Geometric parameters in the measurement of magnetic properties using toroidal specimen

In this study, the derivation of the common formulas for calculating the field quantities of magnetic field strength and magnetic flux density from the physically measurable quantities current and induced voltage is shown in detail for toroidal shaped specimen. The simplifications of the inhomogeneous fields are described, which are based on equivalent geometric parameters and allow the use of the electrical measured quantities. While in the standards and literature no clear definitions of the equivalent geometric parameters are given, suggestions for these definitions are made. A review and comparison of various calculation rules from different standards for the equivalent geometric parameters is done. These calculation methods are further generalized in normalized form as a function of the diameter ratio of the toroidal specimen. Finally, the differences between the field quantities using the different methods of calculating the equivalent geometric parameters are analyzed.