0. Control

Will you be operating in DCM or CCM? DCM is easy to implement (e.g., UC3843 and other peak current mode controllers), but has a large ripple fraction (>100%), so is quite aggressive, both in core loss, and in the ripple current that must be handled by both primary and secondary filter capacitors.

CCM (continuous conduction mode, as opposed to discontinuous) is harder to realize in a flyback supply. Typically CCM uses an average current mode control, and so must monitor the magnetizing current constantly: both primary and secondary side currents need to be measured (or at least estimated). It can be used with peak current mode controllers with slope compensation, to a mild degree (ripple fraction >30% say). CCM only marginally reduces the filter capacitor ripple current (the current waveforms go from sharp triangles to flatter square waves, but the current is still going fully between peak and zero every cycle).

Also, if you're considering CCM, you may consider a forward converter, which exhibits discontinuous primary current (it's still switching fully on and off), but continuous secondary current (due to the filter choke) and so only needs secondary side current sensing. The isolation transformer has high inductance (no gap) so is easier to design.

At 5W, the parts cost to handle DCM ripple is minor, whereas the complexity to handle CCM is higher, so DCM flyback is the most common choice.

1. Material

Ferrite has lower B_sat than powdered iron types. This limits how much flux density you get in the core, for a reasonable amount of magnetization (amp-turns).

Usually we can't operate near saturation, due to the additional limit of core loss. This can be significant at lower B_pk values, ca. 100 mT. With a relatively small converter, you have a more advantageous surface area to volume ratio, so you can probably afford higher core loss in this case.

Relative permeability typically needs to be in the 20-60 range. This can be a bulk property (powder), or an equivalent (gapped ferrite). (For gapped cores, we can calculate the amount of gap required. For others, we can only check against a list of parts and materials to see which ones meet our minimum requirements.)

Note that core loss is prohibitive for the cheapest powdered iron materials (#26, #52), and passable for others (#8, Kool-Mu, etc.). Ferrite is generally low loss.

DCM flyback converters tend to prefer gapped ferrite.

2. Core Size

We need to store some amount of energy at the peak of the switching cycle. That energy is deposited in the load, so the energy is the output power divided by the switching frequency.

E = P_out / F_sw

In this case, about 62.5 uJ.

For a gapped ferrite, we can assume the core material itself stores nearly zero energy, and the airgap stores the rest. Thus we need some volume of airgap.

We also need some thickness of airgap, because this sets the effective permeability:

mu_eff = l_e / (l_e/mu_r + l_g)

The core-energy assumption is saying that mu_r >> 1, which it is (typically ballpark 2000 for ferrites), so we should look for an l_e/l_g ratio around 20-60.

Energy density is:

e = B^2 / (2 mu)

For the airgap, we use mu = mu_0 (1.257 uH/m), and B = B_pk, whatever we've decided upon, say 100 mT. This gives about 4000 J/m^3.

Incidentally, energy density has units of pressure (J/m^3 == N/m^2 == Pa), and this is approximately the pressure attracting the core halves together. Isn't physics cool?

We need an airgap volume v_g = E/e, or 62.5 uJ / (4000 J/m^3) = 15.7 (mm)^3.

Typical E cores have a l_e / sqrt(A_e) ratio around 6. Let's call that alpha. Putting all these together, we get an approximate selection figure:

v_g = l_e^3 / (alpha^2 mu_eff)

so

l_e ~= (v_g alpha^2 mu_eff)^(1/3)

or for this case about l_e = 28 mm.

Looking at TDK's catalog, I see this being very close:

https://www.tdk-electronics.tdk.com/inf/80/db/fer/e_12_7_6_6.pdfNote that they don't offer a standard gapped version, so we might shop around for a nearby (larger) size, or a different shape than E, that is gapped. Otherwise, we can gap the core with shims, BUT note that the gap counts twice (once in the center, once in the legs), so we must use a shim of l_g / 2 thickness.

We still might not be able to realize this transformer, because we haven't wound it yet. The mu_eff assumption gets us close, though -- its value is motivated by the resistivity of copper, and the lower mu is, the more copper we need for a given inductance. (Worst case, mu = 1, i.e. an air cored inductor, which is all copper!)

For mu_eff ~ 40, we need l_g ~ l_e / 40 = 0.7 mm, or 0.35mm shim thickness. This gives us an inductivity of:

A_L = mu_0 mu_eff A_e / l_e

= (1.257 nH/mm) (40) (19.9 mm^2) / (28 mm)

= 35 nH/t^2

(The fake unit of "per-turn-squared" appears out of nowhere; we could put it into mu_0 == H/(m.t) and A_e == mm^2/t for example.)

Now that we're down to winding design, we need to know the supply and output voltages, since we can put on any number of turns to get the desired voltage/current ratio.

Assuming 12 V:

5W is 5/12 = 417 mA DC, or 833 mA average during the on period, or 1.67 A peak assuming a triangular current waveform (DCM). We need to store 62.5 uJ at 1.67 A, or

L = 2 E / I^2

= 45 uH

So we need N = sqrt(L / A_L) = 35 turns. If we're doing 12 V output, we should use the same again for the secondary, or any ratio for any other voltage. We should also consider V_in(min), and if it's to be adjustable, V_out(max), so we don't run out of duty cycle when these conditions vary.

Checking: B_pk = V_in / (2 N A_e F_sw)

= (12) / [2 (35) (19.9) (0.08)] = 108 mT, pretty close (I've rounded off about as much in the process).

The wire would probably be ~0.25mm dia. or so, to handle the current; maybe a bit more. This takes up a copper cross section of 3.4 mm^2, and with packing density and insulating tape we should expect more like 7-10 mm^2 winding area is required. The E12.7/6/6 core has 25 mm^2 winding area, some of which will be taken up by the bobbin as well (which speaking of, they also don't list one, so we might not use this part after all), but this should be quite adequate.

Finally, the windup -- we can do single sections for each winding, which will lay down in about two layers each. This will give a few uH leakage inductance, which isn't terrible, but we will want to handle it with a snubber, probably an RCD rate or peak clamp type. The snubber power dissipation will be on the order of 1/4 W.

If we alternate primary and secondary layers (interleave), we can about cut the leakage in half. Or we could go with finer wire (0.15mm wire should fit enough turns in a single layer), but do more layers in parallel (2-3 layers each), and alternate primary and secondary layers that way; this can go lower, maybe 1 to 0.5 uH.

Or we can use a transmission line transformer construction, where we start with twisted pair (the wire may have to be triple-insulated type to meet isolation requirements) and wind 35 turns of that however we like. Better still if we use "star quad" (two parallel pairs, twisted together so that the primary and secondary wires alternate), which can get to maybe 0.1-0.2 uH, where we may not need a snubber after all.

We can also use a larger core, with higher mu_eff (smaller gap), to get the same B_pk with much fewer turns, saving wire length -- leakage inductance is roughly proportional to winding wire length, so this can be a handy savings.

If we consider planar magnetics (windings made with PCB traces, with a core clamped around it), the cores available for this purpose have a much lower l_e / sqrt(A_e) ratio -- that is, a large A_e for their size -- so we won't need many turns, and the core is also quite low profile (not much thicker than the board itself). More of a production-oriented option, but handy to know about.

Also, of course, if we raise the switching frequency, we don't need as much transformer, and for purposes like this (the assumed 12V input and 5W capacity), controllers and regulators running up to 2MHz are cheap and plentiful.

Tim