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Figure 1. Number of equations needed to solve using Node-Voltage Method Düğüm gerilim yontemiyle cozmek icin gereken denklem sayısı. Node: 2. Number of equations needed to solve using Mesh-Current Method Göz akımları yontemiyle cozmek icin gereken denklem sayısı. Mesh: 3. Figure 1: Node. - PowerPoint PPT Presentation
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1
Figure 1
Node: 2
Mesh: 3
Number of equations needed to solve using Node-Voltage Method
Düğüm gerilim yontemiyle cozmek icin gereken denklem sayısı
Number of equations needed to solve using Mesh-Current Method
Göz akımları yontemiyle cozmek icin gereken denklem sayısı
2
Figure 1: Node
Sadece kırmızı renkli düğümler icin KCL denklemi yazmak gerekiyor.
Yeşil renkli düğümlerdeki gerilimler, gerilim kaynaklarından ötürü bilinen gerilimler.
KCL equations are required only for red colored nodes.
The voltages at green colored nodes are known due to the voltage sources
3
Figure 1: Mesh
Sadece kırmızı renkli gözler icin KVL denklemi yazmak gerekiyor.
Yeşil renkli gözdeki göz akımı, akım kaynağı kullanılarak hesaplanabilir
KVL equations are required only for red colored meshes.
The mesh current at green colored mesh is known due to the current sources
4
Figure 2
Node: 2
Mesh: 1
5
Figure 2: Node
6
Figure 2: Mesh
7
Figure 3
Node: 3
Mesh: 3
(supermesh)
8
Figure 3: Node
9
Figure 3: Mesh
10
Figure 4
Node: 2
Mesh: 3
10 V 20 V
1 mA 5 mA
R1
R2
R3
R4
R5
R6
10 V 20 V
1 mA 5 mA
R1
R2
R3
R4
R5
R6
11
Figure 4: Node
10 V 20 V
1 mA 5 mA
R1
R2
R3
R4
R5
R6
10 V 20 V
1 mA 5 mA
R1
R2
R3
R4
R5
R6
12
Figure 4: Mesh
10 V 20 V
1 mA 5 mA
R1
R2
R3
R4
R5
R6
10 V 20 V
1 mA 5 mA
R1
R2
R3
R4
R5
R6
13
Figure 5
Node: 3
Mesh: 2
7 2.8
4
1
4
7 9
2
8
1.8 A
5
-1 A 3 A
8 V
3 V
7 2.8
4
1
4
7 9
2
8
1.8 A
5
-1 A 3 A
8 V
3 V
(supermesh)
14
Figure 5: Node
7 2.8
4
1
4
7 9
2
8
1.8 A
5
-1 A 3 A
8 V
3 V
7 2.8
4
1
4
7 9
2
8
1.8 A
5
-1 A 3 A
8 V
3 V
15
Figure 5: Mesh
7 2.8
4
1
4
7 9
2
8
1.8 A
5
-1 A 3 A
8 V
3 V
7 2.8
4
1
4
7 9
2
8
1.8 A
5
-1 A 3 A
8 V
3 V
16
Figure 6
Node: 2
Mesh: 2
(supermesh)
2 A
4 A120 V
80 V10
20
40
2 A
4 A
2 A
4 A120 V
80 V10
20
40
17
Figure 6: Node
2 A
4 A120 V
80 V10
20
40
2 A
4 A
2 A
4 A120 V
80 V10
20
40
18
Figure 6: Mesh
2 A
4 A120 V
80 V10
20
40
2 A
4 A
2 A
4 A120 V
80 V10
20
40
19
Figure 7
Node: 1
Mesh: 3+-
+-
+-
V1
V2
V3
R1
R2
R3
R4
+-
+-
+-
+-
+-
+-
+-+-+-
+-+-+-
+-+-+-
V1
V2
V3
R1
R2
R3
R4
20
Figure 7: Node
+-
+-
+-
V1
V2
V3
R1
R2
R3
R4
+-
+-
+-
+-
+-
+-
+-+-+-
+-+-+-
+-+-+-
V1
V2
V3
R1
R2
R3
R4
21
Figure 7: Mesh
+-
+-
+-
V1
V2
V3
R1
R2
R3
R4
+-
+-
+-
+-
+-
+-
+-+-+-
+-+-+-
+-+-+-
V1
V2
V3
R1
R2
R3
R4
22
Figure 8
Node: 2
Mesh: 2
12 V
2 10 6
4 8
5 A
12 V
2 10 6
4 8
5 A
23
Figure 8: Node
12 V
2 10 6
4 8
5 A
12 V
2 10 6
4 8
5 A
24
Figure 8: Mesh
12 V
2 10 6
4 8
5 A
12 V
2 10 6
4 8
5 A
25
Figure 9
Node: 2
Mesh: 2
8 V
-2 V
3 A
075 A
4
8
20
16 10
x
y
8 V
-2 V
3 A
075 A
4
8
20
16 10
x
y
-2 V
3 A
075 A
4
8
20
16 10
x
y
26
Figure 9: Node
8 V
-2 V
3 A
075 A
4
8
20
16 10
x
y
8 V
-2 V
3 A
075 A
4
8
20
16 10
x
y
-2 V
3 A
075 A
4
8
20
16 10
x
y
27
Figure 9: Mesh
8 V
-2 V
3 A
075 A
4
8
20
16 10
x
y
8 V
-2 V
3 A
075 A
4
8
20
16 10
x
y
-2 V
3 A
075 A
4
8
20
16 10
x
y
28
Figure 10
Node: 1
Mesh: 2
I
6
R4
20
RL 15
2.5 A
10 V
I
6
R4
20
RL 15
2.5 A
10 V
29
Figure 10: Node
I
6
R4
20
RL 15
2.5 A
10 V
I
6
R4
20
RL 15
2.5 A
10 V
30
Figure 10: Mesh
I
6
R4
20
RL 15
2.5 A
10 V
I
6
R4
20
RL 15
2.5 A
10 V
31
Figure 11
Node: 2
Mesh: 2
20 mA
25 V1 k
4 k
8 k
2 k
0.5 k
0.2 k
x
y
20 mA
25 V1 k
4 k
8 k
2 k
0.5 k
0.2 k
x
y
x
y
32
Figure 11: Node
20 mA
25 V1 k
4 k
8 k
2 k
0.5 k
0.2 k
x
y
20 mA
25 V1 k
4 k
8 k
2 k
0.5 k
0.2 k
x
y
x
y
33
Figure 11: Mesh
20 mA
25 V1 k
4 k
8 k
2 k
0.5 k
0.2 k
x
y
20 mA
25 V1 k
4 k
8 k
2 k
0.5 k
0.2 k
x
y
x
y
34
Figure 12
Node: 2
Mesh: 3
5 V 1 A15
20
20 9
5 2 V
5 V 1 A15
20
20 9
5
5 V 1 A15
20
20 9
5 2 V
(supernode)
35
Figure 12: Node
5 V 1 A15
20
20 9
5 2 V
5 V 1 A15
20
20 9
5
5 V 1 A15
20
20 9
5 2 V
36
Figure 12: Mesh
5 V 1 A15
20
20 9
5 2 V
5 V 1 A15
20
20 9
5
5 V 1 A15
20
20 9
5 2 V
37
Figure 13
Node: 1
Mesh: 1
2 A 1 A
7 V
R1R2
R3
R4
2 A 1 A
7 V
R1R2
R3
R4
38
Figure 13: Node
2 A 1 A
7 V
R1R2
R3
R4
2 A 1 A
7 V
R1R2
R3
R4
39
Figure 13: Mesh
2 A 1 A
7 V
R1R2
R3
R4
2 A 1 A
7 V
R1R2
R3
R4
40
Figure 14
Node: 3
Mesh: 5
I1
I2
I3
V1
R1R2
R4
R5
R6RL
R3
I1
I2
I3
V1
R1R2
R4
R5
R6RL
R3
(supermesh)
41
Figure 14: Node
I1
I2
I3
V1
R1R2
R4
R5
R6RL
R3
I1
I2
I3
V1
R1R2
R4
R5
R6RL
R3
42
Figure 14: mesh
I1
I2
I3
V1
R1R2
R4
R5
R6RL
R3
I1
I2
I3
V1
R1R2
R4
R5
R6RL
R3
43
Figure 15
Node: 1
Mesh: 2
I1
R4
V1
R1
R2
V2RL
R3I1
R4
V1
R1
R2
V2RL
R3
44
Figure 15: Node
I1
R4
V1
R1
R2
V2RL
R3I1
R4
V1
R1
R2
V2RL
R3
45
Figure 15: Mesh
I1
R4
V1
R1
R2
V2RL
R3I1
R4
V1
R1
R2
V2RL
R3
46
Figure 16
Node: 2
Mesh: 0!!!
-
12 mA
++
-
-3 mAV1
10 k 1 k
vx
1 mA
3.5 mA
0.03vx
-
12 mA
++
-
-3 mAV1
10 k 1 k
vx
1 mA
3.5 mA
0.03vx
47
Figure 16: Node
-
12 mA
++
-
-3 mAV1
10 k 1 k
vx
1 mA
3.5 mA
0.03vx
-
12 mA
++
-
-3 mAV1
10 k 1 k
vx
1 mA
3.5 mA
0.03vx
48
Figure 16: Mesh
-
12 mA
++
-
-3 mAV1
10 k 1 k
vx
1 mA
3.5 mA
0.03vx
-
12 mA
++
-
-3 mAV1
10 k 1 k
vx
1 mA
3.5 mA
0.03vx
49
Figure 17
Node: 2
Mesh: 4
6
0.9Ix
ix
3
6
15
9 6 A 4 A
6
0.9Ix
ix
3
6
15
9 6 A 4 A
(supermesh)
50
Figure 17: Node
6
0.9Ix
ix
3
6
15
9 6 A 4 A
6
0.9Ix
ix
3
6
15
9 6 A 4 A
51
Figure 17: Mesh
6
0.9Ix
ix
3
6
15
9 6 A 4 A
6
0.9Ix
ix
3
6
15
9 6 A 4 A
52
Figure 18
Node: 2
Mesh: 3
(supermesh)
R1R2
R3
R4V1
+-
io
3io
R1R2
R3
R4V1
+-+-+-
io
3io
53
Figure 18: Node
R1R2
R3
R4V1
+-
io
3io
R1R2
R3
R4V1
+-+-+-
io
3io
54
Figure 18: Mesh
R1R2
R3
R4V1
+-
io
3io
R1R2
R3
R4V1
+-+-+-
io
3io
55
Figure 19
Node: 2
Mesh: 3
(supermesh)
+
-+-
+-
R1
R2
R3
R4V1
V2
4vx
+
-
vx
2io
io
+
-+-
+-
+
-
+
-
+
-+-+-
+- +-
R1
R2
R3
R4V1
V2
4vx
+
-
vx
2io
io
56
Figure 19: Node
+
-+-
+-
R1
R2
R3
R4V1
V2
4vx
+
-
vx
2io
io
+
-+-
+-
+
-
+
-
+
-+-+-
+- +-
R1
R2
R3
R4V1
V2
4vx
+
-
vx
2io
io
57
Figure 19: Mesh
+
-+-
+-
R1
R2
R3
R4V1
V2
4vx
+
-
vx
2io
io
+
-+-
+-
+
-
+
-
+
-+-+-
+- +-
R1
R2
R3
R4V1
V2
4vx
+
-
vx
2io
io
58
Figure 20
Node: 2
Mesh: 4
(supermesh)
+-
+-
V1I1 R1
R2
R3 R4
R5
+ -vo
2vo
io
4io
+-
+-
+-
+-
+-+-
+- +-
V1I1 R1
R2
R3 R4
R5
+ -vo
2vo
io
4io
59
Figure 20: Node
+-
+-
V1I1 R1
R2
R3 R4
R5
+ -vo
2vo
io
4io
+-
+-
+-
+-
+-+-
+- +-
V1I1 R1
R2
R3 R4
R5
+ -vo
2vo
io
4io
60
Figure 20: Mesh
+-
+-
V1I1 R1
R2
R3 R4
R5
+ -vo
2vo
io
4io
+-
+-
+-
+-
+-+-
+- +-
V1I1 R1
R2
R3 R4
R5
+ -vo
2vo
io
4io
61
Figure 21
Node: 2
Mesh: 3
(supermesh)
+- +
-
V1
I1
R1
R2
R3ix
Vx/4
4ix+
-
vx
+- +
-
+-+- +
-
+
-
+
-
V1
I1
R1
R2
R3ix
Vx/4
4ix+
-
vx
62
Figure 21: Node
+- +
-
V1
I1
R1
R2
R3ix
Vx/4
4ix+
-
vx
+- +
-
+-+- +
-
+
-
+
-
V1
I1
R1
R2
R3ix
Vx/4
4ix+
-
vx
63
Figure 21: Mesh
+- +
-
V1
I1
R1
R2
R3ix
Vx/4
4ix+
-
vx
+- +
-
+-+- +
-
+
-
+
-
V1
I1
R1
R2
R3ix
Vx/4
4ix+
-
vx
Reference: https://webspace.utexas.edu/egp59/index.htm
