lecture 33

# lecture 33 - Summary of Lecture#33 VI chara of an isolated...

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1 Summary of Lecture #33 11/10/2010 Magnetically coupled circuits Mutual inductance M 12 , M 21 and M Dot convention t-domain VI characteristic s-domain VI characteristic Examples 1 VI chara. of an isolated inductor with i(0 - ) = 0 VI characteristic of coupled coils in time domain, with i 1 (t) and i 2 (t) going into dotted terminals VI characteristic of coupled coils in s domain, assuming i 1 (0 - ) = i 2 (0 - ) = 0 dt di L dt di M ) t ( v dt di M dt di L ) t ( v 2 2 1 21 2 2 12 1 1 1 + = + = ) s ( I s L ) s ( I s M ) s ( V ) s ( I s M ) s ( I s L ) s ( V 2 2 1 21 2 2 12 1 1 1 + = + = di(t) v(t) L , V(s) LsI(s) dt = = + _ v(t) i(t) L L 1 , L 2 : Self inductance M 12 = M 21 = M Mutual inductance If one of currents goes into a dotted terminal and the other current goes into the undotted terminal, then In time domain In s domain, assuming i 1 (0 - ) = i 2 (0 - ) = 0, dt di L dt di M ) t ( v dt di M dt di L ) t ( v 2 2 1 2 2 1 1 1 + - = - = ) s ( I s L ) s ( I Ms ) s ( V ) s ( I Ms ) s ( I s L ) s ( V 2 2 1 2 2 1 1 1 + - = - = OR Dot convention The voltage drop across a coil, arising from the magnetic coupling with the other coil, from the dotted terminal to the undotted terminal, equals M times the time derivative of the current through the other coil, going from the dotted terminal to the undotted terminal. A part of v 1 is due to coil 1 itself and that part is . A part of

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lecture 33 - Summary of Lecture#33 VI chara of an isolated...

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