Frequency Response Analysis (FRA) is regarded as the most effective technique for detecting mechanical faults in transformer windings. However, the main challenge in applying the FRA technique lies in the correct interpretation of the differences between the diagnosis and the reference frequency spectra. A transformer can be modelled as an equivalent circuit network comprising inductances (L) and capacitances (C), where L and C are electrical parameters dependent on the winding geometry; a relationship exists between the winding geometry, the electrical components of the equivalent circuit network and the measured FRA spectra. Through electromagnetic circuit analysis, this paper provides a theoretical basis to develop a fundamental understanding of FRA spectra and their resulting interpretation. The FRA spectra are first explained for a single air core winding with uniform structure, and then the complexity is gradually increased by taking into consideration the iron core, the mutual inductive coupling between parts of the same winding and then between the separate windings of the transformer. Mathematical expressions are developed to represent the relationship between the FRA characteristics and the corresponding electrical components of the equivalent circuit network model. INDEX TERMS Transformer Modelling, Frequency Response Analysis (FRA), Interpretation, Electrical Circuit Analysis NOMENCLATURE Real part of permeability of electrical steel in per unit value Imaginary part of permeability of electrical steel in per unit value Winding series capacitance Winding shunt capacitance to ground α Space coefficient Magnetizing inductance of winding Air core inductance of winding Magnetic coupling factor between parts of winding with iron core present Magnetic coupling factor between parts of air core winding Equivalent series capacitance of winding seen from tested winding terminals in a transformer Equivalent winding shunt capacitance to ground seen from tested winding terminals in a transformer n Number of stages/sections in a lumped element equivalent circuit network model Angular frequency N Voltage ratio of high voltage to low voltage windings of transformer