Comparative study of two analytical methods for calculating the parasitic capacitance in toroidal transformers

Transformers are of paramount importance in the implementation of different power converters such as pulsed power generators and switched-mode power supplies. The role of the transformer network is becoming even more prominent in applications that use networks of transformers or multi-winding configurations, such as series-connected transformers in pulsed power generators to provide several isolated voltages. Recently, toroidal cores have gained more popularity owing to offering compact size, less weight, and less leakage inductance due to the absence of gaps in their structure. However, their parasitic capacitance can adversely influence the performance of the power converters due to the resulting electromagnetic interference (EMI). Therefore, the parasitic capacitance of the transformer is a decisive factor in the system performance and it should be targeted to allow performance boosting. In this paper, the parasitic capacitance of transformers is modeled based on two different analytical methods. In addition, an accurate function is proposed to calculate effective parasitic capacitances considering all capacitive couplings, including turn-to-turn and turn-to-core capacitors. Afterward, these two methods are verified by planar, axisymmetric, and 3-D finite-element simulations via FEMM and COMSOL Multiphysics software, respectively. Finally, different analyses and simulations are compared with experimental results.