?
14.1
1,
ABBA
ABBA
lglglg



III
iii



21
21
)( )s( tfF?
js
2,



)s()(
)()s(
dseF
j
tf
dtetfF
st
jc
jc
st
2
1
0
t < 0,f(t)=0
0
00
0? 0?
0+ 0+
t=0 f(t)
t 0? t 0
f(t)=?(t)? 0


)( )(
)( )(
SFtf
tfSF
1
dtetfdtetfdtetfSF ststst 0000 )()( )()(1
F(s) I(s) U(s)
f(t) i(t),u(t)
2
3 F(s)
dtetf st0 )( te s?
M c f(t)
),0[ )( tMetf ct
dtMedtetf tct
00
)s(s)( CM s
f(t) F(s)
)()( 0 dtetfSF st
)()( ttf
dtettsF st 0 )()]([ )(
0
1 ste
s s
1?
0 dte st
0
1?

t)as(e
as as
1
00 dte)t( st?
)()( ttf
dtettsF st 0 )()]([ )(
10 se
ate)t(f?
dteee)s(F statat 0
dte)t(f)t(f st 0 2211 AA
dte)t(fdte)t(f stst 0 220 11 AA
)S(F)S(F 2211 AA
)S(F)S(F 2211 AA
)S(F)t(f)S(F)t(f 2211 ][,][
)t(f)t(f 2211 AA)t(f)t(f 2211 A A
)t(f)t(f 2211 AA?
)t(Utf)(,


jS
1
jS
1
j2
1 22 S
S
U?
)( )]([ ( s ) tUtUF
) s i n ()(,ttf
)( ( s ) ts i nF )( tjtj eej21


0
stst dtstfe
0
tfe ))(()(
)s(s)0( Ff
vd uuvu d v
)(ss

0f)(F
dt
)t(df
)()( SFtf?
0 stst0 )t(dfedtedt )t(df

dt
)t(df
022 ss 22 s s
)t(tf c o s)(,


)( s i n (1 ][ c o s tω
dt
d
ωtω
dt
tωd
ωtωtωωdt
tωd )s i n (1)(c o s)(c o s)s i n (
)0()0()( '2 fSfSFS
) ()(,tδtf?
dt
tεdtδ )()(?
s
1)]([?tε
])([ n
n
dt
tfd )0()0()( 11 nnn ffSSFS?
])([ 2
2
dt
tfd )0()]0()s(s[s ' ffF
)]([ tεdtd? 1
1
SS)(tδ
0 )( dtetfdsd st 0 ))(( dtettf st
)1( Sdsd )1( 2S?)]([ tεt
)s()]([ Ftf?
)]([ ttf
s
)s()]([
d
dFttf
) ()(,tεttf?
)s !( 1 nn)]([ tεt n )s()1( n
n
n
ds
d
)1( αsdsd 2)( 1αs][ tαte?
) ()(,tεttf n?
attetf)(,
)(1])([ 0 sFsdttf t
00 )()()( t
t dttfsθssF
s
sFsθ )()(
t t d ttεt 02 2)]([?
)(])([ 0 sθdttf t
)()]([ sFtf?



t dttf
dt
d tf
0
)()]([
)()()( tεttft εt)t(f,2
)]([ tεt ss
11?
])([ 0 dttε
)]([ 2 tεt 32s?
dteettf stttst 00
0
)(
0 )(


)(0 sFe st
)()]([ sFtf? )()]([ 00 sFettf st
00 0)( tt ttf
dtettft-f(t st 0 00 )()
ηdeηfe ηsst0 )(0
0tt
0ste?
1 1
T t
f(t)
)()()( Ttttf
Tse
sssF
11)(
)(t? )( t? )( tt? )( tt n
1 1 S 2S1 1! nSn
)(s in tt )(c o s tt )(e t- t )(s i ne t- tt
)(e t- tt n
22?
S 22S
S
S
1
22)(
S
1)(
!
nS
n
)()]()([ 000 SFettttfL
st
dsesF

tf stjc
jc
)(
2
1)(

F(S)
)()()()( 2 sFsFsFsF n1
)()()()( 21 tftftftf n
F(S)
)( sFmn?
F(s)
)(
)(
)()(
1
10
1
10 mn
bsbsb
asasa
sD
sNsF
n
nn
m
mm


n
n
ps
k
ps
k
ps
ksF
2
2
1
1)(
tp
n
tptp nekekektf 21
21)(
nppnsD 10)(1
)( ps
)( ps )( ps )( ps
i pssFk
ipsii
321))((
)(
))((lim
sD
pssNk i
psi i

)(
)())((lim
'
'
sD
sNpssN i
ps i

)(
)(
'
i
i
pD
pN?
65
54)(
2

ss
ssF
32
21
s
K
s
K
3354 21Ss sK 7254 32ss sK
)(7)(3)( 32 tetetf tt
352 54)( )( 2
1
'
1
1

ss
s
pD
pNK
752 54)( 32s
2
'
2
s
s
)(pD
pNK
65
54)(
2

ss
ssF


ωjαp
ωjαp
2
1
)())((
)(
)(
)()(
1 sDωjαsωjαs
sN
sD
sNsF

)(
)(
1
121
sD
sN
ωjαs
K
ωjαs
K?

tp
n
ntptp ne
pD
pNe
pD
pNe
pD
pNtf
)(
)(
)(
)(
)(
)()(
'
2
'
2
1
'
1 21
0)(?sD2
)()( 1)()( tfeeKeeK tωjαθjtωjαθj
)(][ 1)()( tfeeeK θtωjθtωjtα
)()c o s (2 1 tfθtωeK tα
K1,K2
θ-jθj eKK eKK
21
)()()( 1)(2)(1 tfeKeKtf tωjαtωjα
)(52)( 2 tfss ssF
jp,

,.)(,j.js
sK
js

,.)( jsjs
sK
)()6.262c o s (5 59.02)( ttetf t
ss

,.)(
)(
js' 2s
s
sD
sNK
522 SS
S
2222 2)1(
1
2)1(
1


SS
S
tetetf tt 2s i n212c o s)( ).c o s (.
te t
ps asasasF n m
mm
)()(?



n
n
n
n
ps
K
ps
K
ps
K
ps
KsF
)()()()(?





22 2)1(
11


S
S
ωs ω tω ][ s i n
)( sD3
pS
n
n sFpsK )]()[(

psnn sFpsdsdK )]()([



ps
n
n sFpsds
dK )]()(
![







ps
n
n
n
sFpsdsdnK )()()!(
n
n
n
n
ps
K
ps
K
ps
K
ps
KsF
)()()()(?






)()( s
K
s
K
s
K
)()()( tfss ssF
sssK )(
sssK

ssFsds
dK )]()[(
ss
s
ds
d ][
tt teetf)(


)()( ss
ssF
n =m F(s)
n
n
ps
K
ps
K
ps
KAsF

)(
F(s) f(t)
)(
)()( 0
sD
sNAsF


ss
sssF )(


ss
s




ss
)()()( tt eetδtf


ss
sssF )(
KCL KVL
Uu Ii
IZU
0(t)i 0(t)u
0I? 0 U?
)()()()( sIti sUtu
KCL KVL
)()()( sIsZsU?
0)I (s 0)( sU
u=Ri
)()( sGUsI?
)()( sRIsU?
+ u -
i R
+ U(s) -
I(s) R
GsY
RsZ
)(
)(
R
dt
diLu?
)0()(
))0()(()(


LisLIs
isIsLsU
s
i
Ls
sUsI )0()()(
sLsY
sLsZ
1)(
)(
L
i L
sL )0(?Li
U(s)
I(s)
U(s)
I(s )
si )0(
L
dtiCuu t
0
1)0(
s
usI
CssU
)0()(1)(
)0()()( CusCUssI
sCsY
sCsZ
)(
1)(
C
+ u -
i
I (s)
1/sC
u (0 - ) /s
U(s)
+
1/sC
Cu(0-)
I(s) U(s)
C


dt
di
M
dt
di
Lu
dt
di
M
dt
di
Lu
12
22
21
11




)0()()0()()(
)0()()0()()(
1122222
2211111
MisMIsiLsILssU
MisMIsiLsILssU
* *
M i2i1
L1 L2u1
+

u2
+

sMsY
sMsZ
M
M
1)(
)(




)0()()0()()(
)0()()0()()(
1122222
2211111
MisMIsiLsILssU
MisMIsiLsILssU
+
-
+
-
sL2
+ - - +
sM
+ - - +
)(1 sU )(2 sUsL1
)(1 sI )(2 sI
)0(11?iL )0(22?iL )0(1?Mi)0(2?Mi
12
11
uu
Riu

)()(
)()(
12
11
sUμsU
RsIsU
i1
u1
)(1 sU )(1 sUμ )(
2 sU
)(1 sI
0)0( 0)0( Lc iu
t c dtiCdtdiLiRu 01
)(1)()()( sISCsLIsRsIsU
)()()1)(( sZsIsLsRsI
CsLsRsYsZ
1
)(
1)(
RLC
+
u
-
i R L
C U(s)
I(s) R sL
1/SC
+
-
0)0(0)0( Lc i u
s
usI
SCLisLIsRsIsU
C )0()(1)0()()()(

s
uLisUsIsZsI
CsLsR
C )0()0()()()()()1(

)()()( sIsZsU?
)()()( sUsYsI?
+
u
-
i R L
C U(s)
I(s)
R
sL
1/SC
+
-
+
+-
-
Li(0-)
s
uc )0(?
R
RL
L
C
i1
i2
E
0)0( 0)0( Lc iu
R R
L
sL
1/sC
I1( s)
E/s
I2 ( s)
Ω
Ω
Ω
Ω
uC
iL
t=0
uc(0-)=25V iL(0-)=5A
t >0
-
++
-
1/s?
25/s
2.5V
5?
IL(s)
UC(s)
uc(0-),iL(0-)
Vu
uit
C
LL
100)0(
,,0
1
Ω
Ω
uC μiL
Ai L 5)0(
sLs 1.0?
s
sCs
1 0 0 0
101 0 0 0
11
6

Vu c 100)0(
)3(
2
2
1 )200(
)40000700(5)(

ss
sssI
5.02 0 0)(10)1.040)(( 21 ssIssI
ssIssI-
1 0 0)()1 0 0 010()(10
21
)(1 sI
)(2 sI
2
22211
1 )2 0 0(2 0 0)( s
K
s
K
s
KsI
2000:30)( 321 ppp sD
2
2
1 )200(
)40000700(5)(

ss
sssI
01 )( sssFK
52 0 04 0 0 )4 0 0 0 07 0 0(5 022
2
SSS SS
1500)200)(( 200222sssFK
0)()2 0 0( 200221ssFsdsdK
21 )2 0 0(
1 5 0 0
)2 0 0(
05)(
ssssI
Atetiti tL )1 5 0 05()()( 2001
UL(s)
LssIsU L )()( 1?
5.0)()( 1 LssIsU L 2)200( 30000200150 ss
Vteetu ttL 200200 3 0 0 0 01 5 0)(
R C
+
uc
is
0)0(),(cs utδi
CssICsR
RsU
sC
1)(
/1)( )/1( RCsRC
R

1s
s)s()s(
CR
CRsCUI
CC 1
1
1
1


CsRCsR
CsR
)0(1 / teCu RCtc )0(1)( / teRCti RCtc?
R
1/sC
+
Uc(s)
1)(?sI s
2
t
ic
RC
1?
)(t?
+
- Us k
R1 L1 L2
R2
i1 i20.3H 0.1H
10V
Ω
Ω
t = 0 k i1,i2
0)0(
5)0(
2
1
i
Ai
t
uc (V)
C
1
0
3
s
ssI
4.05
5.110
)(1
ss
s
)4.05(
5.110

5.12
75.12
ss
25.121 75.12 iei t
)0()0( 11 ii )0()0( 22 ii
t
i1
5
2
3.75
0
ss
s
)5.12(
75.325

5.1)(3.0)( 11 sIssU L
3 7 5.05.1256.6 s
UL1(s)
)(1.0)(2 sIssU L? 5.1219.2375.0 s
tL etδtu 5.122 19.2)(375.0)(
tL etδtu 5.121 56.6)(3 7 5.0)(
uL1
-6.56 t-0.375?(t)
0.375?(t)
uL2
t-2.19
t
i1
5
2
3.75
0
Aii 75.31.0 3 7 5.0)0()0( 22 iL
Ai 75.33.0 3 7 5.053.0)0(1
tL etδtu 5.121 56.6)(3 7 5.0)(
tL etδtu 5.122 19.2)(375.0)(
0-
uc(0-),iL(0-)
1,H s



)(
)(
(
)(
)(
SE
SR
te
tr
SH
d e f

1
)(
)(
)()( sU
sI
sUsH C
S
C
RC
sC
R
sC 1
11
1
1

R C
+
_
iS
uc
i(t)=?(t) h(t) uC(t)
1/sCIs(s)
UC(s)R
+
_
)(11 11)()()( 11 tεeCRCsC sH tuth RC tC


H(s) E(s)
)(
)()(
SI
SESH?
)(
)()(
SE
SISH?
2,H(s)
U2(s)
I2(s)
U1(s)
I1(s)
( )
)(
)()(
1
2
sU
sIsH?
)(
)()(
1
2
sI
sUsH?
)(
)()(
1
2
sU
sUsH?
)(
)()(
1
2
sI
sIsH?
U2(s)
I2(s)
U1(s)
I1(s)
)(
)()(
sE
sRsH? )()()( sEsHsR?
)t(u)t(u
uu)t()t(i
21
21s
1/4F
2H
2?i(t)
u1
+ +
- -
u21?
65
44
22
1
1
4
1
)(
)(
)( 1
1


ss
s
ss
sI
sU
sH
2
S
65
4
22
)(2
)(
)()( 22
2 ss
s
s
ssU
sI
sUsH
2
S
)65(
44)()()(
11

sss
ssIsHsU
2
)65
4)()()(
22 ss ( s
ssIsHsU
2
3t2t
1 e3
82e
3
2)t(u
3t2t2 4e4e)t(u
IsI UsU Cωj 1sC 1 LωjsL )()(:
)(
)()(

jE
jRjH?
E
R
2U?1U?
1I?I?
ωjssH?)(
IωjHU IωjHU )()(,2211
j?ωjζs
)())((
)())((
)(
)()(
21
210
n
m
pspsps
zszszsH
sD
sNsH


mm1 zzsHzzs 10)(?
nn ppsHpps 11 )(?

42)( 21 zzsH
j?
2 4
-1
2
3
2
3
1
)(
3,2
1
jp
p
sH


364
16122)(
23
2


sss
sssH
)4)(2(216122)( 2 sssssN
)2 323)(2 323)(1(364)( 23 jsjssssssD
e(t) r(t)
)()()( sEsHsR?
)()(),()(
,1)( )()(
thtrsHsR
sEtte


( t )h sH th )]([)( 1
(t) h(t)=r(t)
1 R(s)
)1(
)1()(

ss
sksH
k= 10
s=0 s= 1
H(s) h(t10lim?
h (t)t
t2kek
ss
sk sH th



)1(
)1()]([)( 11
10lim h ( t )t
)1(
)1(10)(

ss
ssH
tp
n
i
i
n
i i
i ieK
ps
k


11
1 ][)]([)( 1 sH th
j?

SSH i
1)(?
aSSH i
1)( aSSH i 1)(
22)(?
SSH i
22)()(?
aSSH i
22)()(?
aSSH i
θj
n
j
j
m
i
i
eωjH
pωj
zωj
HωjH )(
)(
)(
)(
1
1
0?
H(s) s=j? H(j?)?
n
j
j
m
i
i
pωj
zωj
HωjH
1
1
0
)(
)(
)(


n
j
j
m
i
i pωjzωjωjHθ
11
)a r g ()a r g ()(a r g
R
C
+
_
+
uc
_
uS
Cs
R
Cs
1
1
)(
)()(
sU
sUsH
S
C?
RC
s
RC
1
1
RCs
1
ωjs RCH,10
)()(/1)( 0 ωjθωjHRCωj HωjH
RC uC
1
00
/1)( pωj
H
RCωj
HωjH

1pωj? M1
jMe
HjH 0)(?
j?
-1/RC
M1
1
M2
j?1
j?2
|H(j?)|
1
|?(j?)|
-?/2
R
C
+
_
+
u2
_
uS
)(
)()( 2
sU
sUsH
S
RCs
s
1
CsR
R
1
θj
ψj
Me
NeωjH?)(
j?
-1/RC
M1 N1
1?1
|H(j?)|
1/RC
1
0.707
uR