L13- First Order 1

# 0 for 1 a es t s 0 s a es t a es t 0 vs r s

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Unformatted text preview: A e s t ! 0, for 1% A es t \$ s + ' = 0 # !&amp; s A es t + A es t = 0 ! Vs ! R s= ! ! 1 &quot; t ! in = A ! e &quot; ! Adding the two components to get: iL (t ) = in + iss ! iL (t ) = Finding the constant (A): ! iL (t ) = t ! Vs + A!e &quot; ! R t ! Vs + A!e &quot; ! R IniCal CondiCon! ! iL ( 0 ) = ! iL (t ) = Vs + A !! = io R ! A = io ! Vs R Vs &quot; V % !t + \$ io ! s ' ! e ( ! R# R&amp; 7 3/18/12 R vR vL iL Vs iL (0 + ) = io L diL 1 V + iL = s dt ! L D.E. SoluCon: where != L R ! iL (t ) = Vs &quot; V % !t + \$ io ! s ' ! e ( ! R# R&amp; ! iL ( 0 + ) = Vs &quot; V% + \$ io ! s ' ! = io R# R&amp; (iniCal value) ! iL ( ! ) = Vs # V&amp; V + % io &quot; s ( !( 0 )! = s R\$ R' R (ﬁnal value) t ! 0+ Check: !! t = 0 + !! !! t = ! !! R iL (0 + ) = io vR vL iL Vs L D.E. SoluCon: != iL ( ! ) = Vs R L R diL 1 V + iL = s dt ! L ! iL (t ) = Vs &quot; V % !t + \$ io ! s ' ! e ( ! R# R&amp; t ! 0+ ! t ! iL (t ) = ( final ) + ( initial ! final )! e &quot; ! t ! 0+ 8 3/18/12 RC circuit Switch is closed at t=0 t = 0! just before acCon t = 0+ just aTer acCon t=o R C vc Vs Note! vc (0 ! ) = vo Capacitor voltage can not change instantaneously !! vc (0 ! ) = vc (0 + )!! !! t ! 0 + !! !! t = 0 ! !! t=o R R ic vc Vs KVL: !! t ! 0 + !! Vs = vR + vc dvc 1 V + vc = s dt RC RC C vc (0 + ) = vo vc (0 ! ) = vo For vc Vs C Vs = ic R + vc dvc 1 V + vc = s dt ! ! ! dv \$ Vs = C # c &amp; R + vc &quot; dt % ! = RC First orde...
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## This note was uploaded on 02/21/2013 for the course EEL 3004 taught by Professor Gong during the Spring '08 term at University of Central Florida.

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