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Module Overview

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.

Learning Outcomes

With careful study, by the end of this module, one should be able to:
 
• transform a circuit driven by a sinusoidal source from the time domain into the
Phasor domain.
• analyze circuits in the Phasor domain using complex numbers to find a circuit’s
sinusoidal steady-state response.
• define and find the effective or root-mean-squared (RMS) value of a waveform.
• Calculate the real, reactive and complex power in circuits driven by sinusoidal
sources.

Explore Module

Please note that this preview is intended for exploration purposes only. If you'd like to use this interactive module in one of your courses,to ensure playback and tracking, you must upload the SCORM package (downloadable below) to your institution's Learning Management System (ex. Blackboard, D2L, Moodle, etc). 

PROJECT FILES
Type: Assessments
Title Author Description
Problems for Introduction to Sinusoidal Steady-State Analysis | Download File (30.76 KB) Dr. David G. Nairn
Type: Glossary
Title Author Description
Glossary | Download File (84.59 KB) Dr. David G. Nairn

This glossary contains definitions for the modules: Operational Amplifier (opamp) Circuits, First Order Step Response, and Sinusoidal Steady State Analysis.
Type: Instructor Guide
Title Author Description
Instructor Guide (Introduction to Sinusoidal Steady-State Analysis) | Download File (12.15 KB) Dr. David G. Nairn

This document is designed to assist instructors who are interested in using this module as part of their course. It details what is included in the module as well as prerequisites and outcomes.
Type: Modules
Title Author Description
V1_2015_Sinusoidal Steady State Analysis (Storyline File) Dr. David G. Nairn

This Articulate Storyline File can be downloaded and modified to your specific learning objectives (within the bounds of the creative commons licensing selected for this file. This is encouraged, but any technical issues are not supported by the University of Toronto.
V1_2015_Sinusoidal Steady State Analysis (Storyline SCORM Package) Dr. David G. Nairn

This Articulate Storyline SCORM package can be uploaded into your institution's Learning Management System.
V2_2021_Introduction to Sinusoidal Steady-State Analysis (Rise SCORM Package)

This Articulate Rise SCORM package can be uploaded into your institution's Learning Management System
Type: Video Links
Title Author Description
Introduction to sinusiodally driven circuits | Introduction to sinusiodally driven circuits Dr. David G. Nairn
Defining sine waves; amplitude | Defining sine waves; amplitude Dr. David G. Nairn
An example of time domain analysis | An example of time domain analysis Dr. David G. Nairn
Generating complex sources with Euler’s identity | Generating complex sources with Euler’s identity Dr. David G. Nairn
Analysis of a simple circuit driven by a complex source | Analysis of a simple circuit driven by a complex source Dr. David G. Nairn
Introduction to and definition of Phasors | Introduction to and definition of Phasors. Dr. David G. Nairn
Verification of analysis techniques in the Phasor domain | Verification of analysis techniques in the Phasor domain Dr. David G. Nairn
Circuit elements in the Phasor domain and the impedance concept | Circuit elements in the Phasor domain and the impedance concept Dr. David G. Nairn
Finding the impedance of inductors and capacitors | Finding the impedance of inductors and capacitors Dr. David G. Nairn
A simple example of using Phasor analysis | A simple example of using Phasor analysis Dr. David G. Nairn
Using series and parallel combinations to simplify analysis | Using series and parallel combinations to simplify analysis Dr. David G. Nairn
A more complicated example of Phasor analysis | A more complicated example of Phasor analysis Dr. David G. Nairn
Introduction and calculation of instantaneous power | Introduction and calculation of instantaneous power Dr. David G. Nairn
An example of instantaneous power for a sinusoidally driven RL circuit | An example of instantaneous power for a sinusoidally driven RL circuit Dr. David G. Nairn
Calculating the average power for periodic waveforms | Calculating the average power for periodic waveforms Dr. David G. Nairn
An example of calculation the average value of a general cosine function | An example of calculation the average value of a general cosine function Dr. David G. Nairn
An example of average power for a sinusoidally drive RL circuit | An example of average power for a sinusoidally drive RL circuit Dr. David G. Nairn
Defining the effective or RMS value of a waveform | Defining the effective or RMS value of a waveform Dr. David G. Nairn
An example illustrating the calculation of the effective value of cosine | An example illustrating the calculation of the effective value of cosine Dr. David G. Nairn
Computing power with the effective voltage | Computing power with the effective voltage Dr. David G. Nairn
An example that finds the effective value of an offset sine wave | An example that finds the effective value of an offset sine wave Dr. David G. Nairn
An example that finds the effective value of two sine waves | An example that finds the effective value of two sine waves Dr. David G. Nairn
Introduction to complex power | Introduction to complex power Dr. David G. Nairn
The power factor | The power factor Dr. David G. Nairn
An example showing the calculation of complex power and Phasor diagrams | An example showing the calculation of complex power and Phasor diagrams Dr. David G. Nairn
The power triangle | The power triangle Dr. David G. Nairn
An example of power calculations using the power triangle | An example of power calculations using the power triangle Dr. David G. Nairn
Power factor correction | Power factor correction Dr. David G. Nairn
An example illustrating power factor correction | An example illustrating power factor correction Dr. David G. Nairn
Back to Parent Project
Electromagnetics and Circuits

This project is a set of 12 learning modules that support the teaching of foundational level electromagnetics and circuits in engineering programs. These modules could be used for an inverted or hybrid delivery of a first year course, or courses. We envision these modules partially or fully replacing in-person lectures, and being paired with in-person laboratories and other hands-on experiential learning activities to create an effective, active learning experience.

Project Lead(s): Prof. Belinda Wang
Project Collaborator(s): Dr. David G. NairnDr. Ajoy Opal
Project Team Members: Sean McAlary
Details
Used in:
ECE110

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