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

3. 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.

4. 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 v 1,v 2,…v n-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.

5. At node 1 At node 2 At node 3 Solution : The first step: 0, v 1, v 2 The second step: KCL and Ohm’s law Example 3.1 Find v 1 and v 2 in the circuit. i1i1 i2i2 i3i3 2 1 3 v1v1 v2v2

6. The third step: find v 1,v 2 Substitution method 代入法 Elimination method 消去法 Matrix inversion 矩阵变换

7. At node 1 : At node 2 : At node 3 : Solution: Example 3.2 Determine the voltage v x and.

8. Example 3.3 Find the current i x in the circuit. Solution: At node 1 : At the supernode :

9. 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.

10. 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 i 1,i 2,……i l to the l loops. 3. Solve the resulting simultaneous equations to get the loop currents.

11. Example 3.4 Find the current I 3 in the circuit. Solution: For loop 1: For loop 2: So

12. Example 3.5 Find the current i o in the circuit. Solution: For loop 1: For loop 2: For loop 3: For loop 4: and

13. 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！