A Mutual-Impedance Approach to Modelling Transformer and Inductor Windings

Transformer equivalent circuits based on modeling magnetic coupling or mutual inductance describe
important aspects of transformer behavior such as leakage inductance and cross regulation. Transformer
equivalent circuits based on adding L-R networks typically focus on winding losses predicted by Dowell’s
method, but they often don’t model coupling effects, and they typically don’t work well at predicting winding
losses for transformers that supply independent loads or for transformers that have windings connected in
parallel unless very complicated models are used. These threes presentations describe an equivalent circuit for
transformers that models both magnetic coupling effects and winding losses while using a surprisingly simple
structure. The key to this approach is that it is based on mutual impedances that have both inductive and resistive
components. This equivalent circuit models the well-known magnetic coupling coefficients, but also
models the lesser-known resistance coupling coefficients. This allows the model to accurately model
frequency-dependent losses as well as frequency-dependent leakage inductances. The performance of a
simulated phase-shifted bridge converter with two independent loads is compared to hardware results. Various
effects of mutual impedance are illustrated including cross regulation, how an external ZVS inductor
affects the winding losses, and how the frequency dependence of leakage inductances affects diode reverse
recovery and the energy that needs to be snubbed.