# Electrical – How find the optimal frequency of a high frequency transformer

high frequencyinverterpower supplyswitch-mode-power-supplytransformer

I have disassembled a "Chinese" power inverter, I found a High-Frequency Transformer, with no label on it.

I would like to make an inverter using this transformer to generate the High voltage to feed into a full bridge to make a pure/modified sine wave inverter.
I "I reversed engineered" the inverter, I found that the transformer was driven in the following way(using center tapped transformer instead of a full bridge): The question is, how I can calculate the best/optimal switching frequency for this HF transformer, assuming I can measure its resistance and inductance?

I need to know where the core saturates and then apply the reverse of V=4.44*N1*f*Bmax?

How the switching frequency will impact the performance(voltage ripple, idle current, losses)?

How PWM modes(Center aligned vs edge aligned ) will impact performances, assuming that both MOSFETs will be driven with the same duty cycle(regulated by a PID / PD loop on output voltage), but 90 degrees apart?

And I need to put flyback diodes in parallel with the n-MOS?

Core loss factors that may not depend on frequency are :

Core eddy current loss is a function of the volts per turn applied to the windings, and the duty cycle. It can be modelled by placing a resistor across one of the windings. According to "Magnetics Design for Switching Power Supplies" *1 by Lloyd H. Dixon, eddy current losses start to become significant > 200KHz and I believe that depends on better core material choices with lower permeability and higher core conductance.

• For example, a square wave of 5 Volts/turn, applied to the primary, will result in the same eddy current loss regardless of frequency.

# Hysteresis losses increase with frequency.

For acceptable losses, flux density swing ΔB must be restricted to much less than $$\B_{SAT}\$$. This prevents the core from being utilized to its full capability but provides a safety margin to thermal runaway when L drops to 0 when saturated.

Core loss is usually expressed in mW/cm³.

e.g. Ref *1 p15 of 84 ΔB, is calculated from Faraday's Law $$Volt-sec=N_{turns}\cdot A_e \cdot ΔB =LΔI$$ for N turns, and Ae cross-sect. area

At a fixed switching frequency and with the normal steady-state operation, the volt-seconds applied to the transformer windings are constant, independent of line voltage or load current. So for a forward rectified converter, the duty cycle must be limited to 50% to allow for core reset.

Your schematic is for a push-pull centre-tap converter. Here you can go up to 100% duty cycle but in a practical sense, since spectral energy bandwidth, BW increases away from 50% duty cycle operating above 90% increases hysteretic losses more.

# Conclusion

Choosing the optimum operating frequency depends on power losses at 90% duty cycle at the chosen core loss levels and find the frequency where it starts to increase quadratically as opposed to linear loss rise with f at max duty cycle (e.g. 90%) which has a fundamental 1st null at 10x f. These harmonics may interfere with parallel resonant frequency SRF which is well above the switching rate so awareness of this effect, I encourage you to examine the output spectrum or with careful probing to avoid probe resonance >10MHz and measurement error, detect the ringing due to the core LC load effects by monitoring the DC current while observing the waveform.

Flux walking is not a problem with the forward converter if the primary off FET switch has an adequate Zener to decrease the magnetizing current to 0 in time ΔT.