Fast Estimation of Best Achievable Inductor Power Density in Circuit Simulation (with DC-bias Effects)

This paper shows two fast algorithms that when combined, enable inductor volume and loss estimation based only an inductance value and an arbitrary steady-state current waveform. Together, these two algorithms offer an easily accessible way to include magnetic components into multi-objective-circuit-simulation-level topology optimizations for power density, without any reliance on big component/material databases or artificial intelligence approaches. The first algorithm is based on an existing method for finding the optimum number of windings for an inductor, but is expanded here to include DC-bias dependent Steinmetz Parameters. This is initially demonstrated with a precise numeric solution before being reduced to a faster analytic approximation that yields excellent agreement. The second algorithm finds the optimal geometric scaling of a reference core by equating power losses with thermal power dissipation to ensure maximum power density. The algorithms are applied in simulation to a Monte-Carlo optimization of a buck circuit, where the resulting inductor and topology design is fabricated in hardware. The efficiency is measured and compared to the predictions from the circuit optimization.