Ring core transformers are analysed by using a two dimensional axisymmetric model. The primary and secondaries are foil windings surrounding a core with finite permeability. The secondaries are positioned between core and primary winding. They can either be short circuited or connected to a resistive or inductive load. The current in the primary is constant up to the switching point at t = 0. At this moment it is abruptly forced to zero hereby causing transient fields in all windings. The spatial distribution and temporal devolution of these fields is affected by the loading of the secondaries.The scope of the paper is to analyse the current density distribution and the total current in the secondaries and the primary as a function of time. To achieve this the spatial distribution of the magnetic field for t < 0 is expressed by a sum of spatial eigenfunctions each of them decaying with a particular time constant in t > 0. Because of spatial continuity requirements the time constants in adjacent regions with different material properties must be identical.The transformer analysis can easily be modified to become applicable for coils. Also the switching process may be modified: instead of changing source voltage or current material parameters as for instance conductivity can be altered in the framework of the developed formulas.
展开▼
