High Frequency Transformer Design

Main page | Use of the tables         | Calculation of primary turns | Tips                     
Top of page | Design of HF-Transformer | Calculation of wire-diameter | Literature Notes

Use of the transformer-core-tables

The high-frequency transformers are calculated with the help of the effective core volume Ve and the minimum core-cross-section Amin. For a required power output Pout = Vout · Iout and a chosen switching frequency  f  a suitable core volume Ve must be determined. Then an optimal ΔB is selected depending on the chosen switching frequency and also regarding the temperature rise of the transformer. (see [2], [3]).

The program makes suggestions for You can change the suggested value for the primary number of turns N1 according to your desires (the modification must be concluded with "return"). In each case a new value for ΔB will be displayed in the corresponding column. This also results in a change of the number of secondary turns N2 such that the ratio N1/N2 will not be affected. The turns ratio N1/N2 can only be changed on the simulation side.

The wire-diameter proposed by us as well as the wire-cross-section is always calculated for a current density of S = 3A/mm2. If you change the number of primary turns, it can happen that the wire cross-section proposed by us no longer fits into the winding area, especially if you choose a smaller core (Gray writing), than the one suggested by us.

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Design of HF transformers

High frequency transformers transfer electric power. The physical size is dependent on the power to be transfered as well as the operating frequency. The higher the frequency the smaller the physical size. Frequencies are usually between 20 and 100kHz. Ferrite is mainly used as the core material.

Data books for appropriate cores provide information about the possible transfer power for various cores.

The first step to calculate a high frequency transformer is usually to choose an appropriate core with the help of the data book which provides certain tables for this purpose. Another way to choose an appropriate core is described in [1] and [2] where at first a core-weight or core-volume is determined depending on the transfer power and switching frequency.
In the second step, the primary number of turns is calculated because this determines the magnetic flux-density within the core. Then the wire-diameter is calculated, which is dependent on the current in the primary and secondary coils.

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Calculation of the minimum number of primary turns:

Illustration 1: Voltages and currents of the transformer

It is assumed that there is a square-wave voltage V1 at the primary side of the transformer. This causes an input current I1, which consists of the back transformed secondary current I2 and the magnetising current IM (see illustration 1). A core without an air-gap is used in order to keep the magnetising current as small as possible.

The square-wave voltage at the input of the transformer causes a triangular shaped magnetising current IM which is almost independent of the secondary current (see also the equivalent circuit). The magnetising current is approximately proportional to the magnetic flux Φ i.e. to the magnetic flux density B. The input voltage V1 determines the magnetic flux in the transformer core corresponding to Faraday's Law V = N · d(Φ)/dt (see illustration 2).

Illustration 2: Input voltage and magnetic
flux density of the transformer

For the transformer on the right in the diagram above, the following applies:

Eqn 1.0

Now the minimum number of turns N1 can be calculated to ensure that a certain change of flux-density ΔB is not exceeded. The saturation flux density of +/-0.3T, (which means ΔB = 0.6T) cannot be used normally for high frequency transformers. In Push-Pull converters going around the hysteresis loop with every clock cycle would cause unacceptable losses, i.e. heat generation. If no further information concerning core losses and thermal resistance is available, ΔB should be limited to ΔB = 0.3...0.2T with usual frequencies (20kHz to 100kHz). Further information concerning the selection of ΔB can be found in [
1] and [2]. From this a suitable number of turns for N1 results:

Eqn 1.1

(Where Amin is the minimum core cross-section. This determines the maximum flux density. Amin is given in the data-sheet)

With single transistor forward converters, the core is magnetised in one direction only, while with the push pull converter it is magnetised in both directions. If the core is used up to the saturation level, the maximum change in flux density with the push-pull converter may be 0.6T and may amount to 0.3T for the single transistor forward converter, if usual ferrites are used.

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Calculation of the wire-diameter:

The wire-diameter depends on the respective r.m.s. value of the coil current. This can be calculated from the coil power. If the losses are neglected and it is assumed that with Vin_min the maximum duty cycle is achieved, it follows that: In the above calculations the magnetising current can be neglected. The current density S is chosen between 2 and 5 A/mm2, depending on the thermal resistance. The wire cross-section Awire and the wire diameter dwire can be calculated as follows:

Eqn 1.5

Usual cores are designed such that the above calculated coil fits into the available winding area. Primary and secondary windings both need an equal amount of the winding area.

For high frequencies and large wire-diameters, the skin-effect must be taken into account. It is recommended to use copper-foil or HF-wire for frequencies > 20kHz and wire-cross-sections > 1mm2.

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