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The use of hyperconductors presents entirely new conditions in the design of transformer windings. Because of the very large mean free path of electrons, a few parasitic effects of resistivity can no longer be neglected: size effects determine the minimum thickness of the conductors, magnetoresistive effects are much less adverse with ac fields than with dc fields. As regards the low value of the penetration depth of electromagnetic waves, three types of aluminium windings with one single turn per layer have been studied: 1) Wide-Sheet Windings: The supplementary losses due to the radial field are high; their proportion is 340 percent in the example considered. 2) Transposed-Band Windings: The proportion of supplementary losses due to the radial field is reduced to 110 percent if the width of the strips is 0.4 mm. 3) Perfectly-Transposed Windings: An increase in length of the conductors must be accepted. This increase and the radial field result in additional losses of 90 percent for the same width of strips of 0.4 mm. If the geometry of the two windings and the ampere-turns are fixed, and if the lateral dimensions of the conductors remain the same, the losses pass to a minimum value for a value of the apparent resistivity which is a function of these dimensions. The total losses become 3.75 times smaller than those of the wide-sheet winding in reducing the lateral dimensions of the strips and in simultaneously choosing a metal of greater purity. This reduction in the dimensions is, however, limited by the size effect. Beryllium presents less difficult problems.