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lecture 36

lecture 36 - 1 Summary of Lecture#36 • Ideal transformers...

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Unformatted text preview: 1 Summary of Lecture #36 11/17/2010 • Ideal transformers • Unity coupling coefficient ( k = 1 ) • Infinite self and mutual inductance • Basic properties of ideal transformers • Voltage ratio • Current ratio • Impedance Transformation • Examples • Transformers with unity coupling coefficient • Examples • Equivalent T and Π circuits 1 Coupled coils and transformers L 1 , L 2 , M are finite. M =k √ L 1 L 2 ≤ √ L 1 L 2 Ideal transformers M = √ L 1 L 2 , a = √ L 1 /L 2 k = 1 Infinite L 1 , L 2 and M a = N 1 :N 2 , turn ratio Ideal Ideal 0 ≤ k ≤ 1 Two isolated coils Finite L 1 and L 2 M = 0 k = 0 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...
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