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Magnetic Design Considerations

Magnetic Design Considerations. Transformers Used to step-up or step-down voltages Inductors Storage during energy transfer Carries a DC current while supplying current Need to avoid saturation of the core. Transformer Primary Voltage in Terms of Flux. Transformer Powers and Efficiency.

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Magnetic Design Considerations

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  1. Magnetic Design Considerations • Transformers • Used to step-up or step-down voltages • Inductors • Storage during energy transfer • Carries a DC current while supplying current • Need to avoid saturation of the core

  2. Transformer Primary Voltage in Terms of Flux

  3. Transformer Powers and Efficiency • Pt = apparent transformer power • Pi = transformer input power • Po = transformer output power • η = transformer efficiency

  4. Bridge Rectifier Example

  5. Analysis • Primary voltage V1 • V1 = KtfN1Φm (Kt = 4.44 for sinusoids) • Apparent Power of the transformer • Pt = V1I1 + V2I2 • For N1 = N2 = N and I1 = I2 = I • Pt = VI = KtfNΦmI • Pt = KtfBmAcNI • Bm = peak flux density • Ac = cross-sectional area of the flux path

  6. Analysis (continued) • Number of Ampere-Turns • NI = KuWaJ • Ku = fill factor (between 4 and 6) • Wa = window area • Area Product • Ap = WaAc = Pt/(KtfBcKuJ) • Current Density • J = KjApx

  7. Core Configuration Constants

  8. Area Product Ap

  9. Core Area for Various Core Types Wa

  10. Design of a TransformerExample 14.6 f = 60Hz V1 = 120V 60-Hz square-wave Vo = 40V, Io = 6.5A Assume η = 95% and window factor Ku = 0.4 Use E-core

  11. Solution • Kt = 4 for a square wave • Output Power • Po = VoIo = (40V)(6.5A) = 260 W • Total Power • Pt = Po(1/η + 1) = 260(1/0.95 + 1) = 533.7 W • Check Table 14.1 for E-core • Kj = 366 x = -0.14 • Choose Bm = 1.4

  12. Choosing the E-core • Choose a type core2-138EI • Ap = 223.39 cm4 • core weight, Wt = 3.901 kg • core area, Ac = 24.4 cm2 • mean length of a turn, lmt = 27.7 cm

  13. Calculate the number of primary turns

  14. Calculate the number of secondary turns

  15. Calculate the primary current

  16. Calculate the primary wire size Check wire-size Table B.2 in Appendix B AWG #16 has cross-sectional area of 13.07x10-3cm2

  17. Calculate the primary copper loss

  18. Calculate the secondary wire size Check wire-size Table B.2 in Appendix B AWG #11 has cross-sectional area of 41.68x10-3cm2

  19. Calculate the secondary copper loss

  20. Push-Pull

  21. Half Bridge with Center-Tap Transformer

  22. Cores With 2 Permeability Regions

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