Toroid Inductor simulation

FEMM is open-source software that can simulate electromagnetic and electrostatic problems. Recently, I was developing a high-frequency ferrite transformer for high power applications. After designing and assembling the transformer, I measured the inductance parameter of the transformer. The inductance of the transformer was close enough to the theoretical estimates. 

Subsequently, I planned to simulate the transformer in FEMM. I simulated the transformer and calculated the inductance value and the inductance value was quite close to the theoretical and the simulated values. 

Above is the toroidal inductor with the dimension specified as a, b, and H.  a is the inner radius, b is the outer radius and H is the thickness of the toroidal core. 

The inductance of the toroid is given by the equation, 

The dimensions of the chosen toroidal core are, a = 33 mm, b = 51 mm, H = 20 mm.

The relative permeability of the chosen magnetic material is 1600. The calculated inductance value using the above equation is 25.07 uH .

The below figure shows the FEMM simulation result for the above toroidal core. The inductance of the toroidal core can be calculated in two ways. Follow this link for the two methods. 

From the definition of the flux linkage, Flux linkage = LI

The inductance L can be calculated. The circuit parameters used in the simulation can be found by clicking the circuit properties icon in the simulated window. The simulated inductance value is 12.7/(0.5) = 25.1 uH which is the same as the theoretical value. Another way to calculate the inductance value is to calculate total magnetic energy through simulation and use the inductor energy equation. 

One thing to notice here is that magnetic field density is not uniform throughout the cross-section of the core but highest at the inner edge and reduces from inner to the outer edge. The reason is basic. I hope you know the answer. Comment if you do. Thanks for reading the article.