Circuits II EE221 Unit 9 Instructor: Kevin D. DonohueMutual InductanceMutual Inductance Dot ConventionDot Notation for KVLEquivalent Circuits ExampleExamplesSlide 7Circuits IIEE221Unit 9Instructor: Kevin D. DonohueMutual Inductance, Energy in Magnetically 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 inductance.Show that current i1 in first coil induces voltage v2 in 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 apply circuit laws for analyses. 11122122Dot Notation for KVLIf both currents are either entering or leaving the dot then the self and mutual induced voltage will have the same sign.If one current (loop direction) enters the dot and the other current leaves the dot, then the self and mutual induced voltage will have opposing signs. I1I2+V1-+V2-L1L2M I1I2+V1-+V2-L1L2MMsIsLIVMsIsLIV12222111MsIsLIVMsIsLIV12222111Equivalent Circuits ExampleConvert the Mutual Inductance components to an equivalent circuit using current controlled voltage sources. I1I2+V1-+V2-L1L2M I1I2+V1-+V2-L1L2MMsIsLIVMsIsLIV12222111MsIsLIVMsIsLIV12222111Examples Find vo(t), given vi(t) = 2cos(4t) V.Show vo(t) = 0.4851cos(4t-14º) V vi(t)+vi(t)-422H1H1HExamples Equivalent Series InductanceCircuits with Mutual
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