Inductors biased with permanent magnets: Part I ¿ Theory and analysis

It has long been known that when a highly unsymmetrical (Imin¿Imax) current magnetizes a closed iron core in an inductor or transformer, the optimum design includes an air gap in the core to reduce saturation. The presence of the air gap has two opposing effects: 1. it increases the reluctance of the core to both the biasing d-c magnetization and the incremental a-c magnetization; 2. the shift of magnetic operating point due to effect 1 reduces the reluctance of the iron to the incremental magnetization. The result of these two opposing effects is that as an air gap is increased from zero length in an iron core with unsymmetrical magnetization, the inductance of a coil linking the core first increases as the second effect is dominant and then a maximum is reached, after which the inductance decreases as the first effect is dominant.