Ferrite Transformer Design Tool: Push-Pull, Forward and Flyback

The data are those published by Ferroxcube, using a single source for every row. This is not needless precision: the same commercial names can refer to different cores depending on the manufacturer, and combining one manufacturer’s geometry with another manufacturer’s A_L can produce large errors.

The worst case is EE25. The Ferroxcube E25/13/7 has A_e = 52 mm²; cores with 84.7 and 40 mm² cross-sections are also sold under the same commercial name. A factor-of-two difference in cross-section means a factor-of-two difference in the required turns. Before relying on a part designation, measure the centre leg.

The winding area is not the core’s geometric window area but the bobbin winding area: it already accounts for the bobbin wall thickness and is therefore the correct value to use for fill calculations. In a mains-connected power supply, however, insulation distances and safety tape consume additional window area that is not included here.

The three topologies share the same calculation because they share the key feature: the flux swings symmetrically around zero, so the usable excursion is twice the peak flux density. Only the voltage actually applied to the winding changes — in a half-bridge it is half the input voltage because the two capacitors split the DC bus.

The duty cycle is specified per switch and cannot reach 0.5: dead time is required so that the two bridge legs never conduct simultaneously. A value of 0.45 is already close to the practical limit.

The displayed current is the average value; copper-loss calculations use the RMS value, which is higher for pulsed waveforms and depends on duty cycle. This is one reason why a switching transformer can run hotter than the average current alone would suggest.

The estimated efficiency refers only to the transformer. It does not include switch commutation losses, output-diode losses or filter losses, which in a real power supply can be comparable to or greater than transformer losses.

In a forward converter the flux is unidirectional: it rises from zero to its peak during the on-time and must return to zero before the next cycle; otherwise it accumulates and the core saturates after only a few periods. The reset winding performs this function and, with a 1:1 ratio, requires the duty cycle to remain below 0.5 — half a period for magnetisation and half for reset.

There are two costs. For the same core, roughly twice as many turns are required as in a symmetrical topology because only half the flux excursion is used. In addition, during reset the switch sees twice the input voltage: with rectified mains input this means using a transistor rated for at least 800 V.

In return, it is a single-switch topology with no shoot-through risk and no need for an air gap in the core. Below roughly one hundred watts it is a reasonable choice.

In a flyback converter the magnetic component operates primarily as a coupled inductor. When the switch is on, the primary stores energy in the magnetic field and the secondary is off; when the switch turns off, the stored energy is transferred to the secondary. In ideal discontinuous-conduction mode, the transferred power equals the energy stored in each cycle multiplied by the switching frequency.

The air gap is essential, although the reason can seem counterintuitive: the magnetic path is deliberately interrupted to reduce effective permeability, allowing more current before saturation. In a gapped core, almost all the stored energy resides in the air gap rather than in the ferrite — the ferrite mainly closes the magnetic path and confines the field.

This calculation assumes discontinuous conduction: the magnetising current returns to zero during every cycle before the next one begins, which is the defining condition of DCM. Many low-power flyback converters operate this way, and it makes the calculation straightforward. The calculated inductance marks the boundary between the two modes: for the same load, frequency and duty cycle, a higher inductance moves operation into continuous conduction, where different equations apply.

The calculated air gap neglects ferrite reluctance and therefore slightly overestimates the required gap. The final check is performed by measuring the inductance of the completed winding and adjusting the spacer thickness, which is the normal laboratory procedure anyway.

Alternating current does not use the entire conductor cross-section uniformly: it concentrates near the surface in a layer whose thickness decreases with the square root of frequency. At 50 Hz the skin depth is about nine millimetres and the effect is negligible; at 100 kHz it is only slightly above two tenths of a millimetre, so a one-millimetre wire uses less than half of its copper effectively.

A practical rule is to keep conductor diameter below twice the skin depth and, when more copper area is required, use several conductors in parallel rather than one thicker wire. The calculation cards flag this automatically: if the selected wire is too large, they indicate how many parallel conductors should be used.

Simple parallel wires are still affected by proximity effect: adjacent conductors influence one another and current distribution remains uneven. Litz wire addresses the problem more completely by transposing the strands so that each one occupies every position in turn; above 100 kHz and at substantial current, it becomes the effective solution.

The waveform factor is 4 for a square wave and 4.44 for a sine wave: it links the quantity relevant to flux with the quantity relevant to power. Switching topologies use approximately square waveforms, so 4 is the appropriate value in most cases.

The result is a lower bound, even more so at high frequency than at 50 Hz. It does not account for the packing inefficiency of round wires, multiple conductors required by skin effect, or above all safety insulation: in a mains-connected supply, primary-to-secondary insulation tape and creepage/clearance requirements consume a significant fraction of the window in a small core.

Use this result as a starting point: take the first core that is large enough, select it in the card for your topology, and check fill factor and losses. If the winding does not fit, move up one core size.

Cores: data are taken from Ferroxcube datasheets, using a single source because parameters from different manufacturers should not be mixed. The winding area is the bobbin winding area, not the core geometric window. TDK publishes slightly different values for the same nominal cores — for ETD29, for example, l_e is 70.4 mm rather than 72.0 mm — and systematically lower A_L values because N87 and 3C90 are not the same material.

Watch the names: commercial designations do not uniquely identify a core. Parts sold as “EE25” can have cross-sections of 52, 84.7 or 40 mm²; “EE13” parts can have 12.4 or 22.4 mm²; and “EE30” parts can have 60 or 108.7 mm². Before using a row in this table, verify that the core in hand has the same dimensions.

Materials: saturation flux density, permeability and loss data are taken from TDK (N87, PC44) and Ferroxcube (3C90, 3C94) datasheets. Steinmetz exponents are not published directly: they are derived from the loss points published for each material, and the note below the global parameters states exactly which points are used. Where a material does not provide enough data points, the missing exponent is taken from a similar material and this is marked in the table.

Verification: with the exponents derived for N87, the model predicts 185 kW/m³ at 500 kHz and 50 mT versus the published 215 kW/m³, i.e. 14% lower at a point five times higher in frequency than the reference. This is the expected accuracy from a two-exponent model: good near the reference point and indicative farther away.

Fill factor: k_u ≈ 0.29 for bobbin-wound ferrite at 100 kHz is the McLyman value, compared with 0.4 for 50 Hz transformers. The difference comes from thinner wire, which packs less efficiently, and from the reduced usable window area.