contents.kocw.net - / - Ch.3 Methods of Analysis Part 2 Mesh...
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Ch.3 Methods of Analysis
Part 2 – Mesh Analysis
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Mesh Analysis
3Pusan National University
• Mesh : a loop which does not contain any other loops within it
• Mesh current vs. element current
1 1
2 2
3 1 2
I i
I i
I i i
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Mesh Analysis
4Pusan National University
• Planar circuit vs. Nonplanar circuit
Planar Circuit Non-Planar Circuit
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Mesh Analysis
5Pusan National University
• Mesh Analysis의 Procedure
※ Mesh analysis는 planar circuit에만 적용가능
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Mesh Analysis
6Pusan National University
• Example of Mesh Analysis
1 1 1 3 1 2
3 2 1 2 2 2
Mesh 1
( ) 0
Mesh 2
( ) 0
V R i R i i
R i i R i V
1 3 3 1 1
3 2 3 2 2
R R R i V
R R R i V
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Mesh Analysis
7Pusan National University
Example 3.5
Find the branch currents I1, I2 and I3 using mesh analysis
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Mesh Analysis
8Pusan National University
Example 3.6
Find the current i0 using mesh analysis
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Mesh Analysis with Current Src
9Pusan National University
• Case 1 : Current Source only in one mesh
해당 mesh current를 current source값으로 설정
2
1 1
Mesh 2 : 5
Mesh 1 : -10 4 6( 5) 0
i
i i
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Mesh Analysis with Current Src
10Pusan National University
• Case 2 : A current source exists between two meshes
해당 current source와 직렬연결 요소를 supermesh로 정의
1 2 2
1 2
mesh : 20 6 10 4 0
supermesh : 6
i i i
i i
전체
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Mesh Analysis with Current Src
11Pusan National University
• Case 2 : A current source exists between two meshes
𝑉
전류원이 포함된 branch에 걸리는 전압을 V라고 하면,
좌측 loop에 KVL 적용
−20 + 6𝑖1 + 𝑉 = 0 (1)
우측 loop에 KVL 적용
−𝑉 + 10𝑖2 + 4𝑖2 = 0 (2)
(1)식과 (2)식을 더하여 V 소거−20 + 6𝑖1 + 10𝑖2 + 4𝑖2 = 0
이 식은 그림(b)의 회로에 대한KVL 적용 결과와 동일
식이 한 개 부족하므로 i1과i2에 대한 관계식 추가
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Mesh Analysis with Current Src
12Pusan National University
Example 3.7
Find i1 to i4 using mesh analysis
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Nodal Analysis와 Conductance 행렬
13Pusan National University
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Mesh Analysis와 Resistance 행렬
14Pusan National University
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Conductance & Resistance 행렬
15Pusan National University
Example 3.8
Write the node-voltage matrix equation
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Conductance & Resistance 행렬
16Pusan National University
Example 3.9
Write the mesh-current matrix equation
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Nodal vs. Mesh Analysis
17Pusan National University
• 일반적으로 직렬 연결, 전압원이 많은 경우 Mesh법을 적용, 병렬연결, 전류원이 많은 경우 Nodal법을 적용
• Node의 수와 mesh의 수를 비교하여 수식의 수가 적은 쪽을 적용
• 문제에서 요구하는 대상이 node voltage인 경우는 nodal법, branch 또는 mesh current인 경우는 mesh법 적용
• 회로에 Transistor가 있는 경우는 mesh법만 가능한 반면Op-Amp가 있는 경우는 nodal법만 가능
• Nonplanar 회로의 경우는 nodal법만 가능
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Circuit Analysis with Pspice
18Pusan National University
Example 3.10
Calculate the node voltages
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Mesh Analysis
19Pusan National University
Example 3.11
Calculate the currents i1, i2 and i3
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Application – Transistor Circuit
20Pusan National University
• 트랜지스터의 외관 및 Circuit symbol
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Application – Transistor Circuit
21Pusan National University
• NPN 트랜지스터의 전압, 전류 특성
(by KCL)E C BI I I 0 (by KVL)CE EB BCV V V
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Application – Transistor Circuit
22Pusan National University
• NPN 트랜지스터의 Active Mode ( )
• α와 β의 관계
( : common-base current gain, 0.98~0.999)
( : common-emitter current gain, 50~1000)
0.7V
C E
C B
BE
I I
I I
V
0.7VBCV
(1 )
1 or
1
1
E B C B B B
E B C B E E B
I I I I I I
I I I I I I I
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Application – Transistor Circuit
23Pusan National University
• NPN 트랜지스터의 등가회로
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Application – Transistor Circuit
24Pusan National University
Example 3.12
Find IB, IC, and v0 in the following transistor circuit. Assume that the transistor operates in active mode and that β=50.
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Application – Transistor Circuit
25Pusan National University
Example 3.13
Find v0 when β=150 and VBE=0.7V.
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Assignment
26Pusan National University
Chapter 3
3.4, 3.10, 3.16, 3.27, 3.28, 3.32, 3.34, 3.40, 3.55, 3.63, 3.69, 3.74, 3.88
Due date :