An Approximate Theory of Eddy-Current Loss in Transformer Cores Excited by Sine Wave or by Random Noise

An approximate theory is developed for the eddy-current loss in transformer cores excited by high-frequency (megacycle) sine waves and by broad-band (video) random noise. The boundary conditions are established, subject to which the field equations governing the distribution of the electric and magnetic fields in thin rectangular laminae are solved, and from which in turn are determined the skin depth δ
o
and mean eddy-current loss W̄ for current and voltage-fed transformers. The voltage-fed case is considered in greater detail, as it is the more general analytically and the more common in practice. From it the constant-current or current-fed case is readily derived. Curves and formulas are given showing the variation of δ
o
and W̄ with frequency and lamination thickness for a sine wave and for a uniform band of noise (f
2
-f
1
) cycles wide. Among the results it is found that the skin depth decreases, as one would expect physically, with increasing lamination thickness, frequency, core conductivity, and effective permeability. The mean eddy-current loss in the constant-voltage transformer diminishes with increasing frequency or spectral width, because of skin effect, and increases with the thickness of the laminae. For voltage-fed transformers W̄ varies approximately as the inverse square root of the bandwidth. On the other hand, W̄ in the constant-current cases is found to vary about as (bandwidthf
^½
). A short discussion of the advantages and limitations of the theory, of the approximations made, and of some of the considerations involved in reducing eddy-current loss is included.