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RLC kolo
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: :
O RLC O
UNIVERSITY OF KRAGUJEVAC FACULTY OF TEHNICAL
SCIENCE
1. ................................................................................................................................ 1
2. RLC ............................................................................. 4
2.1 ................................................... 10
2.2 RLC ............................................................................................................ 11
2.3 RLC ................................................................................ 14
2.4 RLC ............................................................................................. 16
3. .................................................................................................................... 17
RLC -
FIZIKI OSNOVI ELEKTROTEHNIKE 1
1.
- , ( , , ). . , . , , . .
, :
, . . ( 1.) .
RLC -
FIZIKI OSNOVI ELEKTROTEHNIKE 2
1 -
2 -
3 -
RLC -
FIZIKI OSNOVI ELEKTROTEHNIKE 3
. . , , . .
. . (t) (t). ( 4.)
4 - (t) (t)
RLC -
FIZIKI OSNOVI ELEKTROTEHNIKE 4
2. RLC
RLC : , . (eng. R-Resistor, L-Inductor, C-Capacitor). RLC ( 5.). , , , .
5 RLC
(. resistor) , ( 6.). . O . .
6
, .
RLC -
FIZIKI OSNOVI ELEKTROTEHNIKE 5
ZR = l
S (1)
. ().
ZR = u(t)
i(t) ZR =[
V
A ] = [ ] (2)
7
iR(t) = Im cos t = 2 I cos t (1) uR(t) = R i(t) = 2 R I cos t (2) ( 7.) :
= (3) = = 0
( = 0 )
(4) :
R ( -)
jXR , ( y-)
ZR = R ( ) (5)
uR = ZR iR (6)
RLC -
FIZIKI OSNOVI ELEKTROTEHNIKE 6
( 8.) ( 9.) . :
p = uR(t) iR(t) (7) :
uR = ZR iR iR = uR
ZR (8)
:
p = ZR iR 2
(9)
: p = u
2
ZR (10)
p = [w] = [V A] = [ A2] = [ V2
]
8 9
() . ( 10.). .
10
RLC -
FIZIKI OSNOVI ELEKTROTEHNIKE 7
:
L = 0 N2 S
l (11)
:
L = 0 r N2 S
l (12)
:
0 = 4 107 [H
m] ( ) ,
r , N ,
l S . (H).
11 k
uL(t) = L di
dt = - L Im sin t = 2 XL I cos(t +
2) (13)
( 11. ) :
= +
2 (14)
= = +
2 =
2
RLC -
FIZIKI OSNOVI ELEKTROTEHNIKE 8
2
(15) :
RL ( )
XL = L ZL = j XL (16)
uL = ZL iL (17)
, ( 12.). ( ) .
12
. ()
q
u .
C =
(18)
(F). , .
:
C = 0 r
(19)
:
RLC -
FIZIKI OSNOVI ELEKTROTEHNIKE 9
C = 0 r 2
2
1
(20)
:
C = 0 r 1 2
21 (21)
= 0 r ,
0 = 8,85 10-12 [F
m]
13 k
uL(t) = q(t)
C =
1
C ()
0 =
Im
C sint (22)
uL(t) = 2 cos(t
2 ) (23)
( 13. ) :
= -
2 (24)
= = -
2 = -
2
(25)
RLC -
FIZIKI OSNOVI ELEKTROTEHNIKE 10
:
RC
XC = 1
C = - j
1
C
ZL = j XC (26)
uC = ZC iC (27)
2.1
I , :
I = 1
2()
0 (28)
:
I 2 = 1
2()
0 =
1
2() sin2( + 0)
0 (29)
:
I = Im
2 = 0,707 Im (30)
:
U = Um
2 (31)
:
i = 2 I sin( + ) (32)
, . , , , .
RLC -
FIZIKI OSNOVI ELEKTROTEHNIKE 11
2.2 RLC
, :
i(t) = Im sin t (33) iR(t) = iL(t) = iC(t) = i(t) (34)
uR ,
uL uC , ( 14.):
14 RLC
u(t) = uR(t) + uL(t) + uC(t) (35)
uR = R i (36)
uL = L di
dt (37)
uC = 1
C
0 (38)
u(t) = R i + L di
dt +
1
C
0 (39)
u(t) = R Im sin t + L Im cos t - 1
C Im cos t (40)
:
u(t) = Um sin (t + ) (41) :
Um sin (t + ) = Um sin t + (ULm UCm) cos t (42)
RLC -
FIZIKI OSNOVI ELEKTROTEHNIKE 12
(43)
Um :
a sin ( ) = a sin cos a cos sin (43) Um cos sint+Um sin cost=URm sint+(ULmUCm)cost
:
Um sin = ULm UCm = (L - 1
C) Im (44)
Um cos = R Im (45)
:
Um2 = URm
2 + (ULm UCm)2 (46) (44 45) :
u(t) = R i(t) (47)
(44) , :
(L - )
:
X = XL XC = L - (48) . .
(45) R .
Z . :
15
RLC -
FIZIKI OSNOVI ELEKTROTEHNIKE 13
1 RLC
Z = ZR + ZL + ZC (49)
Z = R + jXL - jXC (50)
Z = R + j(XL - XC)
X = XL - XC = L - 1
C - ( )
R
RLC ( 15.) :
(51)
.
: X > 0
;
RLC -
FIZIKI OSNOVI ELEKTROTEHNIKE 14
X < 0 .; X = 0,
. . 900 + 900. , .
2.3 RLC
16 RLC
.
(52)
(53)
(54)
(55)
(56)
RLC -
FIZIKI OSNOVI ELEKTROTEHNIKE 15
(57)
(58)
(59)
(60)
(61)
(62)
RLC
(63)
(64)
(65)
(66)
RLC -
FIZIKI OSNOVI ELEKTROTEHNIKE 16
(67)
2.4 RLC
17 RLC
RLC ( 17.), :
R = R1 + R2 (68)
X = X1 + X2 (69)
Z Z1 + Z2 (70)
1 + 2 (71)
.
RLC -
FIZIKI OSNOVI ELEKTROTEHNIKE 17
3.
. ,
. , , 2006.
,
http://en.wikipedia.org/wiki/RLC_circuit