Lecture (L7-1,3) Sine Waves and Phasors

Due Jul 19, 2016 by 9:40am
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Question of the Day:

* How do you express a sine wave in the time and frequency (phasor) domains (and convert between them)? Understand phase lag and lead and how to calculate it.

* In the frequency (phasor) domain, how do you convert between rectangular and polar forms?

* How do you add and subtract, multiply and divide sine waves (phasor domain)?

Self-Assessment: ECE1250F14_Assess7_12.pdf Download ECE1250F14_Assess7_12.pdf

Introduction: Sine waves are used in all kinds of communication circuits (radio signals, for instance). Phasors are a mathematical way we can represent and calculate sine wave signals easily.

Reference Material:

Textbook Chapter 7-1 and 7-3 (with 7-2 as a review)

Cookbook: ImpedSinusoidsParam.pdf Download Cookbook: ImpedSinusoidsParam.pdf

Sine Waves Links to an external site.

Complex Numbers & Their Math Links to an external site.

Video Lectures:

There are no required video lectures for today, although the videos below will be useful references. We will cover sine waves and complex numbers in class.

Notes from In Class Lecture: Lecture 7-1 Sine waves.ppt Download Lecture 7-1 Sine waves.ppt

Additional Reference Material:

Here are some MATLAB files you can use to generate plots of sinusoids and phasors:

Matlab code to plot a sine wave (you can change F,A,phi, etc.) cosine time domain plot.m Download cosine time domain plot.m

The following files illustrate how a sinusoid corresponds to the shadow of rotating stick (that represents a phasor):

PhasorMovie0.m Download PhasorMovie0.m Matlab code to generate picture of rotating stick

PhasorMovie0.mpg Download PhasorMovie0.mpg Play media comment. Movie of rotating stick. Shadow on real axis is Acos(wt+phi).

PhasorMovie.m Download PhasorMovie.m Matlab code to generate picture of rotating stick and the waveform of the shadow on the real axis over time. Phasor is picture of stick at time t = 0.

PhasorMovie.mpg Download PhasorMovie.mpg Play media comment. Movie of rotating stick shadow plotted over time.

three_D.m Download three_D.m Matlab code to make a 3-D plot projected onto 2-D display.

Reference videos on complex numbers:

Textbook Chapter 7-1:

Review Complex Numbers:

http://www.youtube.com/watch?v=5Duylj_qRL0 Links to an external site.