Lect_01 - ECE342 1.Networks&Systems JoseE.SchuttAine Electrical&ComputerEngineering [email protected] ECE342 JoseSchuttAine 1 What is

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ECE 342–Jose Schutt Aine ECE 342 1. Networks & Systems Jose E. Schutt Aine Electrical & Computer Engineering University of Illinois [email protected] 1
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ECE 342–Jose Schutt Aine Voltage=0 No Charge No Current 1 2 Voltage build up Charge build up Transient Current 3 Voltage = 6V Charge=Q No Current What is Capacitance? 2
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ECE 342–Jose Schutt Aine Voltage=6V Charge=Q No Current 4 Voltage decaying Charge decaying Transient Current 5 Voltage=0 No Charge No Current 6 What is Capacitance? 3
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ECE 342–Jose Schutt Aine Relation: Q = Cv Q : charge stored by capacitor C : capacitance v : voltage across capacitor i : current into capacitor () dv dQ it C dt dt == 0 1 ( ) t vt i d C τ = Capacitance 4
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ECE 342–Jose Schutt Aine Inductance Total Flux Linked Current = z r H Idl R What is Inductance? Current in wire produces magnetic field Flux is magnetic field integrated over area 5
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ECE 342–Jose Schutt Aine d LN di Ψ = L I Ψ = 2 v BH d v L I = G G Inductance 6
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ECE 342–Jose Schutt Aine Inductance Relation: Ψ = Li : flux stored by inductor L : inductance i : current through inductor v : voltage across inductor () di d vt L dt dt Ψ == 0 1 ( ) t it v d L τ = 7
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ECE 342–Jose Schutt Aine () o RC dv it C dt == iR o vt R i t v t =+ o io dv R C v t dt Low-Pass Circuit Need to solve for v o (t) 8
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ECE 342–Jose Schutt Aine () o RC dv it C dt == iR o vt R i t v t =+ o io dv R C v t dt Low-Pass Circuit Need to solve for v o (t) 9
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ECE 342–Jose Schutt Aine () CR L it =+ Reactive Circuit L x di vL dt = ( ) ix C dv v iC dt = Need to solve for v x (t) 10
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ECE 342–Jose Schutt Aine {} 0 () st Lf t f t e d t F s == Laplace Transforms The Laplace transform F(s) of a function f(t) is defined as: To a mathematician, this is very meaningful; however circuit engineers seldom use that integral The Laplace transform provides a conversion from the time domain into a new domain, the s domain 11
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ECE 342–Jose Schutt Aine 0 () st df t df t Le d t s F s dt dt ⎧⎫ == ⎨⎬ ⎩⎭ Laplace Transforms The Laplace transform of the derivative of a function f(t) is given by Differentiation in the time domain becomes a multiplication in the s domain. That is why Laplace transforms are useful to circuit engineers s = j ω 12
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ECE 342–Jose Schutt Aine () o io dv vt R C v t dt =+ Low-Pass Circuit oo o o Vs dv t sV s dt o s R C V s V s Time domain s domain Time domain s domain 13
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ECE 342–Jose Schutt Aine Low-Pass Circuit - Solution () 1 1( ) 1 io o i Vs V s sRC V s sRC =⇒ = ++ 1/ sR C = − Pole exists at 11 / d o VA B s sRC s s RC == + / tR C o vt A u t B e =+ Assume that V i (s)=V d /s Inversion 14
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