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transformers - lecture 9

# transformers - lecture 9 - Transformers S.D Sudhoff Spring...

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Transformers S.D. Sudhoff Spring 2008

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Spring 2008 ECE321 2 Reading Chapter 1, “Electromechanical Motion Devices,” Section 1.4
Spring 2008 ECE321 3 A Single Phase Transformer

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Spring 2008 ECE321 4 Analysis Voltage Equations (1.4-3) (1.4-4) (1.4-5) dt d i r v 1 1 1 1 λ + = dt d i r v 2 2 2 2 λ + = + = 2 1 2 1 2 1 2 1 0 0 λ λ dt d i i r r v v
Spring 2008 ECE321 5 Analysis Flux linkage equations (1.4-1) (1.4-2) (1.4-6) (1.4-7) 1 2 2 2 m m l Φ Φ Φ Φ + + = 2 1 1 1 m m l Φ Φ Φ Φ + + = 1 1 1 Φ λ N = 2 2 2 Φ λ N =

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Spring 2008 ECE321 6 Analysis Flux Terms (1.4-8) (1.4-9) (1.4-10) (1.4-11) 1 1 1 1 l l i N R = Φ m m i N R 1 1 1 = Φ 2 2 2 2 l l i N R = Φ m m i N R 2 2 2 = Φ
Spring 2008 ECE321 7 Analysis Incorporating (1.4-8)-(1.4-11) into (1.4-1)- (1.4-2) (1.4-12) (1.4-13) m m l i N i N i N R R R 2 2 1 1 1 1 1 1 + + = Φ m m l i N i N i N R R R 1 1 2 2 2 2 2 2 + + = Φ

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Spring 2008 ECE321 8 Analysis Substitution of (1.4-12)-(1.4-13) into (1.4-6)- (1.4-7) (1.4-14) (1.4-15) 2 2 1 1 2 1 1 1 2 1 1 i N N i N i N m m l R R R + + = λ 1 1 2 2 2 2 2 2 2 2 2 i N N i N i N m m l R R R + + = λ
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