ΠΠ°Π΄Π°Π½ΠΈΠ΅ β11. Π‘ΠΎΠ±ΡΠ°ΡΡ ΡΡ Π΅ΠΌΡ Π² ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΠΎΠΉ ΡΡΠ΅Π΄Π΅ Multisim
![Π Π΅ΡΠ΅ΡΠ°Ρ: ΠΠ°Π΄Π°Π½ΠΈΠ΅ β11. Π‘ΠΎΠ±ΡΠ°ΡΡ ΡΡ
Π΅ΠΌΡ Π² ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΠΎΠΉ ΡΡΠ΅Π΄Π΅ Multisim](https://gugn.ru/work/8714061/cover.png)
ΠΠ΅ΡΠ΅Π²ΠΎΠ΄ Π² ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»ΡΠ½ΡΡ ΡΠΎΡΠΌΡ (m-ΠΌΠΎΠ΄ΡΠ»Ρ, a-Π°ΡΠ³ΡΠΌΠ΅Π½Ρ). Z1=20+j*40; z2=30+j*40; z3=40+j*60; z4=60+j*80;z5=60-j*80; z6=50-j*50; z7=60-j*80; z8=40-j*30; Z1=20+j*40; z2=30+j*40; z3=40+j*60; z4=60+j*80;z5=60-j*80; z6=50-j*50; z7=60-j*80; z8=40-j*30; Z1=20+i*40; z2=30+i*40; z3=40+i*60; z4=60+i*80;z5=60-i*80; z6=50-i*50; z7=60-i*80; z8=40-i*30; Π Π°ΡΡΠ΅Ρ ΡΠΎΠΊΠΎΠ² ΠΈ Π½Π°ΠΏΡΡΠΆΠ΅Π½ΠΈΠΉ ΠΏΠΎ Π·Π°ΠΊΠΎΠ½Ρ ΠΠΈΡΡ Π³ΠΎΡΠ°… Π§ΠΈΡΠ°ΡΡ Π΅ΡΡ >
ΠΠ°Π΄Π°Π½ΠΈΠ΅ β11. Π‘ΠΎΠ±ΡΠ°ΡΡ ΡΡ Π΅ΠΌΡ Π² ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΠΎΠΉ ΡΡΠ΅Π΄Π΅ Multisim (ΡΠ΅ΡΠ΅ΡΠ°Ρ, ΠΊΡΡΡΠΎΠ²Π°Ρ, Π΄ΠΈΠΏΠ»ΠΎΠΌ, ΠΊΠΎΠ½ΡΡΠΎΠ»ΡΠ½Π°Ρ)
Π‘ΠΎΠ±ΡΠ°ΡΡ ΡΡ Π΅ΠΌΡ Π² ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΠΎΠΉ ΡΡΠ΅Π΄Π΅ Multisim, ΠΈΠ·ΠΌΠ΅ΡΠΈΡΡ ΡΠΎΠΊΠΈ ΠΈ ΡΠ·Π»ΠΎΠ²ΡΠ΅ Π½Π°ΠΏΡΡΠΆΠ΅Π½ΠΈΡ.
ΠΠ°Π΄Π°Π½ΠΈΠ΅ № 12. ΠΡΠΈΠ»ΠΎΠΆΠΈΡΡ Π² ΠΎΡΡΠ΅Ρ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΡ ΡΠ°ΡΡΠ΅ΡΠ° ΠΠΠ’ ΠΈ ΠΠ£Π Π² ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΠΎΠΌ ΠΏΡΠΈΠ»ΠΎΠΆΠ΅Π½ΠΈΠΈ Matlab
ΠΡΠΈΠ»ΠΎΠΆΠΈΡΡ Π² ΠΎΡΡΠ΅Ρ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΡ ΡΠ°ΡΡΠ΅ΡΠ° ΠΠΠ’ ΠΈ ΠΠ£Π Π² ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΠΎΠΌ ΠΏΡΠΈΠ»ΠΎΠΆΠ΅Π½ΠΈΠΈ Matlab.
1) ΠΠΠ’. Π‘ΠΎΡΡΠ°Π²Π»Π΅Π½ΠΈΠ΅ ΠΌΠ°ΡΡΠΈΡ ΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ ΠΌΠ°ΡΡΠΈΡΠ½ΠΎΠ³ΠΎ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΠΏΠΎ ΠΏΡΠ°Π²ΠΈΠ»Ρ ΠΡΠ°ΠΌΠ΅ΡΠ°:
e1=0;e3=0;e2=10+j*10; e4=20+j*20; J9=20e-3;
z1=20+40*j;z2=30+40*j;
z3=40+60*j;z4=60+80*j;z5=60−80*j;z6=50−50*j;z7=60−80*j;z8=40−30*j;
Z = [z1+z5+z6 -z6 0 -z5;-z6 z2+z6+z7 -z7 0;0 -z7 z3+z7+z8 -z8;-z5 0 -z8 z4+z5+z8] ;
E=[e1;e2+J9*z7;e3-J9*(z7+z8);e4+J9*z8] ;
I=Z^(-1) * E.
i1=I (1).
i2=I (2).
i3=I (3).
i4=I (4).
i5=-I (1)+I (4).
i6=I (1)-I (2).
i7=-I (2)+I (3)+J9.
i8=I (3)-I (4)+J9.
%ΠΠ΅ΡΠ΅Π²ΠΎΠ΄ Π² ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»ΡΠ½ΡΡ ΡΠΎΡΠΌΡ (n-ΠΌΠΎΠ΄ΡΠ»Ρ, a-Π°ΡΠ³ΡΠΌΠ΅Π½Ρ).
n1=abs (i1), a1=angle (i1)*180/pi.
n2=abs (i2), a2=angle (i2)*180/pi.
n3=abs (i3), a3=angle (i3)*180/pi.
n4=abs (i4), a4=angle (i4)*180/pi.
n5=abs (i5), a5=angle (i5)*180/pi.
n6=abs (i6), a6=angle (i6)*180/pi.
n7=abs (i7), a7=angle (i7)*180/pi.
n8=abs (i8), a8=angle (i8)*180/pi.
2) ΠΠ£Π. Π‘ΠΎΡΡΠ°Π²Π»Π΅Π½ΠΈΠ΅ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΠΠ£Π. Π Π°ΡΡΠ΅Ρ Π½Π°ΠΏΡΡΠΆΠ΅Π½ΠΈΠΉ ΠΈ ΡΠΎΠΊΠΎΠ² Π²ΠΎ Π²ΡΠ΅Ρ Π²Π΅ΡΠ²ΡΡ :
e2=10+j*10; e4=20+j*20; J9=20e-3;
z1=20+j*40; z2=30+j*40; z3=40+j*60; z4=60+j*80;z5=60-j*80; z6=50-j*50; z7=60-j*80; z8=40-j*30;
y1=1/z1; y2=1/z2; y3=1/z3; y4=1/z4; y5=1/z5; y6=1/z6; y7=1/z7; y8=1/z8;
y11=y1+y4+y5; y12=-y1; y13=0; y14=-y4;
y21=-y1; y22=y1+y2+y6; y23=-y2; y24=0;
y31=0; y32=-y2; y33=y2+y3+y7; y34=-y3;
y41=-y4;y42=0; y43=-y3; y44=y3+y4+y8;
Y=[y11 y12 y13 y14; y21 y22 y23 y24; y31 y32 y33 y34; y41 y42 y43 y44];
J=[e4*y4; -e2*y2; e2*y2-J9; -e4*y4+J9];
P=YJ;
p1=P (1).
p2=P (2).
p3=P (3).
p4=P (4).
p5=0.
U21=p2-p1.
U23=p2-p3.
U43=p4-p3.
U41=p4-p1.
U51=p5-p1.
U52=p5-p2.
U53=p5-p3.
U54=p5-p4.
i1=(P (1)-P (2))/z1.
i2=(P (2)-P (3)+e2)/z2.
i3=(P (3)-P (4))/z3.
i4=(P (4)-P (1)+e4)/z4.
i5=P (1)/z5.
i6=P (2)/z6.
i7=-P (3)/z7 i8=P (4)/z8.
%ΠΠ΅ΡΠ΅Π²ΠΎΠ΄ Π² ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»ΡΠ½ΡΡ ΡΠΎΡΠΌΡ (m-ΠΌΠΎΠ΄ΡΠ»Ρ, a-Π°ΡΠ³ΡΠΌΠ΅Π½Ρ).
m1=abs (p1), a1=angle (p1)*180/pi.
m2=abs (p2), a2=angle (p2)*180/pi.
m3=abs (p3), a3=angle (p3)*180/pi.
m4=abs (p4), a4=angle (p4)*180/pi.
m21=abs (U21), a21=angle (U21)*180/pi.
m23=abs (U23), a23=angle (U23)*180/pi.
m43=abs (U43), a43=angle (U43)*180/pi.
m41=abs (U41), a41=angle (U41)*180/pi.
m51=abs (U51), a51=angle (U51)*180/pi.
m52=abs (U52), a52=angle (U52)*180/pi.
m53=abs (U53), a53=angle (U53)*180/pi.
m54=abs (U54), a54=angle (U54)*180/pi.
3) ΠΠΠ’. Π‘ΠΎΡΡΠ°Π²Π»Π΅Π½ΠΈΠ΅ ΠΌΠ°ΡΡΠΈΡ ΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ ΠΌΠ°ΡΡΠΈΡΠ½ΠΎΠ³ΠΎ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΡΠΎΠΏΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΠΌ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ. ΠΠ΅ΡΠ΅Π²ΠΎΠ΄ Π·Π½Π°ΡΠ΅Π½ΠΈΠΉ Π² ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»ΡΠ½ΡΡ ΡΠΎΡΠΌΡ:
e2=10+i*10; e4=20+i*20; J9=20e-3;
z1=20+i*40; z2=30+i*40; z3=40+i*60; z4=60+i*80;z5=60-i*80; z6=50-i*50; z7=60-i*80; z8=40-i*30;
B=[1 0 0 0 -1 1 0 0; 0 -1 0 0 0 1 1 0; 0 0 1 0 0 0 1 1; 0 0 0 1 1 0 0 -1];
Z=[z1 0 0 0 0 0 0 0;
0 z2 0 0 0 0 0 0;
0 0 z3 0 0 0 0 0;
0 0 0 z4 0 0 0 0;
0 0 0 0 z5 0 0 0;
0 0 0 0 0 z6 0 0;
0 0 0 0 0 0 z7 0;
0 0 0 0 0 0 0 z8];
E=[0; e2; 0; e4; 0; 0; 0; 0];
J=[0; 0;-J9; 0; 0; 0; 0; 0];
I=(B')*(((B*Z*(B'))^(-1))*B*(E-Z*J));
i1=I (1).
i2=I (2).
i3=I (3)-J9.
i4=I (4).
i5=I (5).
i6=I (6).
i7=I (7).
i8=I (8).
%ΠΠ΅ΡΠ΅Π²ΠΎΠ΄ Π² ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»ΡΠ½ΡΡ ΡΠΎΡΠΌΡ (m-ΠΌΠΎΠ΄ΡΠ»Ρ, a-Π°ΡΠ³ΡΠΌΠ΅Π½Ρ).
m1=abs (i1), a1=angle (i1)*180/pi.
m2=abs (i2), a2=angle (i2)*180/pi.
m3=abs (i3), a3=angle (i3)*180/pi.
m4=abs (i4), a4=angle (i4)*180/pi.
m5=abs (i5), a5=angle (i5)*180/pi.
m6=abs (i6), a6=angle (i6)*180/pi.
m7=abs (i7), a7=angle (i7)*180/pi.
m8=abs (i8), a8=angle (i8)*180/pi.
4) ΠΠ£Π. Π‘ΠΎΡΡΠ°Π²Π»Π΅Π½ΠΈΠ΅ ΠΌΠ°ΡΡΠΈΡ ΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΠ΅ ΠΌΠ°ΡΡΠΈΡΠ½ΠΎΠ³ΠΎ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΡΠΎΠΏΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΠΌ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠΌ. ΠΠ΅ΡΠ΅Π²ΠΎΠ΄ Π·Π½Π°ΡΠ΅Π½ΠΈΠΉ Π² ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»ΡΠ½ΡΡ ΡΠΎΡΠΌΡ:
e2=10+j*10; e4=20+j*20; J9=20e-3;
z1=20+j*40; z2=30+j*40; z3=40+j*60; z4=60+j*80;z5=60-j*80; z6=50-j*50; z7=60-j*80; z8=40-j*30;
y1=1/z1; y2=1/z2; y3=1/z3; y4=1/z4; y5=1/z5; y6=1/z6; y7=1/z7; y8=1/z8;
A=[1 0 0 -1 1 0 0 0; -1 1 0 0 0 1 0 0; 0 -1 1 0 0 0 -1 0; 0 0 -1 1 0 0 0 1];
Y=[y1 0 0 0 0 0 0 0;
0 y2 0 0 0 0 0 0;
0 0 y3 0 0 0 0 0;
0 0 0 y4 0 0 0 0;
0 0 0 0 y5 0 0 0;
0 0 0 0 0 y6 0 0;
0 0 0 0 0 0 y7 0;
0 0 0 0 0 0 0 y8];
E=[0; e2; 0; e4; 0; 0; 0; 0];
J=[0; 0; J9; 0; 0; 0; 0; 0];
P=((A*Y*A')^(-1))*A*(J-Y*E).
p5=0.
U21=p2-p1.
U23=p2-p3.
U43=p4-p3.
U41=p4-p1.
U51=p5-p1.
U52=p5-p2.
U53=p5-p3.
U54=p5-p4.
i1=(P (1)-P (2))/z1.
i2=(P (2)-P (3)+e2)/z2.
i3=(P (3)-P (4))/z3.
i4=(P (4)-P (1)+e4)/z4.
i5=P (1)/z5 i6=P (2)/z6.
i7=-P (3)/z7 i8=P (4)/z8.
%ΠΠ΅ΡΠ΅Π²ΠΎΠ΄ Π² ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»ΡΠ½ΡΡ ΡΠΎΡΠΌΡ (m-ΠΌΠΎΠ΄ΡΠ»Ρ, a-Π°ΡΠ³ΡΠΌΠ΅Π½Ρ).
m1=abs (p1), a1=angle (p1)*180/pi.
m2=abs (p2), a2=angle (p2)*180/pi.
m3=abs (p3), a3=angle (p3)*180/pi.
m4=abs (p4), a4=angle (p4)*180/pi.
m21=abs (U21), a21=angle (U21)*180/pi.
m23=abs (U23), a23=angle (U23)*180/pi.
m43=abs (U43), a43=angle (U43)*180/pi.
m41=abs (U41), a41=angle (U41)*180/pi.
m51=abs (U51), a51=angle (U51)*180/pi.
m52=abs (U52), a52=angle (U52)*180/pi.
m53=abs (U53), a53=angle (U53)*180/pi.
m54=abs (U54), a54=angle (U54)*180/pi.
5) Π£ΡΠ°Π²Π½Π΅Π½ΠΈΠ΅ Π±Π°Π»Π°Π½ΡΠ° ΠΌΠΎΡΠ½ΠΎΡΡΠ΅ΠΉ:
e2=10+j*10; e4=20+j*20; J9=20e-3;
z1=20+j*40; z2=30+j*40; z3=40+j*60; z4=60+j*80; z5=60-j*80; z6=50-j*50; z7=60-j*80; z8=40-j*30;
i1 = 0.1729 — 0.0528i;
i2 = 0.1455 — 0.0238i;
i3 = 0.1144 — 0.0730i;
i4 = 0.1816 + 0.0093i;
i5 = 0.0087 + 0.0621i;
i6 = 0.0274 — 0.0291i;
i7 = -0.0111 — 0.0492i;
i8 = -0.0472 — 0.0823i;
U9=-8.9583 — i*3.9459;
S1=z1*i12+z2*i22+z3*i32+z4*i42+z5*i52+z6*i62+z7*i72+z8*i82.
S2=e4*i4+e2*i2+J9*U9.
6) Π Π°ΡΡΠ΅Ρ ΡΠΎΠΊΠΎΠ² ΠΈ Π½Π°ΠΏΡΡΠΆΠ΅Π½ΠΈΠΉ ΠΏΠΎ Π·Π°ΠΊΠΎΠ½Ρ ΠΠΈΡΡ Π³ΠΎΡΠ°:
e2=10+j*10; e4=20+j*20; J9=20e-3;
z1=20+j*40; z2=30+j*40; z3=40+j*60; z4=60+j*80; z5=60-j*80; z6=50-j*50; z7=60-j*80; z8=40-j*30;
K=[-1 0 0 1 -1 0 0 0;
1 -1 0 0 0 -1 0 0;
0 1 -1 0 0 0 1 0;
0 0 1 -1 0 0 0 -1;
z1 0 0 0 -z5 z6 0 0;
0 -z2 0 0 0 z6 z7 0;
0 0 z3 0 0 0 z7 z8;
0 0 0 z4 z5 0 0 -z8];
u=det (K);
E=[0;0;J9;-J9;0;e2;0;e4];
A1=K; A1(1:8,1)=E;
i1=det (A1)/u.
A2=K; A2(1:8,2)=E;
i2=det (A2)/u A3=K; A3(1:8,3)=E;
i3=det (A3)/u A4=K; A4(1:8,4)=E;
i4=det (A4)/u.
A5=K; A5(1:8,5)=E;
i5=det (A5)/u.
A6=K; A6(1:8,6)=E;
i6=det (A6)/u.
A7=K; A7(1:8,7)=E;
i7=det (A7)/u.
A8=K; A8(1:8,8)=E;
i8=det (A8)/u.
7) ΠΠΎΡΡΡΠΎΠ΅Π½ΠΈΠ΅ ΡΠΎΠΏΠΎΠ³ΡΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ Π΄ΠΈΠ°Π³ΡΠ°ΠΌΠΌ:
%ΡΠΎΠΊΠΈ.
axis equal.
line ([0 0.1729],[0 -0.0528],'Color','red','LineWidth', 3).
grid on.
hold on.
axis equal.
line ([0 0.1455],[0 -0.0238],'Color','green','LineWidth', 3)%2.
line ([0 0.1144],[0 -0.0730],'Color','blue','LineWidth', 3)%3.
line ([0 0.1816],[0 0.0093],'Color','yellow','LineWidth', 3)%4.
line ([0 0.0087],[0 0.0621],'Color','magenta','LineWidth', 3)%5.
line ([0 0.0274],[0 -0.0291],'Color','black','LineWidth', 3).
line ([0 -0.0111],[0 -0.0492],'Color','red','LineWidth', 3).
line ([0 -0.0472],[0 -0.0823],'Color','green','LineWidth', 3).
axis equal.
line ([-0.05 0.18],[0 0],'Color','black','LineWidth', 2)%2.
line ([0 0],[0.07 -0.1],'Color','black','LineWidth', 2)%2.
%ΠΏΠΎΡΠ΅Π½ΡΠΈΠ°Π»Ρ ΠΈ Π½Π°ΠΏΡΡΠΆΠ΅Π½ΠΈΡ.
axis equal.
line ([0 5.4916],[0 3.0359]).
axis equal.
grid on.
hold on.
line ([ -0.0812 5.4916],[-2.8250 3.0359],'Color','green','LineWidth', 3) %21.
line ([-0.0812 4.6022],[-2.8250 3.0359],'Color','red','LineWidth', 3) %23.
line ([-4.3561 4.6022],[-1.8775 2.0683],'Color','black','LineWidth', 6) %43.
line ([-4.3561 5.4916],[-1.8775 3.0359],'Color','blue','LineWidth', 3) %41.
line ([0 5.4916],[0 3.0359],'Color','magenta','LineWidth', 3) %51.
line ([0 -0.0812],[0 -2.8250],'Color','yellow','LineWidth', 3) %52.
line ([0 4.6022],[0 2.0683],'Color','red','LineWidth', 2) %53.
line ([0 -4.3561],[0 -1.8775],'Color','yellow','LineWidth', 3) %54.
axis equal.
line ([-4 5],[0 0],'Color','black','LineWidth', 2)%2.
line ([0 0],[-4 4],'Color','black','LineWidth', 2)%2.