Calculation of self and mutual impedances for coils on ferromagnetic cores

By means of integral transform techniques, the paper establishes a new set of self- and mutual-impedance formulas relating to coils on ferromagnetic cores of circular cross-section. If the core is straight and infinitely long, the formulas are expressed in terms of convergent integrals that may be evaluated numerically. In the case of closed cores, e.g. toroidal cores, the formulas formally reduce to convergent series that may be truncated according to the degree of accuracy required. The formulas follow directly from the solution of Maxwell's equations and therefore offer the ultimate in accuracy.