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In gapped inductors, the fringing field of the air gaps causes additional eddy current losses in the windings and an increase of the inductance. Since this impact of the fringing field is very significant, calculating the additional eddy current losses and the inductance increase is important in the design of inductors. This article proposes analytical formulas to accurately calculate the inductance and the additional eddy current losses in gapped inductors with solid round wire and Litz wire windings. The analytical formulas are verified by measurements, showing that the proposed models are accurate over a wide-frequency range. [ABSTRACT FROM AUTHOR]

For comprehensively optimizing high-frequency foil inductors, calculating the increased inductance and the additional eddy current losses due to a two-dimensional magnetic fringing field caused by air gaps in the center leg is mandatory. This article proposes an analytical model that accurately calculates the inductance and the additional eddy current losses in gapped inductors with foil windings. The analytical field expressions are combined into closed-form winding loss and inductance formulas and verified by measurements. Furthermore, the frequency dependency of the inductance due to the shielding effect of the foil conductors is being discussed. [ABSTRACT FROM AUTHOR]

A fast and accurate model of the transformer leakage inductance is crucial for optimization-based design of galvanically isolated converters. Analytical models are fastly executable, and therefore, especially suitable for such optimizations. This article compares several analytical leakage inductance per unit length models with respect to the accuracy and computational effort. The considered models are applicable to E-Core and U-Core transformers. 2D FEM simulations are used as a benchmark to evaluate the model accuracy, whereas the computation time is extracted as an indicator for computational effort. Six different transformer prototypes provide the geometries for the comparison. Based on the conducted comparisons, Roth's model is the most accurate. Rogowski's model is the fastest low-error model. Margueron's model is the most versatile as it takes the finite permeability of the core into account. The conducted comparisons lay the foundation for accurate and fast Double-2D modeling of the transformer leakage inductance as it is executed for the two main cross sections of E-core and U-core transformers: inside the transformer window, and outside the transformer window. This article is accompanied by a supplementary document summarizing the equations of Roth's and Margueron's model. [ABSTRACT FROM AUTHOR]

This paper presents a combined phase-shift and frequency modulation scheme of a dual–active-bridge (DAB) ac–dc converter with power factor correction (PFC) to achieve zero voltage switching (ZVS) over the full range of the ac mains voltage. The DAB consists of a half bridge with bidirectional switches on the ac side and a full bridge on the dc side of the isolation transformer to accomplish single-stage power conversion. The modulation scheme is described by means of analytical formulas, which are used in an optimization procedure to determine the optimal control variables for minimum switch commutation currents. Furthermore, an ac current controller suitable for the proposed modulation scheme is described. A loss model and measurements on a 3.3-kW electric vehicle battery charger to connect to the 230 \textV_\textrms  / 50-Hz mains considering a battery voltage range of 280–420 V validate the theoretical analysis. [ABSTRACT FROM AUTHOR]