# Why is flyback air gap needed for energy storage?

Why do so many sources say something along the lines "since a flyback transformer stores energy, an air gap is needed"? I have seen this reasoning in textbooks and app notes.

I thought air gaps cannot store energy and I thought also a flyback transformer stores energy with its inductance, and an air gap reduces inductance so I would think it also reduces an inductor/flyback's ability to store energy.

Where am I confused?

Unlike a forward-topology transformer (where the primary and secondary windings are conducting at the same time), the flyback transformer must store energy during the primary switch on-time, delivering it to the load during the primary switch off-time.

A forward-topology transformer doesn't need any gap since the peak flux density is a function of the applied volt-seconds only; the power being delivered 'through' the transformer isn't a variable (other than its effect on duty cycle). It's only the magnetizing current that moves the core along its hysteresis loop, which doesn't pose any saturation risk if everything is well-designed, since the primary and secondary ampere-turns cancel each other out.

A flyback transformer doesn't have the ampere-turn cancellation benefit of a forward converter, so the entire $\frac{1}{2}LI^2$ primary energy moves the core up its hysteresis curve. The air gap flattens the hysteresis curve and allows more energy handling by decreasing the permeability of the core. You will of course need to add more turns to get your desired inductance compared to no-gap, but you avoid core saturation.

• It is another way of saying that I must add the gap to raise the flux saturation point so that more current may flow before saturating? And more DC flux flowing implies a higher energy stored in the core? – EwokNightmares Aug 2 '13 at 19:26
• The core can handle the same peak flux density with or without the gap. You're not changing Bmax by gapping. – Adam Lawrence Aug 5 '13 at 17:25

The key point here is that without an air gap an inductor will saturate if you try to put any current through it so inductance will fall and you can't store any energy.

The term "Flyback Transformer" is a little misleading and its more useful to consider it as coupled inductors rather than a transformer because the action is quite different with a conventional transformer energy is going into the primary and out of the secondary at the same time it does not store energy. With a "Flyback" transformer energy is first stored then released.

Taking some things we know about inductors

$$v = L \frac{di}{dt} = N A \frac {dB}{dt}$$

Where v is voltage, i is current, N is turns, B is flux density and A is the effective magnetic area.

Also

$$H = \frac {N \ i}{l} \Rightarrow i = \frac {H \ l}{N}$$

where H is the magnetic field strength, N is turns and l is magnetic path length

Finally permiability

$$\mu = \frac {B}{H} \Rightarrow H = \frac {B}{\mu}$$

Thus

$$i = \frac{B \ l}{\mu \ N}$$

Now we can calculate Energy

\begin{align} Energy & = \int{i \ v} \ dt\\ & = \int{\left( \frac{B \ l}{\mu \ N} \right) \ \left( N A \frac {dB}{dt} \right)} \ dt\\ & = \frac {A \ l}{\mu}\int{B} \ dB\\ & = \frac {A \ l}{\mu}\frac{B^2}{2}\\ \end{align}

The energy storage is therefore only possible in the air gap and is proportional to be air gap volume and the square of the flux density.

• Energy storage is only possible in the air gap? Then how do all the gap-free inductors of the world store energy then? Or do they not? – Phil Frost Aug 3 '13 at 1:00
• @PhilFrost Distributed gap core materials. There is no mechanical gap which you could slide a piece of paper through. There are microscopic gaps between the material grains, which lower the permeability of the material. – Nick Alexeev Aug 3 '13 at 3:37
• Strictly speaking you can store some energy without the air gap but the permeability of magnetic materials such as ferrite is so much higher than free space that energy storage is negligible in the magnetic material. As pointed out by @NickAlexeev the gap does not have to be air just non-magnetic and it can be distributed into a number separate gaps, including microscopic ones. – Warren Hill Aug 3 '13 at 7:46
• Thank you Warren Hill, your derivation convinces me and its good to filter out the bad information I read elsewhere with this :D – EwokNightmares Aug 8 '13 at 13:41

Contrary to what most people think, including yourself, most of the useful energy is stored in the gap of the core.

For the case of ferrite, the gap is distributed between the tiny metallic particles so it too has as an effective gap used for calculations. This gap linearizes the BH loop and increases the current handling before saturation.

Air gaps are usually used for safety considerations. For a flyback transformer, you do not want arcs between the primary and secondary winding, and use an air gap.

• He's talking about core gapping, not isolation between windings. – Adam Lawrence Aug 2 '13 at 18:51