Analytical Triple-2D Leakage Inductance Model of Cone Winding Matrix Transformers

The transformer leakage inductance is one of the limiting factors for pulse shape quality in high voltage pulsed power (HVPP) applications such as cancer treatment, particle accelerators, and free electron lasers. Cone winding matrix (CWM) transformers are commonly used in HVPP applications as they offer low leakage inductance, low parasitic capacitance, high power density, and high insulation distance. This paper proposes an analytical Triple-2D leakage inductance model for CWM transformers. The model is based on a 2D model applicable to tilted cone windings which is derived by analytically integrating the magnetic potential. The Triple-2D modelling concept enables high accuracy and versatility. The model is verified with 2D FEM simulations and measurements on an existing pulse transformer for the compact linear collider at CERN. The analytical model is not only accurate and generally applicable but also rapidly executable enabling its time-efficient integration in optimisations.