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“Ideal Transformer”

“Ideal Transformer”. E’ P , E’ S = Voltages induced in the primary, secondary E’ HS , E’ LS = Voltages induced at High-side, Low-Side V HS , V LS = Nameplate voltages of High-side, Low-Side. “Ideal Transformer” (continued). Define the turns ratio as “a”

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“Ideal Transformer”

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  1. “Ideal Transformer” E’P , E’S = Voltages induced in the primary, secondary E’HS , E’LS = Voltages induced at High-side, Low-Side VHS , VLS = Nameplate voltages of High-side, Low-Side ECE 441

  2. “Ideal Transformer” (continued) • Define the turns ratio as “a” • If the primary is the High-Side, ECE 441

  3. Input Impedance, Z’in Z’in = Impedance looking into the primary = E’P / IP Turns ratio a = E’P / E’S >>>>> E’P = aE’S ECE 441

  4. Input Impedance, Z’in (continued) • For an IDEAL transformer, VAin =VAout • E’PI*P = E’SI*S • I*P = E’SI*S / E’P = I*S / a • IP = IS / a ECE 441

  5. “Real” Transformer EP = 4.44NPfΦP ES = 4.44NSfΦS ΦP = ΦM + ΦlpΦS = ΦM – Φls EP = E’P + Elp ES = E’S - Els ECE 441

  6. “Real” Transformer (continued) KVL @ primary VT = EP + IPRP = E’P+ Elp +IPRP IP = Ife + IM + IP LOAD ECE 441

  7. Equivalent Circuit of a Real Transformer VT = EP + IPRP = E’P+ Elp +IPRP ECE 441

  8. “Real” Transformer (continued) KVL @ secondary ES = ISRS + VLOAD = E’S – Els E’S = Els + ISRS + VLOAD ECE 441

  9. Equivalent Circuit of a Real Transformer VT = EP + IPRP = E’P+ Elp +IPRP E’S = Els + ISRS + VLOAD ECE 441

  10. Equivalent Circuit using Leakage Reactance ECE 441

  11. Looking into the primary of the Ideal Transformer Z’in = a2ZLOAD = a2(E’S / IS) IS = E’S /(RS +jXls + ZLOAD) >>> E’S / IS = RS + jXls + ZLOAD Z’in = a2RS + ja2Xls + a2ZLOAD ECE 441

  12. Equivalent CircuitParameters Referred to Primary Define ZeqP = The “equivalent impedance” with all parameters referred to the primary ZeqP = RP + a2RS +jXlp +ja2Xls ECE 441

  13. Equivalent CircuitParameters Referred to Secondary ZeqS = RS + RP/a2 +j(Xls + Xlp/a2) ECE 441

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