# “Ideal Transformer” - PowerPoint PPT Presentation

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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”

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

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### “Ideal Transformer” (continued)

• Define the turns ratio as “a”

• If the primary is the High-Side,

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### 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

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### 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

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### “Real” Transformer

EP = 4.44NPfΦP ES = 4.44NSfΦS

ΦP = ΦM + ΦlpΦS = ΦM – Φls

EP = E’P + Elp ES = E’S - Els

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“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

VT = EP + IPRP = E’P+ Elp +IPRP

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“Real” Transformer (continued)

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

E’S = Els + ISRS + VLOAD

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### Equivalent Circuit of a Real Transformer

VT = EP + IPRP = E’P+ Elp +IPRP

E’S = Els + ISRS + VLOAD

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### 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 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 CircuitParameters Referred to Secondary

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

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