Microsoft Word - BE101 T1 2018 Group_project_V2
BE101 Engineering Mathematics Page | 1
Prepared by: Dr. Iryna Khodasevych Moderated By: Dr. Rajan Kadel May, 2018
Assessment Details and Submission Guidelines
Trimester T1 2018
Unit Code BE101
Unit Title Engineering Mathematics
Assessment
Type
Group
Assessment
Title
Investigation of practical applications of complex mathematical concepts using
MATLAB
Purpose of the
assessment
(with ULO
Mapping)
The purpose of this assignment is to investigate practical applications of complex
mathematical concepts and gain understanding of how mathematics is used in
engineering context. At the completion of this unit students are expected to be able to:
a. Develop problem‐solving skills in the context of engineering mathematics;
. Have a practical understanding of mathematics in the engineering context;
c. Gain experience using an extended range of practical applications of complex
mathematical ideas;
d. Apply knowledge of basic science and engineering fundamentals to real‐life situations;
e. Communicate effectively, not only with engineers but also with the community at large;
f. Undertake problem identification, formulation and solutions;
g. Solve a
oad range of problems in mathematical areas;
Weight 100 Marks
Total Marks 25% of total assessment for the unit
Word limit 2000 words
Due Date Lab class week 12, 7 June 2018
Submission
Guidelines
All work must be submitted on Moodle by the due date.
The assignment must be in MS Word format, 1.5 spacing, 11‐pt Cali
i (Body) font and
2.5 cm margins on all four sides of your page with appropriate section headings.
Reference sources must be cited in the text of the report, and listed appropriately at
the end in a reference list using IEEE referencing style.
Extension If an extension of time to submit work is required, a Special Consideration Application
must be submitted directly on AMS. You must submit this application three working
days prior to the due date of the assignment. Further information is available at:
http:
www.mit.edu.au/about‐mit/institute‐publications/policies‐procedures‐and‐
guidelines/specialconsiderationdeferment
Academic
Misconduct
Academic Misconduct is a serious offence. Depending on the seriousness of the case,
penalties can vary from a written warning or zero marks to exclusion from the course o
escinding the degree. Students should make themselves familiar, with the
full policy and procedure available at:
http:
www.mit.edu.au/about‐mit/institute‐publications/policies‐ procedures‐and‐
guidelines/Plagiarism‐Academic‐Misconduct‐Policy‐
Procedure. For further information, please refer to the Academic Integrity Section
in your Unit Description.
BE101 Engineering Mathematics Page | 2
Prepared by: Dr. Iryna Khodasevych Moderated By: Dr. Rajan Kadel May, 2018
Assignment Description
You need to form a team of three to complete the project. Team members are expected to equally
participate, and collaboratively work towards the completion of the project.
This task requires you to research and try to understand the given topic, methods and how MATLAB
is used as a problem solving tool. Modern mathematics requires the use of computational tools in
order to solve difficult real world problems. Tools are required because often the problems are either
too large or not possible to solve analytically, and building physical models is impractical. Using
computational tools is additionally often an open ended exercise, where some formal theory is
implemented, possibly with the aid of pre‐existing analysis or models. This assignment gives you a
chance to investigate into application of complex mathematical concepts and gain hands on
experience in how MATLAB is used as a problem solving tool. The Engineering Mathematics Course
unit assists you to become familiar with the mathematical skills required to solve engineering related
problems. The mathematical skills acquired in this Engineering Mathematics Course unit will provide
necessary background to understand the algorithms and methods used in this document.
You need to
Show how well you have understood the problem and simulations or calculations in this
system and explain how MATLAB is used as a problem solving tool .
The projects are open ended. As long as your program can perform the assigned tasks, there
will be no co
ect or wrong approaches. Certainly, there will be more acceptable and attractive
solutions in comparison with competing solutions.
In the event you cannot complete the task, you should turn in whatever you have completed
and grade will be based on completed work. Bottom line will be, if we cannot get your program
to execute, it will be graded based on what you have completed. In all cases it will be essential
that you submit a complete set of files to test your program. It will also be important to give
clear instructions of how to run your program. This could be done in various ways. One good
way to document how your program executes is to prepare “readme.txt” file.
Each team will interactively present their solutions by demonstrating how the code is
executed.
All members must participate in the presentation and must have a reasonable familiarity with
the project, even if they have not been the lead person on that specific topic.
BE101 Engineering Mathematics Page | 3
Prepared by: Dr. Iryna Khodasevych Moderated By: Dr. Rajan Kadel May, 2018
Antenna Radiation Pattern Calculation
Antenna radiation pattern is a graphical representation of the power radiated by antenna relative to
direction. Antennae radiate differently in different directions. Usually the power is measured far away
from antenna (in the far field) at a fixed distance.
Dipole radiation
Dipole antenna is a wire antenna. Oscillating cu
ent i(t) flowing through the wire gives rise to the
electric field Eθ and magnetic field Hϕ. Figure 1 shows vertically oriented dipole antenna.
Fig. 1. Dipole antenna with cu
ent i giving rise to the electromagnetic field at point Q.
Power per unit area at point Q can be found as
, | | (2), where η0=377 .
Antenna radiation pattern, as shown in figure 2, is a plot of normalised power Sn in polar coordinate
system, where
, , (3)
Fig. 2. Dipole antenna radiation pattern.
BE101 Engineering Mathematics Page | 4
Prepared by: Dr. Iryna Khodasevych Moderated By: Dr. Rajan Kadel May, 2018
Part A: Short dipole radiation pattern
For very short wire (l
), maximum amplitude of the cu
ent on the wire is assumed constant
, while the cu
ent varies in time. Electric field at any point in space far away from antenna
(R
) can be found using formula:
(4)
where R is distance to the point, θ is angle of observation, e. g. polar coordinates of a point where
the field is required, j is imaginary constant, I0 is the maximum amplitude of the cu
ent on the wire,
l is the length of the dipole, k is a wavenumber and η0 is impedance of free space.
Write a program using MATLAB software to calculate electric field of short dipole and plot its
adiation pattern:
Use radiation frequency of 950 MHz.
o Calculate wavelength of radiation =c/f, where c=3*108 m/s is speed of light.
o Calculate k=2*/.
o Assign η0=377
o Assign observation point to be R=10* from the antenna.
o Assign I0= 5 A.
o Use l=/50 for very short dipole antenna.
Create an a
ay of angles θ from 1 to 360 degrees.
o Hint: “a = [0:2:100]” is a one‐dimensional a
ay from 0 to 100 at intervals of 2. 0 is the
starting point, 100 is the end point, and 2 is the step size.
Calculate electric field using formula (4). Take real part of the complex result for the field
Re(Eθ).
Use formula (2) to calculate radiated power S for each angle direction θ, normalize the power
y dividing all values by maximum power.
Plot normalized power Sn versus angle θ using “polar” plot function. Add title to the plot. Save
the plot.
o Note: “polar” plot function, as well as “sin” and “cos” functions require angle in
adians.
o Note: A
ay arithmetic commands require dot in front, e.g. .*, ./, .^2.
BE101 Engineering Mathematics Page | 5
Prepared by: Dr. Iryna Khodasevych Moderated By: Dr. Rajan Kadel May, 2018
Part B: Short dipole electric field
Write a program to plot electric field lines of short dipole antenna from Part A using MATLAB’s
“contour” plot.
Assume antenna is located at the center of the plot. Assume x and y values are in rectangular
coordinates from – 2* to +2*.
In the formula (4) for E convert R and θ to rectangular coordinates x and y. Take real part of
the complex result for the field.
Use “contour” function to plot electric field lines for the radiating antenna. Add title to the
plot. Save the plot.
Fig. 3. Example plot of electric field lines of dipole antenna.
BE101 Engineering Mathematics Page | 6
Prepared by: Dr. Iryna Khodasevych Moderated By: Dr. Rajan Kadel May, 2018
Part C : Long dipole radiation pattern
For long dipole cu
ent varies along the length of dipole as , as shown in figure 4.
Fig. 4. Cu
ent distributions on long dipole.
Total field at point Q (R, θ) is an integral (or sum) of fields created by short lengths dz along the
wire, each having different cu
ent amplitude.
,where (5)
Write a program using MATLAB software to calculate electric field of long dipole and plot its radiation
pattern:
Use the same radiation frequency, wavelength of radiation , k, η0, I0 and observation point R.
Use a different length l for a long dipole antenna, which will be assigned to each group in the
classroom.
Modify the code from part A to calculate the field and power for each angle within a cycle for
different angles θ from 1 to 360 degrees.
o Use “for” cycle for θ in MATLAB
o Within the cycle, calculate electric field using formula (5). Assume cu
ent as
Hint: Using help find out how to define a function using @ sign.
Hint: Using MATLAB’s built‐in function INTEGRAL find the contributions of
each elements of the dipole length to the cu
ent at point (R, θ). Integrate
from –l/2 to l/2.
Save each result E θ for different angle under different index in the a
ay.
Take real part of the complex result for the field.
Calculate radiated power for each angle direction.
Normalize the power by dividing all values by maximum power.
Plot normalized power Sn versus angle θ using “polar” plot function. Add title to the plot. Save
the plot.
BE101 Engineering Mathematics Page | 7
Prepared by: Dr. Iryna Khodasevych Moderated By: Dr. Rajan Kadel May, 2018
Submission guidelines:
1. Each team will submit one project report that must be a PDF or word file. Your MATLAB code
can be submitted as a text attachment in your project report or as a separate .m file and
should contain everything necessary to run the file.
2. Prepare a report summarizing your findings. Your report should include the
following:
o The cover page must identify student (name and number), teaching staff,
and assignment.
o Body of the report should include
i. Introduction –In this section, you need to give a
ief overview and your
understanding of the problem discussed in the document and outline of
the report.
ii. Methods ‐You need to describe your understanding of methods you used
for simulations or calculations in MATLAB. Briefly explain the key files and
functions in your code.
iii. Results and Discussion– Present quantitative and qualitative results of your
approach and discuss the findings. To illustrate the results please pick some
images and show your results on them.
iv. Conclusion – Summarise the findings.
v. References ‐ Sources must be cited in the text of the report, and listed
appropriately at the end in a reference list.
3. Prepare a PowerPoint presentation for 5‐10 minute presentation. No more than 7‐8 slides.
You must present as a group, every member of your group needs to speak. You must have
visual aids to support your presentation and you must acknowledge the source of the
information you present. The presentation should focus on the Mathematics/MATLAB.
4. The assignment must be submitted in soft (electronic) copy under Moodle. The MATLAB
program file and presentation should also be uploaded. The pages of the assignment must
e clear on each page.
BE101 Engineering Mathematics Page | 8
Prepared by: Dr. Iryna Khodasevych Moderated By: Dr. Rajan Kadel May, 2018
Marking criteria:
Description of the section Marks
Coding
Executable MATLAB code
A complete set of files to test your program
20
Presentation Marks for the Presentation will be based on the
material provided (5 marks), presentation skills (5
marks), and understanding of the material (5 marks).
15
Report
Section to be included in
the report
Description of the section
Introduction Brief overview and your understanding of the
problem.
10
Methods Describe your understanding of simulations or
calculations. Briefly explain the key files and
functions in your code.
10
Results Present your results. Part A (10 marks)
Part B (10 marks), Part C (10 marks).
30
Discussion Discuss the results. 5
Conclusion Concluding remarks 5
Reference style 5
Poor writing Inadequate structure, careless presentation, or the
eport is under the word limit
‐30
Plagiarism Type of plagiarism
‐ Copy from other student
‐ Copy from internet source/textbook
‐ Copy from other sources
‐100
Total 100
BE101 Engineering Mathematics Page | 9
Prepared by: Dr. Iryna Khodasevych Moderated By: Dr. Rajan Kadel May, 2018
Marking Ru
ics:
Grade
Mark
HD
80%+
D
70%‐79%
CR
60%‐69%
P
50%‐59%
Fail
50%
Excellent Very Good Good Satisfactory Unsatisfactory
Introduction Logic is clear
and easy to
follow with
strong
arguments
Consistency
logical and
convincing
Mostly consistent
and convincing
Adequate
cohesion and
conviction
Argument is
confused and
disjointed
Effort/Difficulties/
Challenges
The presented
solution
demonstrated
an extreme
degree of
difficulty that
would require
an expert to
implement.
All results were
obtained using
Matlab code.
The presented
solution
demonstrated a
high degree of
difficulty that
would be an
advance
professional to
implement. Most
esults were
obtained using
Matlab code.
The presented
solution
demonstrated an
average degree of
difficulty that would
e an average
professional to
implement.
Some of the results
were obtained
using Matlab code.
The presented
solution
demonstrated a
low degree of
difficulty that
would be easy
to implement.
Minimal
number of the
esults were
obtained using
Matlab code.
The presented
solution
demonstrated a
poor degree of
difficulty that
would be too
easy to
implement.
No results were
obtained using
Matlab code.
Explanation/
justification
All elements
are present and
well integrated.
Components
present with good
cohesion
Components
present and mostly
well integrated
Most
components
present
Lacks structure.
Demonstration Logic is clear
and easy to
follow with
strong
arguments
Consistency
logical and
convincing
Mostly consistent
logical and
convincing
Adequate
cohesion and
conviction
Argument is
confused and
disjointed
Reference style Clear styles
with excellent
source of
eferences.
Clear referencing/
style
Generally good
eferencing/ style
Unclear
eferencing/
style
Lacks
consistency with
many e
ors
Presentation Proper writing.
Professionally
presented
Properly written,
with some minor
deficiencies
Mostly good, but
some structure or
presentation
problems
Acceptable
presentation
Poor structure,
careless
presentation