (because there's no diode directly from M1 to Vo, or from GND to D1). Without explaining how/why (basically, there's always a resistor somewhere), this energy can only be lost. Thus, we require low LL to achieve high efficiency.

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So, in summary: for the flyback converter (and generally similar arguments for other types), we require low LL for high efficiency, good output (cross)regulation, etc.; and we obtain low LL by placing the windings in as close proximity as is feasible. The core has no effect on LL (indeed you can measure this: dismantle a ferrite-core transformer, short the other windings, and measure LL on the remaining winding; insert core and observe LL increases by some percent, if at all), and is used to increase Lm instead.

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Finally, we come to the high voltage driver. What gives? Given all the above, they've maximized leakage! You literally can't put it any farther away, while still being on the same core. And it's a single-switch circuit, so, it's gotta be something flyback-y, right?

Well, never assume anyone truly knows what they are doing. (Which is a much deeper, fundamental truth than is needed here, but as a rule, too.) This is especially true of gimmicky things like high voltage generators. Newbies just want to throw together a couple parts and make sparks, damn the engineering, who needs theory, it's cool and fun (or until it's deadly, but, yeah). So you find a lot of circuits like this out there.

These are basically memes in electronic form. Indeed, they don't even need to function well, if at all; they just need to be passed on, often enough to continue being passed on: the definition of a meme.

Well, anyway, note that the primary windings for these (CRT flyback) transformers are generally within the major winding assembly itself. They knew what they were doing (or, that is to say: to a much greater degree).

Mainly, the added winding is put there, because, well, it's additional, there's nowhere else to put it. And, it seems to work well enough, so who cares.

There is some justification for the leakage, in other circuits, actually; when using the two-transistor oscillator ("ZVS", or sometimes "Royer", but technically it's a Baxandall oscillator), leakage allows the primary circuit to resonate, over a range of frequencies depending on load. This keeps the circuit running even with the output shorted (or, it can, anyway), and limits output current.

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On a more practical note, some converter designs tolerate more leakage, and some use it intentionally (even adding some in series as needed). The two-switch forward converter delivers load current during the forward (on) phase (hence the name), and has clamp diodes to return both magnetizing and leakage inductances to the supply. Resonant converters work much like the above ZVS description, but comprehensively designed along with a controller to adjust frequency and pulse timing as needed to deliver desired output voltage.