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A certain three-winding transformer contains one primary and two secondaries. The operating frequency is 40 kHz. The primary winding contains a total of 60 turns of #26 AWG, arranged in three layers. The secondary windings each consist of five turns of copper foil, one turn per layer. The foil thickness is 0.25 mm. The primary layers have porosity 0.8, while the secondary layer porosity is 1. The primary winding carries a sinusoidal current having rms value I, while each secondary carries rms current 6I. The windings are not interleaved: the primary winding is closest to the center leg of the core, followed by secondary winding #1, followed by secondary winding #2. (a) Sketch an MMF diagram illustrating the magnetic fields in the vicinity of each winding layer. (b) Determine the increased copper loss, due to the proximity effect, in each layer. (c) Determine the ratio of copper loss to dc copper loss, F R , for the entire transformer windings. (d) In this application, it is not feasible to interleave the primary winding with the other windings. However, changing the conductor size is permissible. Discuss how the windings could be better optimized.

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