lecture 37

lecture 37 - Summary of Lecture #37 11/19/2010 Basic...

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1 Summary of Lecture #37 11/19/2010 Basic properties of ideal transformers Voltage ratio Current ratio Impedance Transformation Transformers with k =1 Examples Transformer with k < 1 Examples IV characteristic with initial currents in coupled coils Equivalent T and Π circuits 1 A transf. is ideal if k=1 and L 1 , L 2 and M → ∞ . Basic Properties of ideal transformers : (1) Voltage ratio 2 1 2 1 2 1 2 1 2 1 2 1 N N a ) j ( V ) j ( V N N a ) s ( V ) s ( V N N a ) t ( v ) t ( v = = ϖ ϖ = = = = 2 1 2 1 2 1 2 1 2 1 2 1 N N a ) j ( V ) j ( V N N a ) s ( V ) s ( V N N a ) t ( v ) t ( v - = - = ϖ ϖ - = - = - = - = Basic Properties of ideal transformers : (2) Current ratio 1 2 2 1 1 2 2 1 1 2 2 1 N N a 1 ) j ( I ) j ( I N N a 1 ) s ( I ) s ( I N N a 1 ) t ( i ) t ( i - = - = ϖ ϖ - = - = - = - = 1 2 2 1 1 2 2 1 1 2 2 1 N N a 1 ) j ( I ) j ( I N N a 1 ) s ( I ) s ( I N N a 1 ) t ( i ) t ( i = = ϖ ϖ = = = = i 1 and i 2 go into the transformer terminals. (3) Impedance transformation Valid for dots on the same side or opposite sides ) s ( Z a ) s ( Z 2 in = 2 1 2 1 2 1 N N L L L M M L a = = = = Turn ratio: N 1 /N 2 Z(s) ) s ( Z N N ) s ( Z a ) s ( I ) s ( V a ) s ( I ) s ( V a ) s ( I a 1 ) s ( aV ) s ( I ) s ( V ) s ( Z 2 2 2 1 2 2 2 2 2 2 2 2 2 1 1 in = = - = - = ± = = - i 2 Impedance scaling by a factor of a 2 Transformers with unity
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lecture 37 - Summary of Lecture #37 11/19/2010 Basic...

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