chapter 3 methods of analysis 分析方法 3.1 nodal analysis 3.2 loop analysis

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Chapter 3 Methods of Analysis 分分分分 3.1 Nodal Analysis 3.2 Loop Analysis

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Page 1: Chapter 3 Methods of Analysis 分析方法 3.1 Nodal Analysis 3.2 Loop Analysis

Chapter 3 Methods of Analysis 分析方法

3.1 Nodal Analysis

3.2 Loop Analysis

Page 2: Chapter 3 Methods of Analysis 分析方法 3.1 Nodal Analysis 3.2 Loop Analysis

Having understood the fundamental laws of circuit theory

(Ohm’s law and Kirchhoff’s laws), we are now prepared to

apply these laws to develop two powerful techniques for

circuit analysis:

• nodal analysis(结点分析法) , which is based on

KCL

• loop analysis(回路分析法) , which is based on

KVL.

Page 3: Chapter 3 Methods of Analysis 分析方法 3.1 Nodal Analysis 3.2 Loop Analysis

3.1 Nodal Analysis 结点分析法

• Steps to Determine Node Voltages :

1. Select a node as the reference node (参考结点) . Assign voltages v1,v2,…vn-1 to the remaining n-1 nodes.

2. Apply KCL to each of the n-1 nonreference nodes. Use Ohm’s law to express the branch currents in terms of node voltages.

3. Solve the resulting simultaneous equations (联立方程组) to obtain the unknown node voltages.

Choosing node voltages as circuit variables and write KCL equations.

Page 4: Chapter 3 Methods of Analysis 分析方法 3.1 Nodal Analysis 3.2 Loop Analysis

2121 iiII At node 1

At node 2 322 iiI

At node 3 311 iiI

Solution :

1

11

0

R

vi

2

212 R

vvi

3

23

0

R

vi

The first step: 0 , v1, v2

The second step: KCL and Ohm’s law

Example 3.1 Find v1 and v2 in the circuit.

i1

i2

i32

1

3

v1v2

Page 5: Chapter 3 Methods of Analysis 分析方法 3.1 Nodal Analysis 3.2 Loop Analysis

3

2

2

212

2

21

1

1

21

R

v

R

vvI

R

vv

R

vII

The third step: find v1,v2

Substitution method 代入法 Elimination method 消去法

Matrix inversion 矩阵变换

Page 6: Chapter 3 Methods of Analysis 分析方法 3.1 Nodal Analysis 3.2 Loop Analysis

At node 1 :

At node 2 :

At node 3 :

342

3121

vvvv

Solution:

48223221 vvvvv

xivvvv

284

3231

221 vv

ix

V8.432 vvvxA6.0

832

2

vv

i

V4.2V4.2V8.4 321 vvv

W88.228 ivp x

Example 3.2 Determine the voltage vx and . 8p

Page 7: Chapter 3 Methods of Analysis 分析方法 3.1 Nodal Analysis 3.2 Loop Analysis

Example 3.3 Find the current ix in the circuit .

V101 v

6842323121 vvvvvv

V532 vv

Solution:

At node 1 :

At the supernode :

V2.43 v

A7.063 v

ix

Page 8: Chapter 3 Methods of Analysis 分析方法 3.1 Nodal Analysis 3.2 Loop Analysis

3.2 Loop Analysis 回路分析法

We usually use mesh analysis ( 网孔分析法) to a planar circuit ( 平面电路) .

Choosing loop currents as circuit variables and write KVL equations.

Page 9: Chapter 3 Methods of Analysis 分析方法 3.1 Nodal Analysis 3.2 Loop Analysis

2. Apply KVL to each of the l loops. Use Ohm’s law to express the voltages in terms of the loop currents.

Steps To Determine Loop Currents:

1. Assign loop currents i1,i2,……il to the l loops.

3. Solve the resulting simultaneous equations to get the loop currents.

Page 10: Chapter 3 Methods of Analysis 分析方法 3.1 Nodal Analysis 3.2 Loop Analysis

Example 3.4 Find the current I3 in the circuit.

121311 V)( iiRiR

0)(V 123222 iiRiR

Solution:

For loop 1:

For loop 2:

So 213 iiI

2i1i

Page 11: Chapter 3 Methods of Analysis 分析方法 3.1 Nodal Analysis 3.2 Loop Analysis

Example 3.5 Find the current io in the circuit.

Solution:

For loop 1:

For loop 2:

For loop 3:

For loop 4:

A51 i

02 3ii

0)(8102 4233 iiii

06)(8)(4)(2 43424241 iiiiiiii

30 ii and

1i

4i 2i 3i

A143.20 i

Page 12: Chapter 3 Methods of Analysis 分析方法 3.1 Nodal Analysis 3.2 Loop Analysis

部分电路图和内容参考了: 电路基础(第 3 版),清华大学出版社 电路(第 5 版),高等教育出版社 特此感谢!