TRNG I HC CN TH KHOA CNG NGH
BI TP K THUT XUNGNHM THC HIN NGUYN THANH IN 1090923 THNH DUY 1091011 NGUYN TN T 1090920
Bi tp chng 2 p ng ca mch RL i vi cc xung c bn 1. Tm p ng ca mch i vi cc xung: Hm nc: Uv(t) = Eu0(t). Hm dc: Uv(t) = ktu0(t). Yu cu: ngn gn o Biu thc ng ra: i(t), UR(t), UL(t). o V dng tn hiu: kho st + v. Gii p ng ca mch RL i vi xung hm nc: Uv(t) = Eu0(t). o Phng trnh biu din mch c dng: Uv(t) = UR(t) + UL(t)
Eu0(t) = Ri + L
+
i=
y l phng trnh tuyn tnh cp mt c dng: y + P(x)y = Q(x). p dng cng thc tnh nghim tng qut: y = ( dx + C).
i(t) =
(
dt + C)
Gi =
l thi hng ca mch. t =
=
i(t) =
(
dt + C)
i(t) =
(
+ C) i(t) =
+C
Gi s dng in ban u qua mch bng 0:
2
i(0) = 0
+C=0 C=-
i(t) =
-
=
(1 -
)
= Ri(t) = E(1 -
)
uL(t) = uv(t) uR(t) = E
Nhn xt: o i(t) v uR(t) c dng hm m tng. o uL(t) c dng hm m gim. Ti t = 0+: i(0+) = 0 uR(0+) = 0 uL(0+) = E uL() 0
Khi t :
i()
uR() E
3
Dng th:
uv E
t 0 i
t 0
E
t 0
E
t 0
4
p ng ca mch RL i vi xung hm dc: Uv(t) = ktu0(t). o Phng trnh biu din mch c dng: Uv(t) = UR(t) + UL(t)
ktu0(t) = Ri + L
+
i=
y l phng trnh tuyn tnh cp mt c dng: y + P(x)y = Q(x). p dng cng thc tnh nghim tng qut: y = ( dx + C).
i(t) =
(
dt + C)
Gi =
l thi hng ca mch. t =
=
i(t) =
(
dt + C)
i(t) =
(
-
+ C) i(t) =
-
+C
Gi s dng in ban u qua mch bng 0:
i(0) = 0
+C=0C=
i(t) =
-
+
= (t (1 -
))
5
= Ri(t) = k(t (1 -
))
= uv(t) uR(t) = k(1 -
)
Nhn xt: o uL(t) c dng hm m tng. Ti t = 0+: i(0+) = 0 uR(0+) = 0 uL(0+) = 0
Khi t :
i()
(t )
uR() k(t )
uL() k
6
Dng th:
uv k
t 0i
t 0
t 0
k
t 07
2. Lp bng so sang p ng c mch RC v RL Rt ra kt lun.
Bng so snh: p ng i vi xung hm nc: uv(t) = Eu0(t) RC i(t) = = = Ti t = 0+ : i(0+) = =E =0 Khi t : RL i(t) = Ti t = 0+ : i(0+) = 0 =0 =E
Khi t :
i()
i() 0 E
0 0 =E = =
8
Hm dc: uv(t) = ktu0(t) RC i(t) = = = = Ti t = 0+ : i(0+) = 0 Ti t = 0+ : i(0+) = 0 =0 =0 Khi t : =0 =E =
Khi t : i() i() kC E 0 =
RL i(t) = Kt lun: Da vo bng so snh trn ta thy p ng ca mch RC tng t nh o ng ca mch RL khi ta thay cc linh kin: o T C trong mch RC thay bng in tr trong mch RL. o in tr trong mch RC thay bng cun dy trong mch RL. o Thi hng = RC c thay bng =
9
3. tm v v dng tn hiu ng ra
a.R1
uv(t)
C1
u2R2
u1
u v (t ) = E.u 0 (t )Ta c:
u v (t ) = u R1 (t ) + u R2 (t ) + u C (t )t
1 E.u 0 (t ) = R1 .i (t ) + R2 .i (t ) + i (t ).dt C0Bin i Laplace hai v ta c :
E I ( s) = R1 .I ( s ) + R2 .I ( s ) + s s.C E.C I ( s) = s (R 1 + R2 ).C + 1t
= ( R1 + R2 ).C l thi hng ca mch=1
E.C s +1
I ( s) =
Bin i Laplace ngc ta c :
i (t ) =
E .e t .u 0 (t ) R 1 + R2
u R1 (t ) = R1 .i (t ) =
R1 .E .e t .u 0 (t ) R1 + R2
10
u1 (t ) = u R2 (t ) =
R2 .E t .e .u 0 (t ) R1 + R2
u 2 (t ) = u v (t ) u R1 (t )= E.u0 (t ) R1.E t .e .u0 (t ) R1 + R2
Kho st i(t), u1(t), u2(t) t < 0 i(t) = 0, u1(t) = 0, u2(t) = 0
R2 .E R2 .E E , u1(t) = , u2(t) = R1 + R2 R1 + R2 R1 + R2 t i(t) 0 , u1(t) 0, u2(t) t Et = 0 i(t) =
uv(t) E
t
i(t)
E R1 + R2t u2(t)
E
E.R2 R1 + R2t u1(t)
11
b.C1
R
uv(t)C2
u2 u1
u v (t ) = E.u 0 (t t 0 )
Ta c:
u v (t ) = u R (t ) + u C1 (t ) + u C2 (t )
E.u 0 (t t 0 ) = R .i (t ) +Bin i Laplace hai v ta c :
1 1 i(t ).dt + C 2 i(t ).dt C1 0 0
t
t
E s .t 0 I (s) I ( s) .e = R. I ( s ) + + s s.C1 s.C 2 I (s) = E .e s .t0 C1 + C 2 + s.R.C1C 2C1 + C2 C1 + C 2
Bin i Laplace ngc hai v ta c :.t 0 .t E i (t ) = .e R.C1 .C2 .e R.C1 .C 2 .u 0 (t t 0 ) R
t = R.
C1 .C 2 l thi hng ca mch C1 + C 2 = C1 + C 2 R.C1 .C 2
=i (t ) =
1
E t0 .t .e .e .u 0 (t t 0 ) R E i (t ) = .e (t t0 ) .u 0 (t t 0 ) R
u R (t ) = R.i (t ) = E.e (t t0 ) .u 0 (t t 0 )12
1 u1 (t ) = u C2 (t ) = i (t ).dt C2 0 E E u1 (t ) = .e (t t0 ) .u 0 (t t 0 ) .R.C 2 .R.C 2
t
u 2 (t ) = u1 (t ) + u R (t ) E E = E.e ( t t0 ) + .e ( t t0 ) .u 0 (t t 0 ) .R.C 2 .R.C 2 Kho st i(t), u1(t), u2(t) t < t0 i(t) = 0, u1(t) = 0, u2(t) = 0
E E , u1(t) = 0, u2(t) = R .R.C2 E E t i(t) 0, u1(t) , u2(t) .R.C2 .R.C2t = t0 i(t) = uv(t)
E t t0 i(t)
E Rt0
t
u1(t) E
E .R.C 2t0 u2(t)
t
13
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