Chapter 10 Sinusoidal Steady-State Analysis Part 2166.104.231.29/webpage_limdj/circuit2/Chapter10_2.pdf · Chapter 10 Sinusoidal Steady-State Analysis Part 2. Node Equations. 3 3

Introduction to Electric Circuits

Chapter 10 Sinusoidal Steady-State AnalysisPart 2

Node Equations

33

3

1 1250 36 10 9, 16250 0.25 10

250 80 10 20

j L j j jj C j

j L j j

1 2 3

1 2 3

20 0 4 3, ,8 9 16 20 20

1.2 45

20 0 31.2 458 9 16 20

20 0 1 1 31.2 458 9 8 9 16 20

12.43 81.212.43cos(250 81.2 )

a a a a a

a a a

a

a

a

V V V V VI I Ij j j j

I I I

V V Vj j j

Vj j j j

Vv t

MATLAB>> Vs=20;>> Is=1.2*exp(j*45*pi/180);>> Va=(Vs/(8+9*j)+Is)/(1/(8+9*j)-1/(16*j)-3/(20*j))

Va =

1.8929 -12.2816i

>> abs(Va)

ans =

12.4267

>> angle(Va)*180/pi

ans =

-81.2381

Mesh Equations

1 1 1 3 1 3

2 1 2 3

3 1 3 3 2

100 40 25( ) 200( ) 0200( ) 80( ) 45 0

25( ) 160 80( ) 0

I j I j I I I II I j I I

j I I j I j I I

1

2

3

0.374 150.575 250.171 28

III

MATLAB>> A=[300+j*65 -200 -j*25;-200 200-j*80 j*80;-j*25 j*80 -j*215]

A =

1.0e+02 *

3.0000 + 0.6500i -2.0000 + 0.0000i 0.0000 - 0.2500i-2.0000 + 0.0000i 2.0000 - 0.8000i 0.0000 + 0.8000i0.0000 - 0.2500i 0.0000 + 0.8000i 0.0000 - 2.1500i

>> format shortg>> A

A =

300 + 65i -200 + 0i 0 - 25i-200 + 0i 200 - 80i 0 + 80i

0 - 25i 0 + 80i 0 - 215i

MATLAB>> I=inv(A)*[0;45;0]I =

0.36131 + 0.097915i0.52013 + 0.24536i0.15152 + 0.07991i

>> abs(I)ans =

0.374340.57510.1713

>> angle(I)*180/pians =

15.16325.25427.806

12 1

1

1 2 1 11 2 1 1 2

1 2 1 2

1 1

1 2 1 2

, 10

10 10 0

110 0

S

S

V VI I V VR

V V V V II Z Z V Z Z IZ Z Z Z

R V VZ Z Z Z I

MATLAB>> Z1=5-j*5Z1 =

5.0000 - 5.0000i>> Z2=5+j*5Z2 =

5.0000 + 5.0000i>> A=[1 10;Z1+Z2 Z1*(10-Z2)]A =

1.0000 + 0.0000i 10.0000 + 0.0000i10.0000 + 0.0000i 0.0000 -50.0000i

>> x=inv(A)*[10;0]x =

2.0000 + 4.0000i0.8000 - 0.4000i

>> abs(x)ans =

4.47210.8944

>> angle(x)*180/pians =

63.4349-26.5651

Thevenin and Norton Circuits

Sources Transformations

Superposition

Phasor Diagrams

Op Amps in AC Circuits

Inverting amplifier

Op Amps in AC Circuits

Noninverting amplifier