The complete response of any RC circuit may also be
obtained as the sum of the natural and the forced response.
§ 5-5 The driver RC circuit
)0( ???? tRC
t
eRVdt cdCi ?
Vcffcncc ??? ????
????? tAeVcRCtAenc ??????
VAAVcc ?????????? 00)0()0( ???
va lu ein itia l ? v al u ef or c e d ? tc o n stim e t a n?
)()]()0([)( / ????? ?? fefftf t ?
)0( ???? tRC
t
VeVc?
Example,Find and,)(tc? )(ti
)t(A.)t(i
)t(A.
t
e..)t(c)t(i
0192020060 50
0214010200
????
?
?
??? ?
Solution:
?? tAenc ??
Vfc 2020050 20050
20050 2005060
50 ????
???
??
2.120)( tAetc ???? ?
)0(100)()0(2.18020)( ??????????? tVtctVtetc ??
sCeqR 2.105.0
5012001601
1 ??
?????
80201 0 0 ????? AA
Vcc 100505010 120)0()0( ??????? ??
)()]()0([)( ??????? ftefftf ?or
s
Vcc
Vc
2.1
10 0)0()0(
20)(
?
????
??
?
??
?
)(ti
)(tc?
t
V100
V20
mA)t(u)b(;mA)t(u)a(:iif
),t(ia n d)t(F i n d:E x a m p l e
s
cc
1510
25
?
?
?
)0(2.18020)( ???? tV
t
etc?
)t(A.)t(i
)t(A.
t
e..)t(i
01920
0214010
??
?
?
??
)0(01.0)()( 20 ??? ? tAedt tdCti tcc ?
mAtuia
S o l u t i o n
s )(25:)(
:
?
Vkkk kc 1 0 020328 81025)( 3 ??????? ??
0)0()0( ?? ?? cc ?? sk 05.0105
2
20 6 ???? ??
)0(1 0 01 0 0)( 20 ???? ? tVet tc?
c?
ci
V100
A01.0
t
V40k20k32k8 k81010)0()0( 3cc ??????? ??? ??
)0(601 0 0)1 0 040(1 0 0)( 2020 ??????? ?? teet ttc V?
c?
ciV40
V100
mA6
mA)(1510:)( tuib s ??
V1 0 020328 81025)( 3 ??????? ? kkk kc?
)0(6)()( 20 ??? ? tedt tdCti tcc mA?