Improved Expression for Estimation of Leakage Inductance in E Core Transformer Using Energy Method

This paper proposes a simpler and more accurate expression for estimation of leakage inductance in E core transformer, which is the most widely used transformer structure. The derived expression for leakage inductance accounts for the flux extending into air. The finite element method (FEM) analysis is made on the secondary shorted transformer to observe the H-field pattern. The results obtained from FEM analysis are used for approximating the field that is extending into air to derive an expression for leakage inductance. This expression is experimentally validated on prototype transformers of different core dimensions. 1. Introduction Transformer is one of the basic building blocks of many power converters. The following are some of the cases where accurate estimation of leakage inductance is required.(i)Different resonant converter topologies, discussed in [1–5], use parasitics of transformer as a part of resonant tank network. For designing power converter with such topologies, one requires accurate estimation of leakage inductance.(ii)In hard switched converters, in every cycle the energy stored in the parasitics appears as loss in converter. In estimation of efficiency of such converters, one needs to estimate leakage inductance before hand.(iii)For designing snubber circuits to limit device voltage during turn-off transients [6–8], one needs to estimate leakage inductance. These turn-off transients mainly occur due to energy stored in the leakage inductance of the transformer. Methods that are usually employed for estimation of leakage inductance are (i) energy method [8–13] and (ii) method of mutual fluxes. In energy method, the energy stored in magnetic field of the secondary shorted transformer is calculated and equated to where is the leakage inductance of the transformer when referred to primary, and is current flowing through primary. The -profile inside the coil is calculated using Ampere's law. The energy stored in magnetic field is calculated by evaluating the volume integral in (1): The expression derived for leakage inductance using energy method is independent of frequency. Hence, it does not consider any frequency-dependent effects on leakage inductance. The energy method is used for comparing leakage inductance, in different winding configurations. On the other hand, method of mutual fluxes uses Maxwell's equations to predict the leakage inductance more accurately at high frequencies. As this method accounts for frequency-dependent effects like eddy current losses and altered flux pattern due to eddy currents, it gives more accurate