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“Real” Transformer

“Real” Transformer. E P = 4.44N P f Φ P E S = 4.44N S f Φ S Φ P = Φ M + Φ lp Φ S = Φ M – Φ ls E P = E’ P + E lp E S = E’ S - E ls. “Real” Transformer (continued). KVL @ primary V T = E P + I P R P = E’ P + E lp +I P R P

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“Real” Transformer

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  1. “Real” Transformer EP = 4.44NPfΦP ES = 4.44NSfΦS ΦP = ΦM + ΦlpΦS = ΦM – Φls EP = E’P + Elp ES = E’S - Els

  2. “Real” Transformer (continued) KVL @ primary VT = EP + IPRP = E’P+ Elp +IPRP IP = Ife + IM + IP LOAD

  3. Equivalent Circuit of a Real Transformer VT = EP + IPRP = E’P+ Elp +IPRP

  4. “Real” Transformer (continued) KVL @ secondary ES = ISRS + VLOAD = E’S – Els E’S = Els + ISRS + VLOAD

  5. Equivalent Circuit of a Real Transformer VT = EP + IPRP = E’P+ Elp +IPRP E’S = Els + ISRS + VLOAD

  6. Flux in the “Leakage coils”

  7. Voltage generated by flux through the window of a coil

  8. Similar expression for the secondary

  9. Equivalent Circuit using Leakage Reactance

  10. Equivalent Impedance of a Transformer

  11. Equivalent CircuitParameters Referred to the Primary Define ZeqP = The “equivalent impedance” with all parameters referred to the primary

  12. Equivalent CircuitParameters Referred to Secondary

  13. Note that the excitation branch has been moved to the left! It’s OK as long as the transformer is operated near rated conditions!

  14. Equivalent Circuit for Step-Down Operation Using High-Side Values Use this equivalent circuit to determine the input impedance of the transformer and load.

  15. Equivalent Circuit for Step-Down Operation Using Low-Side Values Use this equivalent circuit to determine the no-load voltage and the voltage regulation.

  16. Equivalent Circuit for Step-Up Operation Using Low-Side Values Use this equivalent circuit to determine the input impedance of the transformer and load.

  17. Equivalent Circuit for Step-UpHigh-Side Values Use this equivalent circuit to determine the no-load voltage and the voltage regulation.

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