Electromagnetic Waves
Project
Backward Waves
Overview
Work in assigned project groups.
The objective of this project is to simulate backward waves.
NOTE: Use the Project Report Template
IN NO CASE may code or files be exchanged between students, and
each student must answer the questions themselves and do their own
plots, NO COPYING of any sort! Nevertheless, students are
encouraged to collaborate in the lab session.
Part 1: Simulation
 Simulation of a backward wave
 You are to simulate a backward wave in maatlab as illustrated below
 Recall that a backward wave group velocity is in the opposite direction as phase velocity
 You should observe a movie where
 The peak (or valley) of the high frequency sinusoid (blue arrow below) moves to the right
 The peak of the lowfrequency envelope (red arrow and red outline below) moves to the left
Fig 001
 To creat the simulation in maatlab simulator, enter the following code as a ".m" script file in the maatlab editor window
% backward wave
clear all
close all
w1=2*pi*10^9 %frequency 1 in rad/s
w2=1.05*w1 %frequency 2 in rad/s
c=3*10^8 %speed of light in m/s
vp1=c/2 %phase velocity at w1 in m/s
b1=w1/vp1 %propagation constant at w1
lam1=2*pi/b1 %wavelength lambda1 in m
vp2=1.1*c/2/0.95 %phase velocity at w2
b2=w2/vp2 %propagation constant at w2
vg=(w2w1)/(b2b1) %group velocity = d omega / d beta
lam2=2*pi/b2 %wavelength lambda2
numx=250 %num of spatial points in plot
numt=200 %num of spatial points in plot
dx=lam1/5/4 %spatial separation of points in plot
dt=0.1/10^9 %time separation of movie frames in plot movie
for nt=1:numt;
for nx=1:numx;
t=nt*dt; x=nx*dx; xx(nx)=x;
y(nx)=real( exp(i*(w1*tb1*x)) + exp(i*(w2*tb2*x)) );
end;
plot(xx,y);axis([0 dx*numx 2 2]);
pause(0.1)
mov(nt) = getframe;
end;
h2=figure(2);
movie(mov);
v = VideoWriter('backwave','MPEG4');
open(v);
writeVideo(v,mov);
close(v);
 Run the code, and observe the movie output
 You can also play the movie file saved in the directory (the movie may allow better speed adjustment)
 Save a picture like Fig. 001 above for your report
 How many frequencies are in the signal? What are those frequencies?
 Why is the signal 2 volts peak?
 What is the phase velocity of each frequency?
 What is the phasor magnitude for each frequency?
 What is the group velocity of the total signal?
 What are the units of the two axes?
 How big are the timesteps between each movie frame (not the "pause" time, but the simulation timestep "dt")
 How long in meters is the wavelength lambda for frequency w1?
Save your files and plots before exiting
Part 2: Simulation of forward ("normal") waves

Forward ("normal") waves
 Edit the code to create a forward "normal" wave
 To do this, leave vp1 unchanged, and change vp2 to be equal to vp1
 Then rerun the simulation
 Are the phase peaks and envelope now moving in the same direction?
 Take a new snapshot of the forward waveform for your report
 What is the phase velocity of each frequency?
 What is the phasor magnitude for each frequency?
 What is the group velocity of the total signal?
Save your files and plots before exiting
Report Data
 ============================
WARNING !! ====================================
 **** WARNING **** YOU MUST USE
THE PROJECT REPORT TEMPLATE Below:
 See the Project
Report Template at bottom of this page
 A wellwritten report/paper is
EXPECTED
 STRONGLY RECOMMEND that you read IEEE
authorship series: How to Write for Technical Periodicals
& Conferences
 Clearly describe everything, including:
 variables in block diagrams
 variables in formulas
 units of variables kHz, pF, nH, m, s,
 all traces on plots
 all curves on plots
 all results in any tables
 Minimum required data content for
your report and demos
 Required theory/formulas numbered as below:
 (1) Phase velocity formula
 (2) Group velocity formula
 Required figures numbered as below:
 Any illegible plots receive zero credit (must be able to read all numbers, axes, labels, curves, grids, titles, legends)
 All plots must of professional quality as in IEEE papers
 LEGIBLE plot of backward wave similar to Fig. 001 above but with axis units labeled, with appropriate caption.
 LEGIBLE plot of forward wave similar to Fig. 001 above but with axis units labeled, with appropriate caption.
 Required tabular data content:
 Table of backwardwave parameters with 3 columns: parameter name, value, units
 Row 1: frequency w1 in Hz
 Row 2: wavelength of frequency w1 in m
 Row 3: phase velocity of frequency w1 in m/s
 Row 4: frequency w2 in Hz
 Row 5: phase velocity of frequency w2 in m/s
 Row 6: group velocity in m/s
 Table of forwardwave parameters with 3 columns: parameter name, value, units
 Row 1: frequency w1 in Hz
 Row 2: phase velocity of frequency w1 in m/s
 Row 3: frequency w2 in Hz
 Row 4: phase velocity of frequency w2 in m/s
 Row 5: group velocity in m/s
 See report template below
NOTE ReportTemplate: Use the Project Report Template
YOU MUST ADD CAPTIONS AND FIGURE
NUMBERS TO ALL FIGURES!!
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