Êóðñîâàÿ ðàáîòà

ïî ïðåäìåòó : «Îñíîâû òåîðèè öåïåé».

                                                                                         Âûïîëíèë:

                                                                                           Ïðîâåðèë :

ã. Íèæíèé Íîâãîðîä

1996 ã.

1.     Îïðåäåëåíèå ïåðåõîäíîé è èìïóëüñíîé õàðàêòåðèñòèê öåïè

Öåïü:                                       i₁               i₂   

                                                                  + I(t)

              R₁                                                                                    R₂        U₂      

                                         C       

Èñõîäíûå äàííûå:

Òîïîëîãè÷åñêèå óðàâíåíèÿ:

I₀=i₁+i₂

I₂R₂=I₁R₁+Uc

(I₀-I₁)R₂= I₁R₁+Uc

I₁(R₁+R₂)+Uc=I₀R₂

Äèôôåðåíöèàëüíîå óðàâíåíèå:

(Ñ (R₁+R₂)/R₂)dUc/dt+Uc/R₂=I(t)

Õàðàêòåðèñòè÷åñêîå óðàâíåíèå:

          (Ñ (R₁+R₂)/R2)p+1/R₂=0

 Íà÷àëüíûå óñëîâèÿ íóëåâûå :

          p=-1/Ñ(R₁+R₂)=-1/t

                           _{t                                                                                                                                                                                    t}

          U_c(t)=e^-t/tò (I(t)1(t)*R₂/ Ñ(R₁+R₂))e^t/t dt=(I₀*R₂/ Ñ(R₁+R₂))t_öe^-t/tòe^t/t dt =I₀*R₂e^-t/te^t/t ½ =

^{0                                                                                                               0}

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

          I₁(t)=CdUc/dt=(IoCR₂1/t_ö) 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]

Ïåðåõîäíàÿ õàðàêòåðèñòèêà:

           h_I2=1-R₂/(R₁+R₂)) e^-t/t=1-0.67 e^-t/t     

h_U2=R₂[1-(R₂/(R₁+R₂)) e^-t/t]1(t)   t_ö=C(R₁+R₂)=0.6 10^-6

h_U2=200[1-0,67 e^-t/t]1(t)

Èìïóëüñíàÿ õàðàêòåðèñòèêà:

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

          g_U2=d h_U2/dt=(R2*R₂/(R₁+R₂)t_ö e^-t/t)) 1(t)+ R₂[1-(R₂/(R₁+R₂)) e^-t/t]d(t)

          g_U2=0,22*10⁹e^-t/t1(t)+66d(0)

2. Îïðåäåëåíèå îòêëèêà öåïè:

Âõîäíîå âîçäåéñòâèå:

I(t)=2*(1-e^-t/0,610  )1(t)

h_I2=1-(R₂/(R1+R2)) e^-t/t1(t)

                          _t               

I_âûõ=I(0)h_I2(t)+ ò I’(y) h_I2(t-y)dy

                         ⁰

I(0)h_I2(t)= 2*(1-e^0/0,610  ) h_U2=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 10}dy= -(0.6 10^-62/0.6 10^-6) e^{-y/0.6 10}½=-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} e^{y/0.6 10} e^{-t/0.6 10}dy=(2,23 10⁶)e^{-t/0.6 10}ò1dy=

                                                      ^{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

Âûõîäíîå íàïðÿæåíèå:

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

3.Îïðåäèëåíèå À×Õ, Ô×Õ :

Ê(jw)=I_âûõ/I_âõ= (U₂/R₂)/(U₂/Z_ý)= Z_ý/ R₂

Z_ý=(R₂(R₁-j/wC))/((R₁+R₂)-j/wC)

Ê(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))} =

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

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

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

ÇÀÄÀÍÈÅ ¹2

1.Îïðåäåëèòü ïàðàìåòðû öåïè : Q₀, r

 Öåïü:                             Rã

  å(t)

                                 C1                        C2

                                                                                        Rí  

                                    R1                        R2             

Èñõîäíûå äàííûå:

Õàðàêòåðåñòè÷åñêîå ñîïðîòèâëåíèå êîíòóðà:

r =  w₀ L₁ = w₀ C

Ðåçîíàíñíàÿ ÷àñòîòà:

w₀ =1 /Ö LC,

L = L₂;

1/C₂ =  1/C +1/C Þ Îáùàÿ åìêîñòü: C = C₁C₂  / C₁+C₂  Þ C = ð C₂ = 1 / 2 C₂=250 ïÔ

w₀ =1 /Ö 250*500*10^-18 =2,8*10⁶

r =  w₀ L₁ = w₀L=2.8*500=1400 Îì

 Äîáðîòíîñòü êîíòóðà:

Q₀⁼r/(R₁+R₂)=1400/10=140

2.Ðàñ÷åò U_k,, U_C1, U₂ ,I_ã:

Òîê ãåíåðàòîðà:

I_ã=E_m/(R_oe+R_ã)

Ðåçîíàíñíîå ñîïðîòèâëåíèå êîíòóðà:

R_oe=(pr)²/( R₁+R₂+ R_âí)                                       p-êîýôèöèåíò ïîäêëþ÷åíèÿ ð=1/2

Âíîñèìîå ñîïðîòèâëåíèå íàãðóçêè

R_âí=(X_C1)²/R_í

X_C1=pr=1400/2=700 Îì

Âíîñèìîå ñîïðîòèâëåíèå íàãðóçêè:

R_âí=(700)²/50000=9.8 Îì

R_oe=1960000/4*(10+9.8)=24747.5 Îì

Òîê ãåíåðàòîðà:

I_ã=200/(25000+24748)=0,004 À

U_k= I_ã* R_oe=0,004*24748=99 Â

I_k= U_k/ pr=99/700=0.14 A

U_C1= U_C2= I_k* X_C1=0.14*700=98 Â

U_L= I_k*r=0.14*1400=196 A

U₂= I_k*ÖR₁²+ X_C²    =0.14*Ö5²+700²   = 98 Â

Àêòèâíàÿ ìîùíîñòü :

P= I_k²* R_k/2=0.14²*19.8/2=0.19 Â

Ïîëîñà ïðîïóñêàíèÿ êîíòóðà:

Ï_ê=w₀/Q₀=2.8*10⁶/140=20000

Ïîëîñà ïðîïóñêàíèÿ âñåé öåïè:

Ï_ö=w₀/Q_ïð                                   Q_ïð=r/(R₁+R₂+R_âíí+ R_âíã)

R_âíã=700²/50000=9,8 Îì

Q_ïð=1400/(10+19.6)=47.3

Ï_ö=2,8*10⁶/47,3=59197

ÇÀÄÀÍÈÅ ¹3

1.Îïðåäåëåíèå ïîñòîÿííîé ñîñòîâëÿþùåé è ïåðâûõ øåñòè ãàðìîíèê

Âõîäíîé ñèãíàë:

Ïðåäñòàâèì ñèãíàë ñëåäóþùèì îáðàçîì:

                    Õ₀(t)

                     Õ₁(t)

                     Õ₂(t)

                                                                 Ñïåêòðàëüíàÿ ïëîòíîñòü äëÿ äàííîãî èìïóëüñà:

                                                                  S₀=(8A/w²t_è)(cos(wt_è/4)- cos(wt_è/2))                                                                        

                       _{-t/2              t/2}               

Äëÿ ñèãíàëà Õ₀(t)=10 Â =À₀/2          À₀=2*10=20 Â

Ñïåêòð ñèãíàëà äëÿ Õ₁(t) :

À_n1=2*S(jw)*e^jwt/2/T=2*8*8(cos(nWt_è/4)- cos(nWt_è/2))e^jnWt/2/T(nW)²t_è

W=2*p/T  ãäå T=12 t_è

À_n1=(32*12/p²n²)(cos(np/24)-cos(np/12)) e^{j np/12}

Ñïåêòð ñèãíàëà äëÿ Õ₂(t) :

À_n2=-(32*12 /p²n²)(cos(np/24)-cos(np/12)) e^{-j np/12}

Ñóììàðíûé ñïåêòð :

À_n=(32*12/p²n²)(cos(np/24)-cos(np/12)) e^{j 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)

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

Cïåêòð ñèãíàëà:

A_0îá=A₀+A_n0=20; A_n1=j0,51; A_n2=j0,97; A_n3=j1,3; A_n4=j1,58; A_n5=j1.6; A_n6=j1.53

Ïîñòîÿííàÿ ñîñòîâëÿþùàÿ:

I₀=10 À

Ãàðìîíèêè:

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.     Îïðåäåëåíèå ïîñòîÿííîé ñîñòîâëÿþùåé è ïåðâûõ øåñòè ãàðìîíèê âûõîäíîãî ñèãíàëà

×àñòîòíàÿ õàðàêòåðèñòèêà

Ê(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_ö=900000

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

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

Ê(j6W)=0,43e^-j25,5 Ê(0)=1

Cïåêòð âûõîäíîãî ñèãíàëà:

À₀=20*1=20

À₁=0.89e^-j17,6*0,51e^j90=0,45 e^j72,4

À₂=0,72e^-j26,8*0,97e^j90=0,65e^j63,2

À₃=0,6e^-j29,5*1,3e^j90=0,78e^j63,2

À₄=0,52e^-j29,1*1,58e^j90=0,82e^j60

À₅=0,46e^-j27,43*1,6e^j90=0,74e^j62,6

À₆=0,43e^-j25*1,53e^j90=0,66e^j65

Ïîñòîÿííàÿ ñîñòîâëÿþùàÿ âûõîäíîãî ñèãíàëà:

I₀=A₀/2=20/2=10 À

Ãàðìîíèêè:

I₁=0.45ños(Wt+72,4^î)

I₂=0,65cos(2Wt+63,2^î)

I₃=0,78cos(3Wt+63,2^î)

I₄=0,82ños(4Wt+60^î)

I₅=0,74cos(5Wt+62,6^î)

I₆=0,66cos(6Wt+65^î)