Лекции ЭЦМ часть1
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, . 5.3, .
. 5.3.
U U 1 U 2
U 2 U 2 (1 R2 / R1 ) ;
U 1 U R2 / R1 U 1 (1 R1 / R2 ) /(R2 / R1 ) U 1 (1 R2 / R1 )
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U (1 R2 / R1 )(U 2 U 1 ) .
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. 5.4.
. 5.4
. . R1=R2=R3=R4=R, . ,
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, . R, U1 U2 U1 -
U2 , . -
104
u=(1 + 2R/R2)N
R2. -
R2.
9.4. - .
( 5.6),
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R 2
. 5.6.
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R1= R2 = R3 = R4 = R 1 = R 2 = R
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U =U , :
U1 + U2 - 3U = –U ,
U3 + U4 - 3U = 0.
U3 + U4– U1 – U2 = U .
, -
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R /R1+ R /R2 + + R /Rm = R /R 1 + R /R 2 + + R /R n ,
m — , n — .
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U = -4U1 - 2U2 + 10U3 + U4.
, 6, 11.
R =R =100 . . U1
R /R1 = 4. R1 =25 . , R2 = R /2 =50 , R3 = R /10=10 , R4=R /1=100
. , 5 -
. , U
105
U = -(4U1 +2U2 +5 U ) + (10 U3 + U4)
U = 0, Rx=100/5=20 .
R =20 – -
. , R x .
, -
. U =U1+U2. ,
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. , R =R 1= R 2. -
2. R1 = R /n= R /2. . 5.7.
R1
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. 5.7.
, . , , U = U1 + 2U2 . , -
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9.5.
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. . 5.8. . -
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Ic C dUc . dt
I = 0 ,
, IR =- IC . Uc= - U , -
Ic C dU U / R I R . dt
dU ,
dU = (–1/RC) U dt,
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1 t
U RC 0 U dt .
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. U -
:
U Uc 1 U t
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a)- 5
)
. 5.8. : — ; — -
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. R=10 , =0,1 . -
1 5 . ( . . 5.8 ). ,
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, , t3 - t1. U = 5B t1 < t
< t2, U = - 5 t2 < t < t3.
. -
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U ,
t
U U 0 RC1 0 Udt
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, . . t1 t2,
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, ( -
).
, -
1.25 . . 5.8, .
( . 5.9 ),
. .
U = –(R /R1)U –1/(R1C) U dt.
, .
( . 5.9 ) .
, . 5.3 nR1 nR2
1= 2 = .
107
U = (1/RC) (U2 – U1)dt.
. -
n . 5.9 . ,
iC = iR1 + iR2 + iRn,
(dU /dt) = (U1 /R1) + (U2 /R1) + + (Un /Rn).
R1 = R2 = Rn =R
dU /dt = –(U1+ U2 + +Un) /CR.
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. 5.9. : — , — ,—
, , -
( , ).
,
( );
, -
. , . 5.10
, -
. :
— .
( ) — -.
( ) — .
. -
, -
. -
, .
. 5.10
U =–(1/R1C) U1 dt + U .,
U – ,
.
U =–(R /R2)U2.
, U2= 0. , -
108
, . =I t/U, t = CU/I,
t .=CU / I ,
I — , U — -
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( ) (K1, K2 )
. ,
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= R .
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. 5.10.
, -
R R2. , -
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( ) , -
U . I -
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( , -
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. , U 2–U 1 ,. . . U
U |
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U dt |
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U dt |
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I dt U |
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, — . -
I U , , -
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, . 5.11.
, . -
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109
1 dU . dt
IR R
C
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R1
. 5.11.
Uc U , -
. , , R
, . . IR=IC. U = –RIR =–ICR,
U = –RC dU /dt.
.
-
. -
.
,
.
9.6.-
,
. -
.
, -
1 = 1/(R1C1),
1 = 1(/R1C1), 2 = 1/(R2C2)
2.
. 5.12. : — -
, ; —
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