chapter 3 methods of analysis 分析方法 3.1 nodal analysis 3.2 loop analysis
TRANSCRIPT
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Chapter 3 Methods of Analysis 分析方法
3.1 Nodal Analysis
3.2 Loop Analysis
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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.
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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.
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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
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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
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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
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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
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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.
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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.
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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
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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
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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!