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# Chap. 4 Techniques of Circuit Analysis

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Chap. 4 Techniques of Circuit Analysis
2017/4/10 Chap. 4 Techniques of Circuit Analysis Contents 4.1 Terminology 4.2 Introduction to the Node-Voltage Method 4.3 The Node-Voltage Method and Dependent Sources 4.4 The Node-Voltage Method: Some Special Cases 4.5 Introduction to the Mesh-Current Method 4.6 The Mesh-Current Method and Dependent Sources 4.7 The Mesh-Current Method: Some Special Cases 4.8 The Node-Voltage Method Versus the Mesh-Current Method 4.9 Source Transformations 4.10 Thévenin and Norton Equivalents 4.11 More on Deriving a Thévenin Equivalent 4.12 Maximum Power Transfer 4.13 Superposition Objectives 1. 了解並能夠使用節點電壓法求解電路。 2. 了解並能夠使用網目電流法求解電路。 3. 對於特定電路能夠決定節點電壓法或網目電流法何者是較佳的求解方式。 4. 了解電源轉換，並能夠使用它來求解電路。 5. 了解戴維寧和諾頓等效電路的觀念，並能針對電路建立等效電路。 6. 了解電阻負載最大功率轉移之情況，並能計算滿足此情況之負載電阻值。

Realistic Resistors

4.1 Terminology 節點 必要節點 路徑 分支 必要分支 迴路 網目 平面電路 Node Essential node Path
Branch Essential branch Loop Mesh Planar circuit A point where two or more circuit elements join A node where three or more circuit elements join A trace of adjoining basic elements with no elements included more than once A path that connects two nodes A path which connects two essential nodes without passing through an essential node A path whose last node is the same as the starting node A loop that does not enclose any other loops A circuit that can be drawn on a plane with no crossing branches Nonplanar Planar

EX 4.1 Identifying Node, Branch, Mesh and Loop
2017/4/10 EX 4.1 Identifying Node, Branch, Mesh and Loop Node Essential node Branch Essential branch Mesh a, b, c, d, e, f, and g. b, c, e, and g. v1, v2, R1, R2, R3, R4, R5, R6, R7, and I . v1 –R1 , R2 –R3 , v2 –R4 , R5, R6, R7, and I . v1 –R1 –R5 –R3 –R2 , v2 –R2 –R3 –R6 –R4 , R5 –R7 –R6 , and R7 –I . Find two paths that not loops or essential branches. Find two loops that not meshes.

Simultaneous Equations—How Many?

4.2 Introduction to the Node-Voltage Method

EX 4.2 Using the Node-Voltage Method
2017/4/10 EX 4.2 Using the Node-Voltage Method 1 a) Node 1: Branch currents: b)

4.3 The Node-Voltage Method and Dependent Sources

4.4 The Node-Voltage Method: Some Special Cases
Case A. 當節點電壓值 v1 = 100 V時，其KCL方程式不需列出， 只需節點2 之KCL方程式。 Node 2: 9

4.4 Case B 1 Supernode (超節點) Case B. 2 3 當電壓源兩端為必要節點且皆非參考點時，可引進一自定未知電流（如圖中之i），然後於方程式求解過程中將它消去。 Node 2: Node 3: ( + The Concept of a Supernode 當電壓源兩端為必要節點且皆非參考點時，可將其兩端節點合併為超節點，而此超節點也符合克希荷夫電流定律(KCL)。 10

Supernode 4.4 Case B Contd. Node 1: Supernode: 電壓源限制: 相依電源控制變數: 11

Node-Voltage Analysis of the Amplifier Circuit
Node a: Supernode: 電壓源限制: 相依電源控制變數: 12

4.5 Introduction to the Mesh-Current Method

Evolution of the Mesh-Current Technique
KCL: KVL: 將(ne -1) 條KCL方程式帶入be - (ne -1) 條KVL方程式 可去除(ne -1) 個分支電流未知數 完全 相同 指定網目電流，直接列出be - (ne -1) 條KVL方程式 網目KVL方程式 以網目電流表示分支電流： 14

EX 4.4 Using the Mesh-Current Method
2017/4/10 EX 4.4 Using the Mesh-Current Method b-(n-1)=7-(5-1)=3 a) Mesh a: Mesh b: Mesh c: b) 15 15

4.6 The Mesh-Current Method and Dependent Sources

4.7 The Mesh-Current Method: Some Special Cases
Case A. 當電流源僅有一個網目電流通過時，其KVL方程式不需列出， 直接指定該網目電流。 Mesh 1: Mesh 2: Mesh 3: 17

4.7 Case B Case B. 當電流源有兩個網目電流通過時，可引進一自定未知電壓（如圖中之v），然後於方程式求解過程中將它消去。 Mesh a: Mesh c: ( + The Concept of a Supermesh 當電流源有兩個網目電流通過時，可將其兩網目合併為超網目，而此超網目也符合克希荷夫電壓定律(KVL)。 18

4.7 Case B Contd. Case B. Supermesh: 電流源限制: Mesh b: 19

Mesh-Current Analysis of the Amplifier Circuit
Supermesh: 電流源限制: Mesh b: 相依電源控制變數: 20

4.8 The Node-Voltage Method Versus the Mesh-Current Method

EX 4.6 Understanding the Node-Voltage Method v.s. Mesh-Current Method
2017/4/10 EX 4.6 Understanding the Node-Voltage Method v.s. Mesh-Current Method a) Supernode: b) Node a: Node b & 相依電源控制變數: 電壓源限制式與相依電源控制變數: Node c: Node 2: 22 22

EX 4.7 Comparing the Node-Voltage and Mesh-Current Methods
2017/4/10 EX 4.7 Comparing the Node-Voltage and Mesh-Current Methods a) Node o: Node a: Node b: 節點電壓法: ne-1 = 4-1 = 3 相依電源 控制變數: 網目電流法: be-(ne-1) = 6-(4-1) = 3 b) Supermesh: 2個電流源限制式與相依電源控制變數: 23 23

4.9 Source Transformations
24

EX 4.8 Using Source Transformations to Solve a Circuit
2017/4/10 EX 4.8 Using Source Transformations to Solve a Circuit absorbing 25 25

Special Source Transformation Techniques

EX 4.9 Using Special Source Transformation Techniques
2017/4/10 EX 4.9 Using Special Source Transformation Techniques Use source transformations to find the voltage vo. b) Find the power developed by the 250-V source. c) Find the power developed by the 8-A source. + - b) (參考原圖) a) (supplied 2800W) c) 27 (參考原圖) (supplied 480W) 27

4.10 Thévenin and Norton Equivalents

Finding a Thévenin Equivalent
2017/4/10 Finding a Thévenin Equivalent a, b 端開路，求解VTh = v1 = vab。 a, b 端短路，求解isc。 29 29

The Norton Equivalents

2017/4/10 EX 4.10 Finding the Thévenin Equivalent of a Circuit with a Dependent Source 31 31

4.11 More on Deriving a Thévenin Equivalent

EX 4.11 Finding the Thévenin Equivalent Using a Test Source
2017/4/10 EX 4.11 Finding the Thévenin Equivalent Using a Test Source vT 為測試電壓源，vT / iT 就是RTh。 33 33

Using the Thévenin Equivalent in the Amplifier Circuit
34

4.12 Maximum Power Transfer
The derivative is zero and p is maximized when CONDITION FOR MAXIMUM POWER TRANSFER (最大功率轉移時的條件) 最大功率轉移量 35

EX 4.12 Calculating the Condition for Maximum Power Transfer
2017/4/10 EX 4.12 Calculating the Condition for Maximum Power Transfer Also, The percentage of the source power delivered to the load is 36 36

4.13 Superposition 重疊原理(superposition)：在線性系統中，將各別獨立電源造成之響應相加，就可以得到總響應。
1) 37

4.13 Contd. v3 v4 2) 將電壓源驅動之電流i’和電流源驅 動之電流i”相加，可得總電流。 38

EX 4.13 Using Superposition to Solve a Circuit
2017/4/10 EX 4.13 Using Superposition to Solve a Circuit 1) 2) 39 39

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