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“Ideal Transformer”

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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

- Define the turns ratio as “a”
- If the primary is the High-Side,

ECE 441

Z’in = Impedance looking into the primary = E’P / IP

Turns ratio a = E’P / E’S >>>>> E’P = aE’S

ECE 441

- 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

EP = 4.44NPfΦP ES = 4.44NSfΦS

ΦP = ΦM + ΦlpΦS = ΦM – Φls

EP = E’P + Elp ES = E’S - Els

ECE 441

“Real” Transformer (continued)

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

IP = Ife + IM + IP LOAD

ECE 441

VT = EP + IPRP = E’P+ Elp +IPRP

ECE 441

“Real” Transformer (continued)

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

E’S = Els + ISRS + VLOAD

ECE 441

VT = EP + IPRP = E’P+ Elp +IPRP

E’S = Els + ISRS + VLOAD

ECE 441

ECE 441

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

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

ZeqP = RP + a2RS +jXlp +ja2Xls

ECE 441

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

ECE 441