. , , ,

,,,

: .

:

:

.

1996 .

1

1.    

: i1 i2


+ I(t)

R1 R2 U2

C


:

I(t)

R1

R2

C

2*(1-e-t/0,6*10 )1(t)

100

200

2000

:

I0=i1+i2

I2R2=I1R1+Uc

(I0-I1)R2= I1R1+Uc

I1(R1+R2)+Uc=I0R2

:

( (R1+R2)/R2)dUc/dt+Uc/R2=I(t)

:

( (R1+R2)/R2)p+1/R2=0

:

p=-1/(R1+R2)=-1/t

t t

Uc(t)=e-t/tò (I(t)1(t)*R2/ (R1+R2))et/t dt=(I0*R2/ (R1+R2))te-t/tòet/t dt =I0*R2e-t/tet/t ½ =

0 0

=I0*R2e-t/t[ et/t-1]= I0*R2 [1-e-t/t]

I1(t)=CdUc/dt=(IoCR21/t) e-t/t =(IoR2/(R1+R2)) e-t/t

I2(t)=Io[1-R2/(R1+R2)) e-t/t]

U2=I2*R2= Io[R2-(R22/(R1+R2)) e-t/t]

:

hI2=1-R2/(R1+R2)) e-t/t=1-0.67 e-t/t

hU2=R2[1-(R2/(R1+R2)) e-t/t]1(t) t=C(R1+R2)=0.6 10-6

hU2=200[1-0,67 e-t/t]1(t)

:

gI= R2/(R1+R2)2C)e-t/t+[1-R2/(R1+R2)) ]e-t/td(t)=1.1*106 e-t/t+0.33d(0)

gU2=d hU2/dt=(R2*R2/(R1+R2)t e-t/t)) 1(t)+ R2[1-(R2/(R1+R2)) e-t/t]d(t)

gU2=0,22*109e-t/t1(t)+66d(0)




2. :

:

I(t)=2*(1-e-t/0,610 )1(t)

hI2=1-(R2/(R1+R2)) e-t/t1(t)

t

I=I(0)hI2(t)+ ò I(y) hI2(t-y)dy

0

I(0)hI2(t)= 2*(1-e0/0,610 ) hU2=0

I(t)=(2/0.6 10-6) e-t/0.6 10

t

ò(2/0.6 10-6 )e-y/0.6 10[1-0,67 e-(t-y)/0.6 10]dy

0

t t

1) ò(2/0.6 10-6)e-y/0.6 10dy= -(0.6 10-62/0.6 10-6) e-y/0.6 10½=-2[e-t/0.6 10-1]= 2[1-e-t/0.6 10]

0                                                                                                                                                                                            0

t t

2) -(2*0,67/0.6 10-6 ) òe-y/0.6 10 ey/0.6 10 e-t/0.6 10dy=(2,23 106)e-t/0.6 10ò1dy=

0 0

=-2,23 106 te-t/0.6 10=-2,23 106 te-t/0.6 10

I(t)2=-2,23*106 te-t/0.6 10-2e-t/0.6 10+2=2-2,23*106*te-t/0.6 10-2e-t/0.6 10

U2= I(t)2*R2

:

U2(t)=400-446*106 te-t/0.6 10-400e-t/0.6 10


3. , :

(jw)=I/I= (U2/R2)/(U2/Z)= Z/ R2

Z=(R2(R1-j/wC))/((R1+R2)-j/wC)

(jw)=(R1-j/wC)/((R1+R2)-j/wC)=Ö(R12+(1/Cw)2)/ (((R1+R2))2+(1/wC)2) *

*e-jarctg(1/wCR1)+ jarctg(1/wC(R1+R2)) =

=Ö((R1w)2+(1/C)2)/ ((R1+R2)w)2+(1/C)2) *e-jarctg(1/wCR1)+ jarctg(1/wC(R1+R2)) =

(jw)=Ö(10000*w2+0,25 1018)/(90000*w2+0,25 1018) * e-jarctg(10/0,2w)+ jarctg(10/w0,6)

(w)=Ö(10000*w2+0,25 1018)/(90000*w2+0,25 1018)

(w)=-arctg(106/0,2w)+ arctg(106/w0,6)



2

1. : Q0, r

: R


(t)

C1 C2


R

R1 R2


:

. .

Em

200

R

25

L2

500

C2 = C1

500

R1 = R2

5

R

50

:

r = w0 L1 = w0 C

:


w0 =1 /Ö LC,

L = L2;

1/C2 = 1/C +1/C Þ : C = C1C2 / C1+C2 Þ C = C2 = 1 / 2 C2=250


w0 =1 /Ö 250*500*10-18 =2,8*106

r = w0 L1 = w0L=2.8*500=1400

:

Q0=r/(R1+R2)=1400/10=140

2. Uk,, UC1, U2 ,I:

:

I=Em/(Roe+R)

:

Roe=(pr)2/( R1+R2+ R) p- =1/2

R=(XC1)2/R

XC1=pr=1400/2=700

:

R=(700)2/50000=9.8

Roe=1960000/4*(10+9.8)=24747.5

:

I=200/(25000+24748)=0,004

Uk= I* Roe=0,004*24748=99

Ik= Uk/ pr=99/700=0.14 A

UC1= UC2= Ik* XC1=0.14*700=98

UL= Ik*r=0.14*1400=196 A


U2= Ik*ÖR12+ XC2 =0.14*Ö52+7002 = 98

:

P= Ik2* Rk/2=0.142*19.8/2=0.19

:

=w0/Q0=2.8*106/140=20000

:

=w0/Q Q=r/(R1+R2+R+ R)

R=7002/50000=9,8

Q=1400/(10+19.6)=47.3

=2,8*106/47,3=59197

3

1.

:


:

0(t)


1(t)


2(t)


:

S0=(8A/w2t)(cos(wt/4)- cos(wt/2))

-t/2 t/2

0(t)=10 =0/2 0=2*10=20

1(t) :

n1=2*S(jw)*ejwt/2/T=2*8*8(cos(nWt/4)- cos(nWt/2))ejnWt/2/T(nW)2t

W=2*p/T T=12 t


n1=(32*12/p2n2)(cos(np/24)-cos(np/12)) ej np/12

2(t) :


n2=-(32*12 /p2n2)(cos(np/24)-cos(np/12)) e-j np/12

:

n=(32*12/p2n2)(cos(np/24)-cos(np/12)) ej np/12-(32*12 /p2n2)(cos(np/24)-cos(np/12))e-j np/12=2j(32*12/p2n2)(cos(np/24)-cos(np/12))sin(np/12)

An=j(8/p2n2)*(sin(np/16)/(np/16))*(sin(np/12)/(np/12))sin(np/12)

C :

A0=A0+An0=20; An1=j0,51; An2=j0,97; An3=j1,3; An4=j1,58; An5=j1.6; An6=j1.53

:

I0=10

:

I1=0,51cos(Wt+90)

I2=0.97cos(2Wt+90)

I3=1.3cos(3Wt+90)

I4=1.58cos(4Wt+90)

I5=1.60cos(5Wt+90)

I6=1.53cos(6Wt+90)

2.    

(jw)=Ö(10000*w2+0,25 1018)/(90000*w2+0,25 1018) * e-jarctg(10 6/0,2w)+ jarctg(10 6/w0,6

W=p/6t=900000

(jnW)=Ö(10000*n29000002+0,25 1018)/(90000* 9000002n2+0,25 1018) * e-jarctg(5.6/n)+ jarctg(1.9/n)

(jW)=0.89e-j17,6 (j2W)=0,72e-j26,8 (j3W)=0,6e-j29,5 (j4W)=0,52e-j29,1 (j5W)=0,46e-j27,43

(j6W)=0,43e-j25,5 (0)=1

C :

0=20*1=20

1=0.89e-j17,6*0,51ej90=0,45 ej72,4

2=0,72e-j26,8*0,97ej90=0,65ej63,2

3=0,6e-j29,5*1,3ej90=0,78ej63,2

4=0,52e-j29,1*1,58ej90=0,82ej60

5=0,46e-j27,43*1,6ej90=0,74ej62,6

6=0,43e-j25*1,53ej90=0,66ej65

:

I0=A0/2=20/2=10

:

I1=0.45os(Wt+72,4)

I2=0,65cos(2Wt+63,2)

I3=0,78cos(3Wt+63,2)

I4=0,82os(4Wt+60)

I5=0,74cos(5Wt+62,6)

I6=0,66cos(6Wt+65)


頠 : .

 

 

 

! , , , .
. , :