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

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CE 442 ECE 442 1. Networks & Systems Jose E. Schutt Aine lectrical & Computer Engineering Electrical & Computer Engineering University of Illinois jschutt@emlab.uiuc.edu ECE 442–Jose Schutt Aine 1
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What is Capacitance? 1 2 3 Voltage=0 No Charge No Current Voltage build up Charge build up Transient Current Voltage = 6V Charge=Q No Current ECE 442–Jose Schutt Aine 2
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What is Capacitance? 4 5 6 Voltage=6V Charge=Q No Current Voltage decaying Charge decaying Transient Current Voltage=0 No Charge No Current ECE 442–Jose Schutt Aine 3
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Capacitance Relation: Q = Cv charge stored by capacitor Q : charge stored by capacitor C : capacitance oltage across capacitor v : voltage across capacitor i : current into capacitor () dv dQ it C t dt  dt 1 ( ) t vt i d ECE 442–Jose Schutt Aine 0 C 4
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What is Inductance? urrent in wire produces magnetic field z Current in wire produces magnetic field Flux is magnetic field integrated over area r H otal Flux Linked Idl R Inductance Total Flux Linked Current ECE 442–Jose Schutt Aine 5
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Inductance d LN di L I 2 v BH d v L I  ECE 442–Jose Schutt Aine 6
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Inductance Relation: = Li flux stored by inductor : flux stored by inductor L : inductance current through inductor i : current through inductor v : voltage across inductor () di d vt L t dt  dt 1 ( ) t it v d ECE 442–Jose Schutt Aine 0 L 7
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Low-Pass Circuit ) () dv t C it o RC dt  iR o vt R i t v t  o io dv R C v t dt Need to solve for v o (t) ECE 442–Jose Schutt Aine 8
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Low-Pass Circuit ) () dv t C it o RC dt  iR o vt R i t v t  o io dv R C v t dt Need to solve for v o (t) ECE 442–Jose Schutt Aine 9
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Reactive Circuit () CR L it  Need to solve for v x (t) L x di vL t   ix dv v iC ECE 442–Jose Schutt Aine dt C dt 10
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Laplace Transforms The Laplace transform F(s) of a function f(t) is defined as:  () st Lf t f t e d t F s  0 To a mathematician, this is very meaningful; owever 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 ECE 442–Jose Schutt Aine 11
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Laplace Transforms The Laplace transform of the derivative of a function f(t) is given by () df td f t 0 st ff L e d ts F s dt dt    Differentiation in the time domain becomes a multiplication in the s domain. That is why Laplace transforms are useful to circuit ngineers engineers = j ECE 442–Jose Schutt Aine s = j 12
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Low-Pass Circuit Time omain s omain () oo vt Vs domain domain o o dv t sV s dt Time domain domain o io dv R C v t t  o s R C V s V s s domain ECE 442–Jose Schutt Aine dt 13
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Low-Pass Circuit - Solution () 1 ( ) 1 io o Vs V s C V s sRC  1( i sRC  1/ sR C   Pole exists at Assume that V i (s)=V d /s     11 / d o VA B s sRC s s RC  / ) tR C t A u t B e Inversion ECE 442–Jose Schutt
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Lect_01 - ECE 442 ECE 442 1. Networks & Systems y Jose...

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