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

• How do you express a sine wave in the time and frequency (phasor) domains (and convert between them)?  
• What is 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)?

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

Cookbook: ImpedSinusoidsParam.pdf Download Cookbook: ImpedSinusoidsParam.pdf

Cookbook: Rect/Polar Conversion Download Cookbook: Rect/Polar Conversion

Please watch this video before class: Sine waves and phasors (simplified explanation)

Sine Waves:

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

• Wikipedia: Sine Waves Links to an external site.

Phasors and Sine Waves:

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: ECE1250_Assess7_12.pdf Download ECE1250_Assess7_12.pdf

Reference videos on complex numbers (from Lee Brinton): 

Textbook Chapter 7-1:

Review Complex Numbers:

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

(CC Links to an external site.)

Wikipedia: Complex Numbers & Their Math Links to an external site.

Review Polar & Rectangular Forms

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

(CC Links to an external site.)

Review the complex exponential

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

(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.

(CC Links to an external site.)

 Example of complex number calculations

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

(CC Links to an external site.)

RMS Root Mean Squared

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

(CC Links to an external site.)

 Chapter 7-2 in Ulaby Textbook:

The Phasor

L7 2 1 The Phasor Links to an external site.

(CC Links to an external site.)

Example Trig using phasors

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

(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.

(CC Links to an external site.)

Impedance of an Inductor

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

(CC Links to an external site.)

Impedance of a Capacitor

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

(CC Links to an external site.)

 (Links to an external site.)

Additional videos from Dr. Furse

Lecture Notes: L4.doc  Download Lecture Notes: L4.doc 

Power Point to take notes on complex numbers.ppt Download complex numbers.ppt

1. 4.  download  (Links to an external site.)

    

   Go Deeper into Phasor Math:Tutorial: Phasors Download Tutorial: Phasors

2. Additional Examples

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

Worksheet: InClass 7-1to3.docx Download InClass 7-1to3.docx

Slides: Lecture 18.pptx Download Lecture 18.pptx

HW 7-1 & 7-3

L7-1,2,3 Sinusoids & Phasors