page_title: Proximity effect (electromagnetism)
section_title: Dowell method for determination of losses
hierarchical_section_title: Proximity effect (electromagnetism) / Dowell method for determination of losses
caption_attribution_description: English: AC resistance of a portion of a transformer winding according to Dowell's method.
context_page_description: In a conductor carrying alternating current, if currents are flowing through one or more other nearby conductors, such as within a closely wound coil of wire, the distribution of current within the first conductor will be constrained to smaller regions. The resulting current crowding is termed the proximity effect. This crowding gives an increase in the effective resistance of the circuit, which increases with frequency.
context_section_description: This one-dimensional method for transformers assumes the wires have rectangular cross-section, but can be applied approximately to circular wire by treating it as square with the same cross-sectional area.
  The windings are divided into 'portions', each portion being a group of layers which contains one position of zero MMF. For a transformer with a separate primary and secondary winding, each winding is a portion. For a transformer with interleaved (or sectionalised) windings, the innermost and outermost sections are each one portion, while the other sections are each divided into two portions at the point where zero m.m.f occurs.
  The total resistance of a portion is given by
  RDC is the DC resistance of the portion
  Re(.) is the real part of the expression in brackets
  m number of layers in the portion, this should be an integer
   Angular frequency of the current
   resistivity of the conductor material
  Nₗ number of turns per layer
  a width of a square conductor
  b width of the winding window
  h height of a square conductor
caption: The ratio of AC to DC resistance for a portion of a strip winding at different frequencies (δ is Skin depth). It can be seen that increasing the number of layers dramatically increases the resistance at high frequencies.
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