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 ?????? 1. ??? ????????????? ?????, ??????????????? ?????? ???????? (????. 1.3) ? ???????????? ?? ???. 1.22 - 1.41, ????????? ?????????:
1. ?? ????????? ??????? ???????? ????????? ? ????? ???? ??????? ????????? ??? ??????? ????? ?? ???? ?????? ????, ??????? ?? ? ???? ??????: ?) ????????????????; ?) ?????????????.
2. ?????????? ????????? ??????????? ???????? ????? ?? ???? ??????, ???????????????? ????? ?? ??????? ??????? ???????? ????????????? ?????.
??? ?????????? ?.2. ??????, ??? ???? ?? ??? ? ????. 1.3 ????? ???? ?????? ???????????? (?? ??????????). ????? ????????? ???????? ?? ? ???? ???????????? ?????, ??????? ???? ?? ??????????? ??????? ? ?????????.
3. ?? ???????????, ?????????? ? ?.2, ?????????? ????????? ?????????.
4. ????????? ??????????????? ?????????, ??????????? ? ????????? ?????????? ?????, ????????? ????? a, ????????? ?? ?????, ??????? ?????? ????.
???????16???????1.30L_1, ???6L_2, ???-L_3, ???0C_1, ???0,8C_2, ???-C_3, ???0,4R_1, ??-R_2, ??100R_3, ??-f, ??4000?e'?_1, ?169*sin??(?t+180)??e''?_1, ?-?e'?_2, ?0?e''?_2, ?169*cos???t=169 sin??(?? ? t+?90?^�)?e'?_3, ?169*sin??t?e''?_3, ?0
??????? ??????????? ???????? ???????? ?? ??????? ???????.
1)??????? ????????? ? ???????????????? ????? ??? ???? b ? ???????? kabdk ? bmdpb:
{�(i_1+i_2+i_3=0@-1/C_1 ?�?i_1 dt?+L_1 (di_1)/dt-R_2 i_2=e_1-e_2@1/C_3 ?�?i_3 dt?-R_2 i_2=e_3-e_2 )�
??????? ????????? ? ????????????? ?????
{�(I ?_1+I ?_2+I ?_3=0@(Z ?_(L_1 )-Z ?_(C_1 ) )�I ?_1-R_2�I ?_2=E ?_1-E ?_2@-Z ?_(C_3 )�I ?_3-R_2�I ?_2=E ?_3-E ?_2 )�
??????????? ??????? ?????
?=2pf=2*3,14*2000=25120?^(-1)
?????????? ??????????? ?????????????:
Z ?_(L_1 )=j?L_1=j*25120*6*?10?^(-3)=j150,72 ??
Z ?_(C_1 )=-j/(??_1 )=-j/(25120*0,8*?10?^(-6) )=-j50,00 ??
Z ?_(C_3 )=-j/(??_3 )=-j/(25120*0,4*?10?^(-6) )=j100,48 ??
????????? ??????????? ???????? ???:
E ?_1=169/v2 e^(j180�)=120e^(j180�) ?
E ?_2=169/v2 e^(j90�)=120e^(j90�) ?
E ?_3=169/v2=120 ?
?????????????? 90� ? ?????????? ???? ??????? ????????, ??? ??? ??????? ????????? ????? ?? 90�. 2) ??? ??? ???? ???????? ????? 2 ????, ?????? ???? ??????? ???? ?????
U ?=(E ?_1/j(Z_(L_1 )-Z_(C_1 ) ) +E ?_2/R_2 -E ?_3/(jZ_(C_3 ) ))/(1/j(Z_(L_1 )-Z_(C_1 ) ) +1/R_2 -1/(jZ_(C_3 ) ))=((119,50e^(j180�))/(100e^(j90�) )+(119,50e^(j90�))/100+119,50/(100e^(-j90�) ))/(1/j100+1/100-1/j100)=
=360e^(j90�) B I ?_1=((-U) ?+E ?_1)/j(Z_(L_1 )-Z_(C_1 ) ) =(-360e^(j90�)+120e^(j180�))/100=-3,6+1,2e^(j90�)=-3,6+j1,2=3,795e^(j162�) A
I ?_2=((-U) ?+E ?_2)/R_2 =(-360e^(j90�)+120e^(j90�))/100=2,4e^(-j90�) A
I ?_3=(-U++E ?_3 ) ?/(-jZ_(C_3 ) )=(-360e^(j90�)+120)/(100e^(-j90�) )=-3,6+1,2e^(j90�)=-3,6+j1,2=3,795e^(j162�) A ???????????? P_1-???????????? ???????? ? ?????????? ?? P?_2-???????? ?????????? ??? ???????? ??????? ?????????.
P_1=?_(i=1)^3�?Re(E ?_i ?*I ?_i)=
=E_1 I_1 cos??(?180?^�-?162?^0 )+? E_2 I_2 cos??(?90?^�+?90?^0 )+? E_3 I_3 cos??(0^�+?18?^0 )= ? =120(3,795*(+0,951)-2,4+3,795*(+0,951))=578 ?? P_2=|I ?_2 |^2�R_2=?2,4?^2*100=576 ?? P_1�P_2
U ?_ak=I ?_1�Z ?_(L_1 )=569,25e^(?j252?^� ) B U ?_kd=-I ?_3�Z ?_(C_1 )=189,75e^(?j72?^� ) B
U ?_bp=I ?_2*R_2=240e^(?-j90?^� ) B
U ?_md=-Z ?_(C_3 )*I ?_3=379,5e^(?-j72?^� ) B
j
E ?_3
E ?_1a+1
p
E ?_2
k
??????????????? ????????? ?????????? (??????? 1?? = 10?)
? ????????? ????????? ????? (??????? 1?? = 1?)
????????? ????????? ????????? ?? ???????:
P=|I ?_1 |^2�R_2,
P=?3,795?^2�100=1440,20??
?????? 2. ?????? ? ?????????? ?????????????? ? ?????????? ???????? ???????? ?????? ????????????? ?? ???????? ??????? f_0(????? ????? ?_0) ??? ?????? ????????????? ??????????? ???????????? ?_?, ??????? ????? ?????????? ??????????????? ? ??????????? ? ???????? ????????????? ?. ?? ??????????? ? ??????? ?????? ????????? ???????? ?_? ? ??????? ?????? ????????? ???????????? ?_?.
? ???????U_1, ?f_0, ????_0, ??, ?f, ???L, ????C, ??16--1000--200700
???????
????????? ??????????? ?????????.
????? ??????? ? ???????
f=1/T, (1)
??????????? ??????? ?????????
f=1/(2p*vLC), (2)
f=?_0/?_0 (3)
??? ?_0=3�?10?^8 ?/? - ???????? ????? ? ???????.
?? (2), (3) 1/(2p*vLC)=?_0/?_0 (4)
?? (4) ??????? ?_0:
?_0=2p?_0 vLC (5) ?? (5) ??????? C:
?=(?_0^2)/(4p*?_0^2 L)=?10?^6/(4*?3,14?^2*9*?10?^16*200*?10?^(-6) )=1,4*?10?^(-9) ?
???????????? ??????????
C_1=C+C_x=1,4 C_x=1,4-C=1,4-0,7=0,7??
2.???????????????? ?????????? ?_1=(C*C_x)/(C+C_x )=1,4??
1,4C+1,4C_x=C*C_x
C_x (C-1,4)=1,4C
C_x=(1,4*0,7)/(0,7-1,4)=-1,4?? ?????: ????????????? ??????? ???? ?? ?????, ?????? ?????????? ??? ???????????? C?_x ????? ?????????? ?????? ???????????.
?????? 3. ?? ??????? 2.22 ???? ????? ?? ????, ??????? ???????????? ???? ?? ????????????? ??????????.
U_1 (t) ????????? ? ??? ????? ?? 5 ????????? ????????????. ????????? ??????????? ? ??????? ?????????? ?????? U_1 (t).
??? ????? ?????????? ??? ? ??? ? ????????? ??.
?????????? ??? ????? ??? U_1 (t) ? ?????????.
????????? ?????? U?_??? (t) ??????? 16L,???5,4C,???3T,??1,34 U_m,?12,78R_h,??55,2 ???.2.22
???.2.28
???????
?????????? ??????????? ???????
?=2pf=2p/(1,34*?10?^(-3) )=1,49p*?10?^3
0<t<t f(t)=U_m
T/4<t<3T/4 f(t)=0 a_0/2=1/T ?_0^(T/4)�?f(t)? dt=1/T ?_0^(T/4)�?U_m dt+1/T? ?_(3T/4)^T�?U_m=U_m/T? (T/4+T-3T/4)=U_m/2=6,39
a_k=1/T ?_0^T�?f(t)*cos??k ?tdt=? ? U_m/T(?_0^(T/4)�cos??k?tdt+?_(3T/4)^T�cos??k?tdt)=? ? =U_m/Tk?(sin?k?t+sin??k?t)=U_m/2pk? (sin??kp/2?+sin??2pk-sin?sin??3kp/2? ? )=
U_m/2pk(sin??kp/2?-sin??(p+p/2?)k)=U_m/2pk(sin??kp/2?-sin??pk*cos??kp/2? ?-sin??kp/2? cos??kp)=?
=U_m/2pk sin??kp/2? (1-cos??kp)=?(-1)?^m*U_m/pk?
b_k=1/T ?_o^T�?f(t) sin?k?t ? dt=1/T ?_0^(T/4)�?U_m sin??k?tdt+? ? 1/T ?_(3T/4)^T�U_m sin??k?tdt=?
U_m/T(-1/k? cos??k?t-? 1/k? cos??k?t)=-U_m/k?t? (cos??k?t/4?-1+cos??k?t-cos??3k?t/4? ? )
=U_m/(k 2pT/T) (cos??k p/2?-1+cos??2pk-cos??3pk/2? ? )= =-U_m/2pk (cos??k p/2?-1+1-cos??(p?+p/2 k)==-U_m/2pk(cos??k p/2?-cos??pk cos??pk/2?+sin??pk sin??pk/2? ?)=?-U_m/2pk(cos??pk/2? (1-cos??pk))=0 ?
C_k=v(a_k^2 )+b_k^2=a_n=(2U_m)/pk=(2U_m)/(2m+1)p=(2*4,07)/(2m+1)=8,14/(2m+1) f_k=arctg b_k/a_k =p/2
012345?_k=k?_101,49p*?10?^32,98*?10?^34,47*?10?^35,96*?10?^37,45*?10?^3
U_1 (t)=a_0/2+2?_(k=0)^8�?a_k sin??k?t+b_k ? ? cos??k?t= ? =6,39+8,14 cos???t-2,71 cos??3?t+1,63 cos??5?t-1,16 cos??7?t+0,9 cos??9?t B ? ? ? ? ?
Z=-jx_c+(jx_(l (R_h-jx_c)))/(R_h+j(x_L-x_(c)) )
i_1=U_1/Z i_3=(jx_L)/(R_h+j(x_L-x_c ) ) i_1=(jx_L)/(Z?(R?_h+j(x_L-x_c ))) U_1 U_2= i_3 R_(h=) (jx_L)/(Z?(R?_h+j(x_L-x_c ))) U_1 U_2/U_1 =H(j?)=(jx_L R_h)/(Z?(R?_h+j(x_L-x_c )))=
=(jx_L R_h)/(-jx_c (R_h+j(x_L-x_c )+jx_L (R_h-jx_c))=
=(jx_L R_h)/(-jx_c R_h+x_L x_c-x_c^2+jx_L R_h+x_L x_c )=
=(jx_L R_h)/(2x_L x_c-x_c^2-jR_h (x_L-x_c ) )=
=(R_h^2 x_L (x_L-x_c )+jx_L R_h (2x_L x_c-x_c^2))/(?(2x_L x_c-x_c^2)?^2+?R_h^2 (x_L-x_c )?^2 )=A(?)e^jf?
A(?)=H(j?)=(x_L R_h)/v((2x_L x_c-x_c^2 )^2+?R_h^2 (x_L-x_c )?^2 )=
=(?LR_h)/v((2 L/C-1/(?^2 C^2 ))^2+?R_h^2 (?L-1/?C)?^2 )=
=0,298?/v(?(3600-(1,11*?10?^11)/?^2 )?^2+3047,04?(5,4*?10?^(-3) ?-(3,3*?10?^5)/?)?^2 )
f(?)=arctgH(j?)=arctg (x_L R_h (2x_L x_c-x_c^2 ))/(R_h^2 (x_L-x_c ) )=
=arctg (2x_L x_c-x_c^2)/(R_h (x_L-x_c ) )=arctg (2 L/C-1/(?^2 C^2 ))/(R_h (?L-1/?C) )=
= arctg (3600--(1,11*?10?^11)/?^2 )/(3047,04(5,4*?10?^(-3) ?-(3,3*?10?^5)/?))
???
???
???????????? ??? ????? ??? U_2 (t)
U_2=H(j?) U_1=(U_1 H(j?)+U_3 H(j3?)+) ?U_5 H(j5?)+U_7 (j7?)+U_9 (j9?)
?=2p/T=4,67*?10?^3 (U_2=) ?U_0 H(0)=0
(U^' ) ?_2=3,883e^(j?91?^� ) B
(U^' ) ?_3=U_3 H(j3?)=-2,706e^(j?91?^� ) B
(U^' ) ?_5=U_5 H(j5?)=1,608e^(j?90?^� ) B
(U^' ) ?_7=U_7 (j7?)=-1,15e^(j?90?^� ) B
(U^' ) ?_9=U_9 (j9?)=0,895e^(j?90?^� ) B U_2 (t)=8,14 cos??(?t+1^� ?)-2,706 cos??(3?t+? 1^�)+1,608 cos??5?t-1,15 cos??7?t+? ? 0,895 cos??9?t B?
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