Sinusoidal SteadyState Analysis

1
Chapter 10

• Sinusoidal Steady-State Analysis

2
Introduction

• Circuit analysis on Nodal, Mesh, Superposition,
  Source Transformation, Thevenin and Norton.
• Approaches used are similar to the steps involved
  as in chapter 3 and 4.
• The only new thing introduced is, in ac we are
  dealing with complex numbers.

3
Introduction

• Steps to analyze ac circuits
• Transform the circuit to phasor/frequency domain.
• Not necessary if the problem already in the
  phasor/frequency domain.
• Solve the problem using circuit analysis
  techniques (i.e. nodal, mesh, superposition,
  e.t.c.).
• Perform the analysis in the same manner as dc
  circuit analysis, except that complex numbers are
  involved.
• Transform the resulting phasor to time domain.

4
Circuit Analysis

• Nodal Analysis
• The basis is based on KCL.
• Mesh Analysis
• The basis is based on KVL.
• Since KCL and KVL is valid for phasors, ac
  circuits can be analyzed by nodal and mesh
  analysis.

5
Superposition Theorem

• Applies to ac circuits the same way as in dc.
• Extra caution when the sources are operating at
  different frequencies.
• Different frequency domain for each frequency.
• Total response must be obtained by adding the
  individual responses in the time domain.

6
Source Transformation
7
Thevenin and Norton Equivalent Circuits

• Analysis are applied similarly to dc.
• VThZNIN ZThZN
• VThopen cct voltage.
• INshort cct current
• If the circuit has sources operating at different
  frequencies, the Thevenin and Norton equivalent
  circuit must be determined at each frequency
  domain.

8
Nodal Analysis

• Example 1
• Calculate V1 and V2 in the circuit.

9
Mesh Analysis

• Example 2
• Find I0 using mesh analysis.

10
Superposition Theorem

• Example 3
• Calculate v0 in the circuit using superposition.

11
Source Transformation

• Example 4
• Find I0 using source transformation

12
Thevenin and Norton Equivalent Circuits

• Example 5
• Find VTh and ZTh