Deriving and validating an electrodynamic model of a voltage transformer from scratch

Abstract

Comprehending the in-depth functioning of a voltage transformer beyond the trivial voltage ratio, generally deducted from the application of Faraday’s law to an open secondary circuit, can be quite challenging for both students and teachers. In this paper, the authors propose an approach that uses Faraday’s and Ohm’s laws alone to derive an electric equivalent circuit for a transformer, with which is possible to accurately explain and predict currents and voltages in its primary and secondary coils under different load resistors connected to the secondary. The authors intend to use a common real-world application as motivation for students to learn Faraday’s law in the context of a modelling and simulation framework, which consists of deriving a model from fundamental physical laws that, after experimental validation, is capable of accurately predicting and explaining a complex phenomenon.

Complete cycle of modeling and simulation for wireless power transfer using circuit theory, simple electronics, and open-source software

“…The model used to simulate the WPT circuit in figure 1 is the transformer model [22] illustrated in figure 2, in which each coil is modeled as a series connection of a self-inductance, a mutual inductance and a parasitic resistance.…”

Actual vs textbook transformers

“…In that case equations (1) and ( 2) are not relevant since the transformer is not connected to a voltage source. More detailed descriptions of transformer operation, in terms of its equivalent circuit, are given in [5] and [6] and in textbooks dealing with electrical circuits.…”