-
, : )
, IL RL ,
) IL .
2002,
UR4R3
RL
R1 R2
IL
) :
43 III L += ,
33 R
UUI L
= ,
44 R
UUI LA
=
+=
1
21RR
UU LA ,
U R4 R3
RL
R1 R2
IL
I3 I4
UA
UL
IL U, UL .
41
2
4
1
2
4
1
RRR
UR
URR
UI L
LL
=
+
= , IL U UL RL:
+= 1
41
32
33 RRRR
RU
RUI LL ,
RL: LLL IRU = ,
=1
41
323 RR
RRRR
UI
L
L
IL ( RL) RL :
4132 RRRR = ) , IL :
3RUI L =
-
, ()
2
, : )
IL RL UI;
) , IL RL UL .
2002,
UI
R4R3
r
RL
UL
R1 R2
IL
) :
=+==
434 RR
Ur
UUIII LLArL
++= 431
RRr
rU
rU LA (1)
LLL IRU = . (2)
IL U.
U
R4R3r
RL
UL
R1 R2
IL
UAI1= I2
I3= I4
Ir
U :
43
3
RRR
UUU L +== + , 112 RUU
II +== , :
++== + 433
1
2
43
322 RR
RUU
RR
RRR
UIRUU LLA
1
21
43
3
1
2
RRR
RRRUU
RRU LA
+++=
U 1. :
=
++
++= 43121
43
3
1
2 1RR
rR
RRRR
Rr
URR
rUI LL
( ) ( )14131323114312 1 rRRRRRRRRR
RRRrU
RR
rU L +++= .
( ) ( )[ ]rRRRRRRRrU
RR
rUI LL +++= 41321431
2 1 .
) IL RL UL :
( ) 04132 =+ rRRRR
-
II
3
, : ) W(j)=UO(j)/U(j), ) W()=W(j), ) ()=arg W(j), , , 2002
U
R1
C
R2 R3
U
uo(t)u(t)
) , :
+ =UU ( ),
223 R
UUII == (
),
UZR
RU
C+=+
1
1 , Cj
ZC 1= (
)
2333 R
UURUIRUU O
++==
, U+ U, R1 C, :
CRjCRj
UU1
1
1
+=+ , U ( ) :
U
R1
C
R2 R3
U
U-
U+
I2 I3
UCRj
CRjRR
URR
URR
URR
U O1
1
2
3
2
3
2
3
2
3
111
+
++=
++= + .
:
( )CRj
CRjRR
UCRj
CRjRR
CRjRR
UU O1
12
3
1
12
31
2
3
11
11
++
=+
+++
= , :
-
, ()
4
CRj
CRR
Rj
RR
UCRj
CRR
Rj
RR
U O1
3
21
2
3
1
3
21
2
3
1
1
1
1
+
=+
= . , :
( ) ( )( ) 13
21
2
3
1
1
CRjRR
CRj
RR
jUjU
jW O
+
==
:
( ) ( )( )jWjW
RR
jW2
1
2
3= , :
( ) ( ) ( ) 113
211 1
jeWRR
CRjjW == ( ) ( ) ( ) 2212 1 jeWCRjjW =+=
( ) ( ) 213
2111
+==
RR
CRjWW ( ) ( ) ( )21 122 CRjWW +==
( ) ( )
==
3
2111 R
RCRarctgjW arg ( ) ( ) ( )122 CRarctgjW == arg
:
( ) ( )21
2
3
21
2
3
1
1
CR
RR
CR
RR
W
+
+
=
) : ( ) ( ) ( ) 21 = , o (arc tg(-x) = - arctg x):
( ) 11
21 CRarctgR
RCRarctg =
-
II
5
, , )
, W(s)=UO(s)/U(s); )
, W(), )
, ()=arg W(j), )
, u(t), , uo(t), R1 = R2 = R3 = R .
2002
u(t)R1
C
R2
R3
uo(t) U
UO
) , :
CC Z
UUI 1
= ,
URR
RU
21
11 += ,
( ) CCO IRZUU 3+= .
U
R1
C R2
R3 U
U1
IC
U ( ) :
( ) ( )C
CC
CO ZRR
RUU
RZUZ
UURZUU 21
1
31
3++=+= ,
URR
RZR
UUC
O21
231 +
+=
+=++= CCO ZR
RRRR
RUU
RRR
ZR
URR
RU
1
32
21
1
21
23
21
1 1 .
sC
ZC1= :
( ) ( )
+= CRR
Rs
RRR
sUsU O 31
2
21
1 1 .
, , :
-
, ()
6
( )( )
+== CRR
Rs
RRR
sUsU
)s(W O 31
2
21
1 1 .
) W() js = : :
2
31
2
21
1 1
++= CRR
RRR
R)(W
) : ( )
1
23 R
RCRarctg =
) , R1 = R2 = R3 = R, :
( ) ( )( ) ( )sRCsUsU
sW O == 121 ,
: ( ) ( )( )sRCsUsU O = 12 ,
: ( ) ( ) ( )sUsRCsUsU O +=2 ,
s :
( ) ( ) ( ) ( )tusU,tusU,dtds OO ,
, u(t), , uo(t):
)t(udtduRC)t(uO +=2 .
-
II
7
, : ) )
R1 = R2 = R3 = R
U R1
C
R2 R3
U
uo(t)u(t)
2003
)
. , , . :
02OO1 == UUU 01OO2 =
=U
UU ,
R2
C R1
U
R3 U2 = U
U1 = U
2O1O UUU O += .
U2 ,
++=
++= 2
3
12
3
11O 11
11RR
CRjUU
RR
ZRZ
UC
C
,
CjZC
1=
U
R2
C R1
U1
R3
-
, ()
8
U1 , i :
URR
U2
32O = ,
U R2
C R1
U2
R3
( )CRj
CRjRR
RR
UUU O1
12
3
2
3
2O1O 1
11
+++
=+=
CRj
CRR
RjUUO
1
2
31
1
1
+
=
:
( ) ( )( ) CRjRR
CRj
sUsU
sW O1
2
31
1
1
+
==
) (R1 = R2 = R3 = R) a
( ) ( ) 111
21
2
2
31
=+
+
=CR
RR
CRW
-
II
9
, : )
; )
; )
; )
ui(t) uo(t).
2002, 2002
uiR
C
R
R
R
uo
) , :
Cuuu == + , (1) ( )
kRuu
Ruu
iii COCFiC+=+= , (2)
kRRu
Ru
i O+== , (3)
( ), ( ) ( ) ( ) jIjZjU CCC = , (4)
uiR
C
R
R
R
uouC=u+
u-iC
ii
iF
i
(1) (3) u ( ) uC :
( ) ( ) ( ) CO ukRu
kRRikRRu +=+=+= 1 . (2) : ( )
Ru
Ru
Ruu
kRuuk
Ruu
i CCCCCC =+=++= 1 :
UR
ZIZU CCCC == ,
( ) ( ) UR
ZkUkU CCO
+=+= 11
-
, ()
10
Cj
ZC 1= :
( ) ( ) ( ) jURCjkjU O
+= 1 . , : ( )
( ) RCjk
jUjU
)j(W O +== 1
) :
RCk)(W
+= 1 ) :
( )2 == arctg
) j= s : ( ) ( )( ) sRC
ksUsU
sW O +== 1 , :
( ) ( ) ( )sUkssRCU O += 1 . s :
( ) ( ) ( ) ( )tusU,tusU,dtds OO ,
, u(t), , uO(t):
( ) )(1 tukdt
duRC O += .
-
II
11
, , . UC(s) = UC[s, C, R, U1(s), U2(s)]
u1
R
C
R R
r
u2 r
uC
2003
, , ( CUUU == + ): ( ) CC ZIIU O1 += ,
RUU
I A= 11 , R
UUI AOO
= ,
+=+=
CC Z
RUZ
ZRUU 1
C
CCA ,
2CO rIUU = , rUU
I C22=
U1
R
C
R R
r
U2r
I1
IO
UA
UO
UCI2
: ( ) ( ) ( )RZUZUUZUUURU CCCOCO ++=+= 22 1A1C ( ) ( ) CCC
ZUUZRU O123 +=+ , 2CO 2 UUU = ,
:
( )R
ZUUU CC 321
= .
sC
ZC1= :
( ) ( ) ( )sRC
sUsUsU C 3
21 = .
( ).
-
, ()
12
, , .
R
R
R ZI
U
1
e :
RUU
I O= , U
RRUU O 21 =
+= , :
RUI = .
RIURi ==
R
R
R
UI
1
-
II
13
, ,
C
R
R
R
RUO U
Z
e :
RUU
RUU
I OCC== ,
+=
CCO Z
RUU 1 ,
ZC C R:
sRCRRXZ CC +== 1 .
:
+==
CCCOCC Z
RUUUUUU 1
C
R
R
R
R U
I
UO UC
ZC = R||XC
=
CC Z
RUU 1
RZZ
UUC
CC = ,
RZU
RUU
IC
C
==
sRCCsR
IUZ +== 1
2
-
, ()
14
, , )
. R1 = R2 = R, C1 = C2 = C: )
;
) ;
) .
R1
C1
R2
U UO
C2
2003
) , , :
OUUU == + ,
1C
AOO Z
UUI
= , 1
1 RUU
I A= ,
22
C
O
ZU
I = , OIII += 12 , ( )222 CA ZRIU += ,
11
1sC
ZC = , 2
21
sCZC =
R1
C1
R2UUO
C2UAI1 I2
IO
:
( ) ( ) ( )22222
222 1 RsCUZRZU
ZRIU OCC
OCA +=+=+=
112 C
AOA
C
O
ZUU
RUU
ZU += ,
( ) 1121 CsRUUUUUCsR AOAO += . :
( ) ( ) UCsRUCsRCsRU AO =++ 111121 1 ( ) UCsRCsRCRCRsCsRCsRU O
=++++ 2211221121121 1 . :
( )[ ]121222112 +++= RRsCCRCRsUU O , :
-
II
15
( ) ( )( ) ( ) 11
21222112 +++== RRsCCRCRssU
sUsW O .
) R1 = R2 = R, C1 = C2 = C, :
( ) ( ) ( )22 11
121
sRCsRCsRCsW +=++=
:
( ) ( ) RCjRCjRCjjW ++=+= 11
11
11
2
:
( ) ( )211RC
W += . ) : ( ) ( ) WW L log20= .
( ) ( )[ ]2120 RClogdBW L += .
WL()
0
log
g
-40 dB/dec = -12 dB/oct
10 g
-40 dB
dB
:
RCg1=
) : ( ) CRarctgCRarctg = .
( ) CRarctg 2=
-
, ()
16
, . ) O
. )
. A R1 = R2 = R: )
.
) .
) , u(t), , uo(t).
R1 R2
u(t)
C
R uO(t)
) , , :
URR
U1
22 = ,
CZRUU
I += 2 ,
sCZC
1= RIUU O = ,
:
sRC
CRR
sRUU O +
=
1
11
2
.
R1 R2
CR
UO
U UO
U2
I
A2
A1
, W(s), :
( ) ( )( ) sRCC
RR
sR
sUsU
sW O +
==1
11
2
) , W(j), :
( ) ( ) jssWjW == ',
-
II
17
( ) ( )( ) RCjC
RR
Rj
jUjU
jW O
+
==
1
11
2
. (1)
, W(), :
( ) ( )2
2
1
2
1
1
RC
RR
RCW
+
+
= . ) A R1 = R2 = R: ( ) 1=W .
( ) 0=LW .
WL() 0
log dB
) (1) :
( ) CRarctgRR
CRarctg =1
2 .
A R1 = R2 = R, : ( ) CRarctg 2= . , , (). ) :
( ) ( ) ( ) ( )sUsRCsRCsUsWsU O +
==11 ,
: ( )( ) ( )( )sRCsUsRCsUO =+ 11 . ( ) ( ) ( ) ( )ssURCsUssURCsU
OO =+ , u(t), , uo(t) :
( ) ( )dtduRCtu
dtdu
RCtu OOO =+
-
, ()
18
, : )
. R1 = R2 = R, C1 = C2 = C : )
; )
.
R1
C1 R2
U UO
C2
) , , :
OUUU == + , 21 III O =+ ,
22 R
UI O= ,
11
C
A
ZUU
I= ,
1RUU
I AOO= ,
( )222 CA ZRIU += , 1
11
sCZC = ,
22
1sC
ZC =
R1 C1
R2
U UO
C2
UA I1 I2
IO
U U:
( ) ( )22
2222
2222
1RsC
RsCUZR
RU
ZRIU OCO
CA+=+=+= .
112 RUU
ZUU
RU AO
C
AO += , ( ) 1121 CsRUUUUUCsR AOAO += .
: ( )[ ]12112211222112 +++= CCsRCRCRsUCRCRUs O , (1)
( ) ( )( ) ( ) 1211221122211
2
+++== CCsRCRCRsCRCRs
sUsU
sW O .
) R1 = R2 = R, C1 = C2 = C, :
( ) ( )( )( )
( )22
2
2
112 sRCsRC
sRCsRCsRCsW +=++=
:
( )RCj
RCjRCj
RCjRCj
RCjjW
++=
+= 1112
-
II
19
:
( ) ( )( )22
1 RCRCW
+= : ( ) ( ) WW L log20= . ( ) ( )[ ]2012040 RClogRClogdBWL +=
.
WL()
0 log
40 dB/dec = 12 dB/oct
P dB
:
RCP1=
) : ( ) CRarctg 2= .
(1)
( )[ ]12112211222112 +++= CCsRCRCRsUCRCRUs O : ( ) ( )(
)12222222 ++= RCsCRssUCRssU O ,
( ) ( ) ( ) ( ) ( ) ( )sUsRCsUsUsRCsUsRC O ++= 22222 , u(t), ,
uo(t) :
( ) ( ) ( )tudt
duRC
dtud
RCdt
udRC OOO +++= 2
2
22
2
22
-
, ()
20
, , 1 2, . ZI .
RC
R
RR
R
RR
ZI
UI
21
2, 2002
) , , U I. I I1 I2. I1 I2 U.
( ) ( )( )sIsUsZ I =u i
RC
R
RR
R
R
RU
I
21
I2 I1
U2U1
UC
1 :
RUU
I 11= . (1)
URRUU 211 =
+= . (2) :
RUI =1 . (3)
-
II
21
2 e :
RUU
RUU
I CC 22== . (4)
+=
CC Z
RUU 12 . (5)
ZC C R:
sRCRRXZ CC +== 1 . (6)
C
R
R
R
RU
2
I2
U2UC
ZC = R||XC (4) (5) :
+==
CCCCC Z
RUUUUUU 12 (7)
2:
RZZ
UUC
CC = , (8)
I2 U:
CsRU
RU
sRCRRU
RU
RsRCR
sRCR
RU
RU
RU
RUI C 22
1
1 +==+
+== .
CsRUIII 221 =+= . (10)
( ) ( )( ) CRjjIjUjZ 2 == .
-
, ()
22
, : ) , ZI,
Z1, Z2, Z3, Z4, Z5 Z6 ; ) ZI Z1 = Z2 = Z3 = Z4 = Z6 = R, Z5
=1/C. (10)
Z4
Z6
Z5
Z3
Z2
Z1
ZI
2, 2002
) , :
u i U(j) I(j)
Z4
Z6
Z5
Z3
Z2
Z1
1
2
U
I1I I6
U1 U2
( ) ( ) ( ) jIjIjI 61 += , ( ) ( ) ( )( )
jZ
jUjUjI
1
11
= ,
( ) ( ) ( )( )
jZjUjU
jI6
26
= .
( ) ( )( ) ( ) jU
jZjZ
jU
+=
3
21 1 ,
( ) ( )( ) ( ) ( ) jU
ZZZ
ZZ
jUjZjZ
jU3
32
4
51
4
52
+== , :
-
II
23
UZZ
ZI
31
21 = , ( ) UZZZ
ZZZZZU
ZZZ
ZZ
I643
52343
6
4
5
3
2
6
11 ++=
++
= . : ( )
UZZZZ
ZZZZZZZZZZI
6431
6421523431 ++= .
( ) 64215234316431
ZZZZZZZZZZZZZZ
Z I ++= ) Z1 = Z2 = Z3 = Z4 = Z6 = R, Z5 =1/C , :
323
4
12 RCj
RR
RZ I+
=
CRjZ I2
21 =
, , 1 2. 2, , :
( ) ( ) jURCjjU 121= .
R
R
C
R
R
R
1
2
U
I1I I6
U1 U2
UU 21 = , U
RCjU
22 = ,
RUI =1
( I1 !) ,
CRjU
RUI
262+=
UCRj
I2
2=
-
, ()
24
, , )
Zi; )
Z1 = Z2 = Z3 = Z5 = R, Z4 = 1/jC, ) Ui
(), Ii () , .
Maj 2002
Z1
Z2
Z3
Z4
Z5
1
2
Ui Ii
) , :
iA UU = AB UU = ,
3
1
2
223 Z
UUZ
UUII ii
=== ,
554 Z
UII i== ,
iUZZZ
U5
541
+= ,
3
1232222 Z
UUZUIZUIZUU iiiA
+=+=+= .
Z1
Z2
Z3
Z4
Z5
1
2
Ui Ii
UA =Ui
UB= UA I4 = I5
U1
U2
A
B
:
=
++=
53
42
5
54
3
22 11 ZZ
ZZU
ZZZ
ZZ
UUU iii
Ii :
ii
i UZZZZZ
ZUU
II531
42
1
21 === ,
-
II
25
42
531
ZZZZZ
IU
Zi
ii ==
) Z1 = Z2 = Z3 = Z5 = R, Z4 = 1/jC CRjZ i
2= )
:
( ) ( )( ) ( ) ( )
jZjY
jUjIjW 1=== ,
( )CRj
jW 21
= ( ) CRlogWL 21020 = .
.
WL() log
-20 dB/dec= -6 dB/oct
()0
log
- /2
-
, ()
26
, , ) Zi; ) UI (), II
() W(j) Z1 = Z3 = Z4 = Z5 = R, Z2 = 1/jC,
Z1
Z2 Z3 Z4
Z5UI
1 2
2002
) , , :
IUUU == + , (1) ( )
3
232 Z
UUII I
== , (2)
IUZZZ
U5
542
+= , (3) ( ),
221 IZUU I = , (4)
1
11 Z
UUII I
== , (5)
Z1
ZI
Z2 Z3 Z4
Z5
UI
II
1 2 UI
UI U2U1
I2 = I3
) (1) (4) :
=
+
==53
42
3
5
4
23
221 1
1
ZZZZ
UZ
UUZZ
ZUZ
UUZUU I
II
II
I .
(5) :
531
42
1
1
ZZZZZ
UZ
UUI II == ,
-
II
27
42
531
ZZZZZ
IU
ZI
II ==
) UI () (), II () (), , W(j), , , :
( ) ( )( ) ( ) jYjUjIjW == .
Z1 = Z3 = Z4 = Z5 = R, Z2 = 1/jC,
( )CRjZZZ
ZZjW
2531
42 1 ==
-
, ()
28
, : ) W(j)=UO(j)/ U(j); ) W()=W(j); ) ()= arg W(j); )
.
u
C3
uo
+
OP1
OP3 OP2+
+R1
R4R5
R2
R3R6C2
2003
) , , :
OUCsRU
332
1= ,
24
53 UR
RU = ,
61 II = ,
11 R
UI I= .
6
36 R
UI =
ui
C3
uo
+
OP1
OP3 OP2+
+R1
R4R5
R2
R3 R6C2
I1I6
U3 U2
:
IO URR
UCRsR
RU
1
6
343
53 == ,
( ) 3351
64. CsRRRRR
UUsW
I
O ==
) :
-
II
29
( ) ( ) 3351
64 CRRRRR
jjs
sWjW === :
( ) ( ) 351
643 CRR
RRRjWW ==
)
/2.
)
.
WL()
log
20 dB/dec= 6 dB/oct
-
, ()
30
, : ) U= f(U); ) U= f(U)
: Ra = Rb; ) U UA,
UOU
Ra Rb
Rc
RL UA
D2
D1
OP
OPB D3
D4
2003 ) U ,
2.2.
UOUI > 0 Ra Rb
Rc
RL UA
D1
OPA
OPB D3
Ia Ib
Ia + Ib
Ic = 0
OPB ( D3). D4 . , , Ra , aa. OP D1. D2 .
0>= UUUO Ka U ,
.
-
II
31
UO > 0UI < 0 Ra Rb
RL
UA
D2 OPA
OPB D4
Ia = Ib
PB ( D4). D3 . OP D2 D1 . OP
0
-
, ()
32
, : U= f(U), UO(t)
U.
UO
rRU
R
D1
D2
A
B
Rr U(t)U
- U
0
t
TT/2
2, 2002
) ,
. 1 ( ). B ( , ). 2 .
UO < 0
rR
U < 0
RB=R
D1
D2
A
B
Rr
UA > 0
UB = 0
I1 I2
1 2
RUI =1 , (1)
URrU A = , (2)
rU
I A=2 , (3)
AO UrRU = . (4)
, U , U , :
0
-
II
33
, .
UO < 0
rR
U > 0
R
D1
D2
A
B
Rr
UA = UB /2
UB < 0
I1 I
UB < 0
IB
1 2
RUI =1 , (5)
rU
I BA 2= , (6)
RU
I BB = , (7) BA III +=1 . (8)
(6) (8) :
RrU
rU
RU
I BBB221
== (9)
rRrU
RRr
UU B 222+== (10)
rRrU
rRUURIUU BBBABO 2
22
+=+== (11) , U , U , () .
0>= UUU O .
>
-
, ()
34
, : ) U= f(U); ) UO UA,
: Ra = Rb, Rd = 2Rc
UO
UI
Ra Rb Rc RdUA
2002 ) U ,
.
UOU > 0
Ra Rb Rc Rd
Ia = Ib Ic = Id
D1U
U
UA>U
ba
a IRUI == , (1)
+=
a
bA R
RUU 1 , (2)
dc
Ac IR
UUI == , (3)
ddO RIUU = . (4)
(2) (3) :
URR
RI
ca
bc = ,
=
ca
dbO RR
RRUU 1
U , .
-
II
35
UO
U < 0
Ra Rb Rc RdIa Ic = Id = 0
D2
U U
UA=U
Ib = Ic = 0
1 ( D2). aa ( e Rb Rc ). 2 ( Rd , ).
0
=
0
01
UU
URRRR
UU cadb
O
Ra = Rb, Rd = 2Rc :
=00
UUUU
U O
) UO(t) UA(t) U .
U(t)U
- U
0 t T T/2
U(t)
- U
0 t T T/2
U(t)2U
- U
0 t T T/2
-
, ()
36
, ZD1 ZD2 - ( ), ) UO
U, UZ R1, R2 R3;
) z U = 5 V, UZ = 2.5 V R1 = R2 = R3;
) - , U(U); U
R1R3
R2
Uo
ZD1 ZD2
U
IAK
UZ
2002, ) Ui, , - . Ui, - . :
+=
1
21RR
UU O
R2 -, UZ. U :
Zk U
RU
RIRU ===1
2222 ,
2
1
RR
UU Zk = .
U
R1R2
Uo
U2=R2 I2< UZ
I2
-
II
37
U .
U>UK
R1 R3
R2
Uo
UZ
U
R1 RT
Uo
UT
, , . :
32
2
RRR
UU ZT += , 3232
RRRR
RT += :
kTO UU;URR||R
UU +
+=
1
321
) Uk = UZ = 2,5 V,UT=1,25 V,UO(5 V)= 8,75 V
) - .
0
U
U
2
1
RRUU ZK =
ZT URRRU
22
2
+=
+
2
11RRU Z
-
, ()
38
, ,: ) UO(Ui, U)
D1 D2 ( , );
) - , U(Ui, U) : R = R1 = R2 = R3;
) - , U(Ui, U) : R = R1 = R2, R3 = ;
Ui R R3
R1
R2
Uo
R1
R2
+U
-U
D1
D2
UAK
IAK
2002,
) U, - . .
iO URR
U 3= :
RR
k 31 = , D1 ( 2).
UR
RRU
RRR
U iO2
1313 = - Ui UiG :
RRR
UU
ki
O 132 =
=
-
II
39
D1 ( 2).
UR
RRU
RRR
U iO2
1313 = . - Ui UiG :
RRR
UU
ki
O 132 =
=
Ui R R3
Uo
R1
R2
+U
D1
) - . UiG ,
21 RU
RU OG = ; iGOG UR
RU 3= , U
RRRR
U iG32
1= , URR
U OG2
1=
0
U
UUG
-UG
-UG
UG
k1
k2
UR
RR
2
13
) - R3 = .
0
U
U
