Lecture (L7-1,2,3) Sine Waves and Phasors

  • Due Nov 18, 2021 by 11am
  • Points None

Text ## Lecture (L7-1,2,3) Sine Waves and Phasors

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.

Questions of the Day (Learning Objectives)

  1. * 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)?

Lectures

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.

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.mpgPlay 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.mpgPlay 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.

Self-Assessment:  Download ECE1250_Assess7_12.pdf

Reference videos on complex numbers: 

Textbook Chapter 7-1:

Review Complex Numbers:

L7 1 1Review Complex Numbers Links to an external site.L7 1 1Review Complex Numbers

(CC Links to an external site.)

Review Polar & Rectangular Forms

L7 1 2Review Polar And Rectangular Forms Links to an external site.L7 1 2Review Polar And Rectangular Forms

(CC Links to an external site.)

Review the complex exponential

L7 1 3Review The Complex Exponential Links to an external site.L7 1 3Review The Complex Exponential

(CC Links to an external site.)

Review the nuances of j

http://www.youtube.com/watch?v=j-TO7TDOFc8

(CC Links to an external site.)

Characteristics of Sine Waves

L7 1 6Characteristics of Sinusoid Waveforms Links to an external site.L7 1 6Characteristics of Sinusoid Waveforms

(CC Links to an external site.)

 Example of complex number calculations

L7 1 5Example Complex Calculations Links to an external site.L7 1 5Example Complex Calculations

(CC Links to an external site.)

RMS Root Mean Squared

L7 1 7Root Mean Squared RMS Links to an external site.L7 1 7Root Mean Squared RMS

(CC Links to an external site.)

 Chapter 7-2 in Ulaby Textbook:

The Phasor

L7 2 1 The Phasor Links to an external site.L7 2 1 The Phasor

(CC Links to an external site.)

Example Trig using phasors

L7 2 2 Example Trig using Phasors Links to an external site.L7 2 2 Example Trig using Phasors

(CC Links to an external site.)

Introduction to the Impedance of a Resistor

L7 2 3 Introduction of Impedance of Resistor Links to an external site.L7 2 3 Introduction of Impedance of Resistor

(CC Links to an external site.)

Impedance of an Inductor

L7 2 4 Impedance of Inductor Links to an external site.L7 2 4 Impedance of Inductor

(CC Links to an external site.)

Impedance of a Capacitor

L7 2 5 Impedance of Capacitor Links to an external site.L7 2 5 Impedance of Capacitor

(CC Links to an external site.)

Additional Examples

 (Links to an external site.)

Phasor<->inverse-phasor xform:
  Ex1 (Links to an external site.), Ex1cont (Links to an external site.)
  Ex2 (Links to an external site.), Ex2cont

 

 

 

Links to an external site.

1637258400 11/18/2021 11:00am