Ci it IICircuits IIEE221EE221Unit 9Instructor: Kevin D DonohueInstructor: Kevin D. DonohueMutual Inductance, Energy in Magnetically Coupled Circuits Analysis of Mutual Coupled Circuits, Analysis of Mutual Inductance CircuitsMutual InductanceCoils with current flowing in them emit magnetic energy that induce voltages in other coils in close proximity. The effects of the magnetic link between these circuits is called mutual of the magnetic link between these circuits is called mutual inductance.Show that current i1in first coil induces voltage v2in second coil of the form:1122211212 wheredidNMdtdiMv1112Mutual Inductance Dot ConventionThe geometry of the coil and flux paths are expressed in the dot convention below. This notation is important for applying circuit laws for analysis. circuit laws for analysis. 12112122Dot Notation for KVLIf both currents are either entering or leaving the dot then the self and mutual induced voltage will have the same sign.MI1I2+V1+V2L1L2MMsIsLIVMsIsLIV12222111If one current (loop direction) enters the dot and the other current leaves the dot then the self and mutual induced --121222current leaves the dot, then the self and mutual induced voltage will have opposing signs.IIMMsIsLIV I1I2+V1-+V2-L1L2MsIsLIVMsIsLIV12222111Equivalent Circuits ExampleConvert the Mutual Inductance components to an equivalent circuit using current controlled voltage sources. MI1I2+V1+V2L1L2MMsIsLIVMsIsLIV12222111 --12M1222I1I2+V1+V2L1L2MsIsLIVMsIsLIV12222111 --Examples Examples Find vo(t), given vi(t) = 2cos(4t) V. 41H vi(t)+vi(t)22H1H -Show vo(t) = 0.4851cos(4t-14º) VExamples Examples Find Norton equivalent circuit wrt ab 20 j20 a 3060j10 j5aj5 bShow Ith= A Zth= 4.669.0 1.8752.19Examples Examples Find equivalent inductance wrt aba1H6 H4H1 H2 H5H1 HShow Leq= H
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