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
| Title | Author | Description | Copyright |
|---|---|---|---|
 Problems for Introduction to Sinusoidal Steady-State Analysis |  Download File (30.76 KB) |
Dr. David G. Nairn |
| Title | Author | Description | Copyright |
|---|---|---|---|
 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. |
| Title | Author | Description | Copyright |
|---|---|---|---|
 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. |
| Title | Author | Description | Copyright |
|---|---|---|---|
 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. |
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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. |
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|
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 |
| Title | Author | Description | Copyright |
|---|---|---|---|
 Using series and parallel combinations to simplify analysis | Link |
Dr. David G. Nairn | ||
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An example of power calculations using the power triangle | Link |
Dr. David G. Nairn | ||
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A more complicated example of Phasor analysis | Link |
Dr. David G. Nairn | ||
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Power factor correction | Link |
Dr. David G. Nairn | ||
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Introduction and calculation of instantaneous power | Link |
Dr. David G. Nairn | ||
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An example illustrating power factor correction | Link |
Dr. David G. Nairn | ||
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An example of instantaneous power for a sinusoidally driven RL circuit | Link |
Dr. David G. Nairn | ||
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Calculating the average power for periodic waveforms | Link |
Dr. David G. Nairn | ||
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An example of calculation the average value of a general cosine function | Link |
Dr. David G. Nairn | ||
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Introduction to sinusiodally driven circuits | Link |
Dr. David G. Nairn | ||
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An example of average power for a sinusoidally drive RL circuit | Link |
Dr. David G. Nairn | ||
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Defining sine waves; amplitude | Link |
Dr. David G. Nairn | ||
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Defining the effective or RMS value of a waveform | Link |
Dr. David G. Nairn | ||
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An example of time domain analysis | Link |
Dr. David G. Nairn | ||
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An example illustrating the calculation of the effective value of cosine | Link |
Dr. David G. Nairn | ||
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Generating complex sources with Euler’s identity | Link |
Dr. David G. Nairn | ||
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Computing power with the effective voltage | Link |
Dr. David G. Nairn | ||
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Analysis of a simple circuit driven by a complex source | Link |
Dr. David G. Nairn | ||
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An example that finds the effective value of an offset sine wave | Link |
Dr. David G. Nairn | ||
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Introduction to and definition of Phasors | Link |
Dr. David G. Nairn | ||
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An example that finds the effective value of two sine waves | Link |
Dr. David G. Nairn | ||
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Verification of analysis techniques in the Phasor domain | Link |
Dr. David G. Nairn | ||
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Introduction to complex power | Link |
Dr. David G. Nairn | ||
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Circuit elements in the Phasor domain and the impedance concept | Link |
Dr. David G. Nairn | ||
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The power factor | Link |
Dr. David G. Nairn | ||
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Finding the impedance of inductors and capacitors | Link |
Dr. David G. Nairn | ||
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An example showing the calculation of complex power and Phasor diagrams | Link |
Dr. David G. Nairn | ||
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A simple example of using Phasor analysis | Link |
Dr. David G. Nairn | ||
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The power triangle | Link |
Dr. David G. Nairn |
