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