# HBFEM for Magnetic Field and Electric Circuit Coupled Problems

In most cases, pulse width modulation and zero-current switched resonant converters (including LLC converters, DC biased HVDC transformers and HV transformers) can be considered as a voltage source to the magnetic system, which is always coupled to the external circuits. In that case, the current in the input circuits will be unknown, and the saturation of the current waveform occurs because of the nonlinear characteristic of the magnetic core and power electronic device.

# HBFEM for a Nonlinear Magnetic Field with Voltage Driven

When a high-frequency transformer of switching mode power supply is excited by a voltage source, such as pulse-width modulation (PWM) converters and zero-current switched (ZCS) resonant converters, the numerical analysis of the magnetic field should be carried out by taking account of the voltage source and the external circuits. If the excitation waveform is a square wave or triangular wave, it can be considered as a linear combination of harmonics. For a DC-biased transformer problem in the HVDC power system, the voltage source and the external circuits will be considered in the HBFEM simulation, which is a magnetic field- and electric circuit-coupled problem.