ch.3 methods of analysis part 1 nodal...
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Ch.3 Methods of Analysis
Part 1 – Nodal Analysis
Nodal Analysis
3
• Node voltage vs. Element voltage
- Element voltage : element 양단의 전위차
- Node voltage : reference node에 대한 노드의 전압
(reference node = datum node = ground)
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Element voltage
Node voltage
Nodal Analysis
4
• Nodal analysis의 procedure
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Nodal Analysis
5
• Example of Nodal analysis
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Nodal Analysis
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• Example of Nodal analysis
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1 2 1 2
2 2 3
11 1 1 1
1
1 22 2 2 1 2
2
23 3 3 2
3
0
( )
0
I I i i
I i i
vi or i G v
R
v vi or i G v v
R
vi or i G v
R
Nodal Analysis
7
• Example of Nodal analysis
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1 2 1 2
2 2 3
11 1 1 1
1
1 22 2 2 1 2
2
23 3 3 2
3
0
( )
0
I I i i
I i i
vi or i G v
R
v vi or i G v v
R
vi or i G v
R
1 2 1 1 2 1 2
2 2 1 2 3 2
( )
( )
I I G v G v v
I G v v G v
1 2 2 1 1 2
2 2 3 2 2
G G G v I I
G G G v I
Review of Cramer’s Rule
8
• n-th order system equation
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Review of Cramer’s Rule
9
• Calculation of determinant
Mij : ith row와 jth column을 삭제한 행렬의 determinant
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Review of Cramer’s Rule
10
• Determinant of 2x2 matrix
• Determinant of 3x3 matrix
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Review of Cramer’s Rule
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Example A.2
Determine x1, x2, and x3 for the following simultaneous equations:
Nodal Analysis
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Example 3.1
Calculate the node voltages in the following figure
Nodal Analysis
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Example 3.2
Determine the node voltages in the following figure
Nodal Analysis w. Voltage Src.
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• Voltage source between the reference node and non-reference node non-reference node의 전압을 voltage source의 전압으로 지정
1 10v V
Nodal Analysis w. Voltage Src.
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• Voltage source between two non-reference nodes
두 non-reference node를 super node로 정의
먼저 supernode를 하나의
node로 취급하여 nodal
analysis를 수행한 후, KVL
을 적용하여 supernode내
의 각 node의 전압을 계산
Nodal Analysis w. Voltage Src.
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• Voltage source between two non-reference nodes
5V 전압원에 흐르는 전류를 i라고 하면
V2노드에 KCL 적용𝑖1 − 𝑖2 − 𝑖 = 0
V3노드에 KCL 적용𝑖 + 𝑖4 − 𝑖3 = 0
두 식을 더하여 i 소거𝑖1 − 𝑖2 + 𝑖4 − 𝑖3 = 0
식이 하나 부족하므로 v2와v3에 대한 관계식 추가
Nodal Analysis w. Voltage Src.
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• Example
1
1 4 2 3
1 3 31 2 2
2 3
1) @node 1 : 10
2)@supernode :
2 4 8 6
3) Applying KVL to the
supernode loop
5 0
v V
i i i i
v v vv v v
v v
Nodal Analysis w. Voltage Src.
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Example 3.3
Find the node voltages
Nodal Analysis w. Voltage Src.
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Example 3.4
Find the node voltages