Improved equivalent circuit representation of air-core transformer for higher-frequency operation

Purpose The purpose of this work is to develop an improved equivalent circuit model for air-core transformers operating at higher frequencies. By refining the classical Cauer-based representation, this study aims to achieve more accurate impedance and current behavior over a wide frequency range, with particular emphasis on improving low-frequency performance. Design/methodology/approach This research uses a full field-circuit modeling approach. Initially, a finite element method (FEM) of coupled coils is formulated to capture electromagnetic interactions. These complex matrix equations are then reduced using the Padé via Lanczos (PvL) method, which accurately approximates the frequency response while significantly lowering the computational order. Based on the reduced model, impedance characteristics are determined for both magnetizing and horizontal branches. A modified circuit structure is then proposed and rigorously validated by comparing its performance − specifically impedance characteristics and current waveforms − against field-model simulations under various load conditions. Findings The analysis demonstrates that the classical equivalent circuit fails to accurately reproduce the impedance behavior of the magnetizing branch at lower frequencies. The proposed modified structure rectifies this, achieving significantly better agreement with results of field-model. Simulation results confirm that the proposed equivalent circuit in the more accurately replicates both the amplitude and phase of load currents, eliminating the discrepancies found in the classical model. Originality/value This study identifies a limitation of the classical Cauer-based representation of the magnetizing branch in air-core transformers, related to its improper low-frequency behavior. It is shown that the traditional structure does not satisfy the zero-pulsation boundary condition, leading to a non-zero remainder in the PvL approximation and reduced modeling accuracy at low frequencies. To overcome this issue, a physically consistent modification is proposed by introducing an additional resistance R0 into the magnetizing branch. By combining field-based parameter extraction with PvL reduction, the method preserves computational efficiency while significantly improving low-frequency accuracy, providing a reliable tool for wide-frequency analysis of higher-frequency coupled systems.