ch.3 methods of analysis part 1 nodal...

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

6

• 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