Lect_01 - ECE 442 ECE 442 1. Networks & Systems...

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Unformatted text preview: ECE 442 ECE 442 1. Networks & Systems Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois jschutt@emlab.uiuc.edu 1 Jose E. Schutt " Aine " ECE 442 1 2 3 What is Capacitance? 1 2 3 Voltage=0 No Charge Voltage build up Charge build up Voltage = 6V Charge=Q N C 2 Jose E. Schutt " Aine " ECE 442 No Current Transient Current No Current 4 5 6 What is Capacitance? 4 5 6 Voltage=6V Charge=Q Voltage decaying Charge decaying Voltage=0 No Charge No Curren 3 Jose E. Schutt " Aine " ECE 442 No Current Transient Current 4 5 6 What is Capacitance? 4 5 6 Voltage=6V Charge=Q Voltage decaying Charge decaying Voltage=0 No Charge No Curren 3 Jose E. Schutt " Aine " ECE 442 No Current Transient Current No Current Capacitance Relation: Q = Cv Q : charge stored by capacito Q : charge stored by capacitor C : capacitance : voltage across capacito v : voltage across capacitor i : current into capacitor ( ) dv dQ i t C dt dt ! ! dt dt 1 ( ) ( ) t v t i d " " ! # 4 Jose E. Schutt " Aine " ECE 442 C # What is Inductance? z- Current in wire produces magnetic field- Flux is magnetic field integrated over area r H Total Flux Linked Idl R Inductance Total Flux Linked Current ! 5 Jose E. Schutt " Aine " ECE 442 Inductance d $ d L N di $ ! $ L I $ ! ! ! 2 v B Hdv L I % ! # 6 Jose E. Schutt " Aine " ECE 442 Inductance Relation: $ = Li $ : flux stored by inducto $ : flux stored by inductor L : inductance : current through inducto i : current through inductor v : voltage across inductor ( ) di d v t L dt dt $ ! ! dt dt 1 ( ) ( ) t i t v d " " ! # 7 Jose E. Schutt " Aine " ECE 442 L # Low-Pass Circuit ( ) ( o dv i t C i t ( ) ( ) o R C i t C i t dt ! ! ( ) ( ) ( ) i R o v t Ri t v t ! & ( ) ( ) o i o dv v t RC v t dt ! & Need to solve for v o (t) 8 Jose E. Schutt " Aine " ECE 442 Reactive Circuit ( ) ( ) ( ) C R L i t i t i t ! & Need to solve for v x (t) L x di v L dt ! ( i x C d v v i C ) ! 9 Jose E. Schutt " Aine " ECE 442 dt C dt Laplace Transforms The Laplace transform F(s) of a function f(t) is defined as: * + ( ) ( ) ( ) st L f t f t e dt F s , ) ! ! # To a mathematician, this is very meaningful; however circuit engineers seldom use that however circuit engineers seldom use that integral The Laplace transform provides a conversion from the time domain into a new domain, the s domain 10 Jose E. Schutt " Aine " ECE 442 Laplace Transforms The Laplace transform of the derivative of a function f(t) is given by ( ) ( ) st df t d f t , )- . ( ) st L e d t s F s dt dt )- . ! ! / 1 2 # Differentiation in the time domain becomes a multiplication in the s domain. That is why Laplace transforms are useful to circuit engineers s = 3 11 Jose E. Schutt " Aine " ECE 442 s = j 3 Low-Pass Circuit Time s ( ) ( ) o o v t V s 4 domain domain ( ) ( ) o o dv t sV s dt 4 Time domain ( ) ( ) o i o dv v t RC v t dt ! & ( ) ( ) ( ) i o o V s sRCV s V s ! & Time domain s domain 12 Jose E. Schutt " Aine " ECE 442 dt Low-Pass Circuit - Solution ( ) ( ) 1 ( ) 1 ( ) 1 i o o i V s V s...
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Lect_01 - ECE 442 ECE 442 1. Networks & Systems...

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