Chapter 7 Sinusoidal Steady-State Analysis 正弦稳态电路分析 7.1 Nodal Analysis 7.2 Mesh Analysis 7.3 Superposition Theorem 7.4 Source Transformation 7.5 Thevenin and Norton Equivalent Circuits

Steps to Analyze AC Circuits: Transform the circuit to the phasor or frequency domain. 2. Solve the problem using circuit techniques (nodal analysis, mesh analysis, superposition, source transformation, Thevenin’s or Norton’s theorem, etc). 3. Transform the resulting phasor to the time domain.

7.1 Nodal Analysis The basis of nodal analysis is Kirchhoff’s current law. KCL is valid for phasors. Example 7.1 Find the current ix in the circuit using nodal analysis. Solution: At node 1 : At node 2 :

7.2 Mesh Analysis Kirchhoff’s voltage law forms the basis of mesh analysis. KVL is valid for ac circuits. Example 7.2 Find the voltage in the circuit using mesh analysis. Solution: For loop 1: For loop 2: For loop 3: For loop 4: so:

7.3 Superposition Theorem Since ac circuits are linear, the superposition theorem applies to ac circuits the same way it applies to dc circuits. The theorem becomes important if the circuit has sources operating at different frequencies.

and in the circuit, calculate iL using superposition theorem. Example 7.3 Given Solution: + Converting to the time domain,

+ + Example 7.4 Find vo in the circuit using superposition theorem. Solution: + + ?

7.4 Source Transformation Source Transformation in the frequency domain involves transforming a voltage source in series with an impedance to a current source in parallel with an impedance, or vice versa.

Example 7.5 In the circuit, Calculate the current using source transformation. Solution:

7.5 Thevenin and Norton Equivalent Circuits Thevenin’s and Norton’s theorems are applied to ac circuits in the same way as they are to dc circuits. The only additional effort arises from the need to manipulate complex numbers. Thevenin equivalent

Norton equivalent

Example 7.6 In the circuit, Calculate the current using Thevenin’s theorem. Solution: The open circuit voltage： The equivalent impedance：

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！