Introduction to Sinusoidal Steady-State Analysis

In this module, the analysis of sinusoidally driven circuits and the calculation of ac power is studied. This module begins with a brief analysis of sinusoidally driven circuits in the time domain to illustrate that it is tedious. The Phasor transform and Phasor analysis techniques are then introduced to greatly simplify the analysis of these circuits. The analysis of instantaneous and average power is then introduced with a strong emphasis on sinusoidally driven circuits. Complex power is then introduced along with some Phasor diagrams to illustrate various power relations and their calculations. The main emphasis of the module is on developing the basic tools used in the field.

Introduction

In many first courses on linear circuits, the analysis of sinusoidally driven circuits and the calculation of ac power is studied. In this module, the analysis of sinusoidally driven circuits in the time domain is covered very briefly, mainly to illustrate that it is tedious. The Phasor transform and Phasor analysis techniques are introduced to greatly simplify the analysis of these circuits. While Phasor diagrams are interesting, it is the experience of this author that Phasor diagrams do not add significant value at this point. So they are not introduced here. The analysis of instantaneous and average power is then introduced with a strong emphasis on sinusoidally driven circuits. Complex power is then introduced along with some Phasor diagrams to illustrate various power relations and their calculations. The main emphasis of the module is on developing the basic tools used in the field.

This module consists of a sequence of 29 videos with self-assessment questions keyed to specific videos. It is expected that the course instructor, will supplement the module with additional questions and perhaps one or two laboratory exercises.

Prerequisites

Before starting this module, it will be helpful to be familiar with;

• circuit elements such as resistors, capacitors, inductors and sources1,
• basic circuit analysis techniques,
• the sine and cosine function along with their derivatives and integrals,
• Euler’s Identity and complex numbers or imaginary numbers.