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EE203-SUNYBuffalo-27-Chapter13-08 - SMALL for Big...

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EE203-SUNYBuffalo-27-Chapter13-08

EE203-SUNYBuffalo-27-Chapter13-08 - SMALL for Big...

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Unformatted text preview: SMALL for Big ThingsUniversity at BuffaloSMALL for Big ThingsUniversity at BuffalonanobioSensors & MicroActuators Learning LabThe State University of New YorknanobioSensors & MicroActuators Learning LabThe State University of New YorkEE 203 Circuit Analysis 2Lecture 26Chapter 13.8Impulse Functionin Circuit AnalysisKwang W. Oh, Ph.D., Assistant ProfessorSMALL (nanobioSensors and MicroActuators Learning Lab)Department of Electrical EngineeringUniversity at Buffalo, The State University of New York215E Bonner Hall, SUNY-Buffalo, Buffalo, NY 14260-1920Tel: (716) 645-3115 Ext. 1149, Fax: (716) 645-3656E-mail: kwangoh@buffalo.edu, http://www.SMALL.Buffalo.eduEE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-BuffaloLecture 27 | Chapter 13 | 8/8 | 1/12Impulse Function by a Switching OperationCapacitor Circuit (1)C1 is charged to an initial voltage of V0 at the timethe switch is closed. The initial charge on C2 is zero.Q: find the expression for i(t) as R 0.Vo11= I(+R+)ssC1sC2As R gets smaller, the current starts from a largerinitial value and then drops off more rapidlyidlVoQ R() Initial Current ()RR () Time Constant RCe ()EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-BuffaloLecture 27 | Chapter 13 | 8/8 | 2/12SMALL for Big ThingsUniversity at BuffaloSMALL for Big ThingsUniversity at BuffalonanobioSensors & MicroActuators Learning LabThe State University of New YorknanobioSensors & MicroActuators Learning LabThe State University of New YorkImpulse Function by a Switching OperationCapacitor Circuit (2)AsAs R gets smaller, the current starts from a largerinitial value and then drops off more rapidlyas R zero, i is approaching an impulse functionR 0: i VOCe(t)Impulse Function by a Switching OperationSeries Inductor Circuit (1)Q:Q: find the time-domain expression forvo after the switch has been opened.Opening the switch forces aninstantaneous change in the current ofL2, which causes vo to contain animpulsive component.Initial condition at t = 0-When R = 0, a finite amount of charge istransferredtransferred to C2 instantaneously.Set R = 0The current in the 3 H inductor = 10 AThe current in the 2 H inductor = 0 A100+ 30+ 30=s10 + 3s + 15 + 2 s 5s + 2520+ 6 6 s + 20 42=s==+s + 5 s( s + 5) s s + 5I=100si = ( 4 + 2 e 5 t )u ( t )EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-BuffaloLecture 27 | Chapter 13 | 8/8 | 3/12EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-BuffaloLecture 27 | Chapter 13 | 8/8 | 4/12SMALL for Big ThingsUniversity at BuffaloSMALL for Big ThingsUniversity at BuffalonanobioSensors & MicroActuators Learning LabThe State University of New YorknanobioSensors & MicroActuators Learning LabThe State University of New YorkImpulse Function by a Switching OperationSeries Inductor Circuit (2)Vo = (15 + 2 s ) I= (15 + 2 s )6s + 20s( s + 5)12( s 2 + 5s ) 60s + 90s + 40s + 300s 2 + 5s70s + 300= 12 +s( s + 5)K1K60 10= 12 ++ 2 = 12 ++s s+5s s+530070 s + 300= 60K1 = [12 s +=s+55s =0=K1 = [12( s + 5) +100+ 30+ 30=s10 + 3s + 15 + 2 s 5s + 2520+ 6 6 s + 20 42=s==+s + 5 s( s + 5) s s + 5I=70s + 300 350 + 300= 10=s5s = 5vo = 12 (t ) + (60 + 10e 5t )u (t )EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo100si = ( 4 + 2 e 5 t )u ( t )Lecture 27 | Chapter 13 | 8/8 | 5/12Impulsive SourcesImpulsiveImpulsive functions can occur in sources as well asresponsesA mechanical analogy is striking a bell with an impulsiveclapper blow. After the energy has been transferred to theAfterbell, the natural responses of the bell determines the toneemitted (that is, the frequency of the resulting sound waves)andand the tones duration.Initial conditionWhen the impulse voltage source is applied, the initialenergyenergy in the inductor is zeroTherefore the initial current is zero.There is no voltage drop across R, so the impulsivevoltage source appears directly across L.An impulsive voltage at the terminals of an inductorestablishes an instantaneous current.EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-BuffaloLecture 27 | Chapter 13 | 8/8 | 6/12SMALL for Big ThingsUniversity at BuffaloSMALL for Big ThingsUniversity at BuffalonanobioSensors & MicroActuators Learning LabThe State University of New YorknanobioSensors & MicroActuators Learning LabThe State University of New YorkInternally Generated and Externally Applied Impulses Simultaneously (1)100+ 50 + 30+ 80 20 + 16=s=s10 + 3s + 15 + 2 s 5s + 25s+516s + 20 K1K4 12==+ 2= +s( s + 5)s s+5 s s+5InitialInitial Condition at t = 0-I=i1(0-) = 10 Ai2(0-) = 0 ASMALL for Big ThingsUniversity at BuffalonanobioSensors & MicroActuators Learning LabThe State University of New YorkImpulse Function by a Switching Operation100si = ( 4 + 12e 5t )u(t )Series Inductor Circuit (1)Vo = (15 + 2 s ) I = (15 + 2 s )Q: find the time-domain expression forvo after the switch has been opened.Opening the switch forces aninstantaneous change in the current ofL2, which causes vo to contain animpulsive component.Initial condition at t = 0-16s + 20s( s + 5)32( s 2 + 5s ) 160s + 240s + 40s + 300s 2 + 5s120s + 300KK= 32 + 1 + 2= 32 +s( s + 5)s s+560 60= 32 ++s s+5vo = 32 (t ) + (60 + 60e 5t )u(t )=The current in the 3 H inductor = 10 AThe current in the 2 H inductor = 0 A100100+ 30s + 30=s10 + 3s + 15 + 2 s 5s + 2520+ 6 6 s + 20 42=s==+s + 5 s ( s + 5) s s + 5I=i = ( 4 + 2 e 5 t )u ( t )EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-BuffaloKwang OhInternally Generated and Externally Applied Impulses Simultaneously (2)Lecture 27 | Chapter 13 | 8/8 | 4/12EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-BuffaloLecture 27 | Chapter 13 | 8/8 | 7/12K1 = [32 s +120s + 300300== 60s+55s =0K1 = [32( s + 5) +EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-Buffalo120s + 300 600 + 300== 60s5s = 5Lecture 27 | Chapter 13 | 8/8 | 8/12SMALL for Big ThingsUniversity at BuffaloSMALL for Big ThingsUniversity at BuffalonanobioSensors & MicroActuators Learning LabThe State University of New YorknanobioSensors & MicroActuators Learning LabThe State University of New YorkInternally Generated and Externally Applied Impulses Simultaneously (3)Summary (1)InitialInitial Condition at t = 0i1(0-) = 10 Ai2(0-) = 0 ASwitching Off (t 0+)i = ( 4 + 12e 5t )u (t )it =0+ = 16 Ai1 = 10 A 16 Ai1 = 6Ai2 = 0 A 16 Ai2 = 16Ait = = 4 AEE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-BuffaloLecture 27 | Chapter 13 | 8/8 | 9/12EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-BuffaloLecture 27 | Chapter 13 | 8/8 | 10/12SMALL for Big ThingsUniversity at BuffaloSMALL for Big ThingsUniversity at BuffalonanobioSensors & MicroActuators Learning LabThe State University of New YorknanobioSensors & MicroActuators Learning LabThe State University of New YorkSummary (3)Summary (2)inputoutput, responseh(t)(t)impulsesourcesystem,circuit,black boximpulseresponseEE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-BuffaloLecture 27 | Chapter 13 | 8/8 | 11/12EE 203 Circuit Analysis 2 | Spring 2008 | Prof. Kwang W. Oh | EE@SUNY-BuffaloLecture 27 | Chapter 13 | 8/8 | 12/12...
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