Calculation of the Inductance and Resistance Matrices of Medium-Frequency Transformers

Abstract

Due to the ever-increasing switching speeds of wide band gap (WBG) devices, the high-frequency behavior of magnetic components, such as medium-frequency transformers, is becoming increasingly significant. To describe this complex high-frequency behavior, large multiconductor networks are commonly employed. The frequency-dependent parameters of these networks are typically represented as matrices. However, accurately calculating these matrices often necessitates time-consuming finite element analysis (FEA), which significantly limits the investigation of various geometries within a practical timeframe. This paper addresses this problem by proposing a model based on analytical formulations for the frequency-dependent resistance and inductance matrices of transformers with litz wire windings. The model is experimentally verified showing good agreement to the measurements over a wide frequency range. Compared to FEA only a marginal deviation of less than 2% is noticeable, whereas the calculation is more than 200 times faster.

Keywords

• Eddy currents
• high-frequency effects
• inductance
• magnetic energy
• ac resistance
• impedance matrix