Ideal transformer
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“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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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

VHS , VLS = Nameplate voltages of High-side, Low-Side

ECE 441


Ideal transformer continued

“Ideal Transformer” (continued)

  • Define the turns ratio as “a”

    • If the primary is the High-Side,

ECE 441


Input impedance z in

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


Input impedance z in continued

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


Real transformer

“Real” Transformer

EP = 4.44NPfΦP ES = 4.44NSfΦS

ΦP = ΦM + ΦlpΦS = ΦM – Φls

EP = E’P + Elp ES = E’S - Els

ECE 441


Ideal transformer

“Real” Transformer (continued)

KVL @ primaryVT = EP + IPRP = E’P+ Elp +IPRP

IP = Ife + IM + IP LOAD

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Equivalent circuit of a real transformer

Equivalent Circuit of a Real Transformer

VT = EP + IPRP = E’P+ Elp +IPRP

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Ideal transformer

“Real” Transformer (continued)

KVL @ secondaryES = ISRS + VLOAD = E’S – Els

E’S = Els + ISRS + VLOAD

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Equivalent circuit of a real transformer1

Equivalent Circuit of a Real Transformer

VT = EP + IPRP = E’P+ Elp +IPRP

E’S = Els + ISRS + VLOAD

ECE 441


Equivalent circuit using leakage reactance

Equivalent Circuit using Leakage Reactance

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Looking into the primary of the ideal transformer

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

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Equivalent circuit parameters referred to primary

Equivalent CircuitParameters Referred to Primary

Define ZeqP = The “equivalent impedance” with all parameters referred to the primary

ZeqP = RP + a2RS +jXlp +ja2Xls

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Equivalent circuit parameters referred to secondary

Equivalent CircuitParameters Referred to Secondary

ZeqS = RS + RP/a2 +j(Xls + Xlp/a2)

ECE 441


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