A numerical study of the coupling coefficients for pot core transformers

When a circuit containing a transformer is to be simulated, one must know the coupling coefficient or equivalent leakage inductances in addition to the other transformer properties. When other inductances in series with a transformer winding are large compared to the leakage inductance the leakage inductance may be neglected in a simulation. Otherwise, the coupling coefficient must be known or the simulation will be inaccurate. Since the degree of coupling depends on the nature of the winding as well as the core, and is difficult to estimate accurately, we have used numerical techniques to study the trends in coupling with geometric parameters for cores having cylindrical symmetry. Magnetic vector potential has been found using the TOPAZ2D finite element code, and then correspondingly interpolated numerical integration has given the inductances for an equivalent circuit. Results from our calculations show that although the magnetizing inductance changes greatly as a core saturates, the coupling coefficient changes slowly so long as some reasonable effective permeability remains. Actual values depend on the turns ratios and any air gaps present. For a typical pot core geometry without an air gap the coupling coefficient ranges from 0.997 to 0.999 for effective permeabilities from 600 to 1800. With air gaps the coupling coefficient drops, but stays even more constant with permeability