# Leakage inductance and turns ratio

I am trying to design 9V-6.5A flyback SMPS using PI-Expert design tool. I used reference design to make flyback transformer. It gave maximum permissible leakage inductance of 16.38uH for design with ETD-29x16x10 core, but practically I got around 30uH of leakage inductance. Such vast difference between design value and practical value was not observed for higher voltage design say 15V,24V for same ETD 29x16x10 core. My analytical observation says.... Low voltage (High turn ration) -> High leakage inductance. It there theoretical relation for that????

• Actually, winding structure does affect on leakage inductances and parasitic capacitances. You can go for "1/2 primary -> Secondary -> 1/2 primary approach" for smaller leakage. Please note that leakage is important; because it's a flyback transformer and leakage inductance causes spikes which can show itself as a voltage stress on the switch element even higher than supply voltage. – Rohat Kılıç Dec 20 '16 at 6:46
• What frequency and method did you use to measure it? – Andy aka Dec 20 '16 at 10:31
• You need to go for as low leakage inductance as you can afford. Google interleaved windings and bifilar. Make sure you choose core geometry and wire size to "go even out" (lack of English expression) making only full layers. – winny Dec 20 '16 at 11:21
• @RohatKılıç I already use split winding(sandwich winding) configuration. For 9V SMPS 35 T (Prim1) + 6 T (Sec1) + 35 T (Prim2) used with full layer winding. But similar 13V SMPS have 28 T (Prim1) + 7 T (Sec1) + 29T (Prim2). Both use ETD 29 core with same ferrite grade but different turns ratio. – Dhaval Lalani Dec 29 '16 at 4:18
• In 13V design I got ~7uH of leakage.It is half than permissible of 11uH by PI Expert, but in case of 9V design I got ~30uH while maximum required was 16.38uH..!!!! All these comparisons are made for same core with similar power rated power supply. – Dhaval Lalani Dec 29 '16 at 4:29

Just think about the primary on its own...

If each turn on the primary is ideally coupled to every other primary turn, one would expect inductance to quadruple for every doubling of turns. This doesn't quite happen - take one turn in the primary; the turns closest to it couple well with that turn but turns further away couple less well. This is because of the finite permeability of the core material. If the inductor were air-cored this would be obvious - turns further away hardly couple to each other at all.

So, having a core with significant permeability does help alleviate the problem but there are still local lines of flux around each turn that just do not enter the core and therefore do not couple with turns at some distance from them.

If you had a single turn secondary, it would couple more readily to the primary turns closest to it but those turns further away it would couple less effectively. The more "distributed" secondary turns you have the better are your chances of coupling with those far-away primary turns.

Here's my approach:

As a rule of thumb, the winding with highest output power should be placed closest to the primary. And the sandwich winding method is best for better coupling and lowest leakage:

Since the secondary winding has a few number of turns, spacing this winding across the window width instead of bunching together will help reducing the leakage.

Another thing to consider is skin effect. It plays an important role on coupling. Using multiple strands instead of single wire does increase the coupling. For copper, skin depth is approximately $d[mm]=72/\sqrt{f_{SW}[Hz]}$.

Example:

Vi = 185..265 Vac, Vo = 9VDC, Io = 6.5ADC, f = 100kHz, target eff. = %85

For current density of J = 420A/cm², required cross sectional area for primary winding wire is 0.1mm² (Iin = (Vo x Io) / (eff x Vimin) = 0.38Arms and S=0.38/4.2=0.1mm²), so the wire diameter will be dp=0.35mm. Copper has a skin depth of d=0.23mm; so using multiple strands with a diameter of maximum 0.2mm wires provides better fill factor and efficiency. Let's pick 0.1mm wire. Cross sectional area of this wire is 0.008 mm² but we need 0.1mm², so we should use at least 0.1/0.008 = 13 strands of 0.1mm wire.

For secondary winding wire, required cross sectional is 1.55mm² and wire diameter is 1.4mm. But since the secondary has a few turns and the current is quite high, single 1.5 or 1.6mm thick wire can be used.

Result: 15x0.1mm for primary, 1.5mm for secondary.

Don't forget to follow sandwich winding approach.