ECE 222A – Fall 2017

Antennas and their System Applications


Latest Announcements

12-12:   Final Exam is at 11.30-2.30 pm on Wednesday Dec. 13.

           - Bring blue books(2x). Black or blue ink only.

           - Closed book, closed notes. You can bring two sheets of paper and write anything that you wish on it.

           - Caculators (non-programmable, no plotting functions) are allowed for complex calculations.

           - We will have an overflow room and will let you know at the exam.

12-08:   Due to a mixup, the last lecture will be at 4.40pm to 6pm in Room 2512/Jacobs Hall. 

12-01:   The make-up lecture today is in Jacobs Hall, room 2512(Booker Room) at 4.10-5.30pm. The make-up lecture on Friday December 8 is in Jacobs Hall, room 2512(Booker Room) at 4.10-5.30pm.

11-25:   Grading: As discussed in class, the homework weighting will be increased and the final exam weighting will go down. The new weighting is : Homework 20%, Midterm 35%, Final Exam 45%. Also, the homeworks will be weighted as: Hwk1: 1 Hwk2(a+b): 1.5 Hwk3: 1 Hwk4:1 Hwk5:1 Hwk6(Project): 2.

11-21:   HW5 posted.

11-21:   Due to a critical meeting next Tuesday at 10-12pm, Prof. Rebeiz is not able to give the lecture. Therefore,we will have two make up lectures, one on Dec.1 at 4pm and the other on Dec.8 (time to be determined).

11-15:   The preliminary solution for the Midterm is posted.

11-14:   There is no class on Thursday Nov.16. Lecture for the rest of the term: Nov.21, Nov.28, Nov.30, Dec.1 (make up, room tbd), Dec 5, Dec.7

11-14:   ECE222A overflow room is not going to be posted. Just meet at the classroom and the extra students will walk with me to the overflow room.

11-10:   Midterm is at 11-12.20pm on Tuesday Nov.14.

             -Bring blue books (2x). Black or blue ink only.

             -Closed book, closed notes. You can bring a single sheet of paper and write anything that you wish on it(both sides)

             -Caculators (non-programmable, no plotting functions) are allowed for complex number caculations.

             -We will have an overflow room and will let you know on Tuesday morning.

11-09:   Friday make-up lecture will be in Jacobs Hall/Room 2315 10.40am~12pm(turn right after the elevator). We will keep the main-entrance Jacobs Hall doors open for you from 10.30am to 10.45am.

11-01:   Due to a schedule conflict, the Nov.10 make-up lecture is now at 10.40am~12pm(in WLH2114). If we find in the morning that it is locked due to Univ holiday, then we will post on the web the location of a new room in the Jacobs Building and we will open for main building doors for you.

11-01:   HW3 posted and due on Thursday Nov.9.

10-31:   Make-up lecture: Friday Nov.10 at 9.30-11am in Room 2114/WLH.

10-28:   Schedule for the coming two weeks: Tuesday October 31: Class; Thursday Nov.2: Class( Prof Sievenpiper); Tuesday Nov.7: No Class; Thursday Nov.9: Class; Friday Nov.10: Make-up Lecture(room tbd); Tuesday Nov.14: Midterm exam.

10-27:   Midterm Date Change: The ECE222A midterm has been changed to Thursday November 16.

10-26:   Make up on 10/27/17 lecture is at 4-5.20 pm (we can do it at 4.10-5.25pm) in WLH 2112. Hwk_2B posted and will be due on Tuesday October 31st.

10-19:   HW2 Solution posted

10-13:   Make-up lecture will not be on Friday October 20, but it will be on Friday October 27.

10-13:  ‘’Due to missing lecture on Tuesday next week, this is ''half a homework'' and is due  next Thursday''. ''No lecture on Tuesday October 17. Make up Lecture on Friday October 20 at 4.10 to 5.30pm. Room TBD.''

10-12:  OH have changed to 1.30-3pm for Professor. No lecture on Tuesday October 17. Make up lecture is on Friday October 20 at 4.10-5.30 pm. HW1 solution posted.

10-11:  See HW1-v2 for corrections/clarifications underlined.

10-10:  Midterm is on Nov.7 in class(11 to 12.30pm).

10-3:    HW1 posted and due on Thursday October 12.

10-1:    TA details updated.

9-26:    Welcome to ECE 222A - Fall 2017.


Course Information


Instructor:    Prof. Gabriel M. Rebeiz

                   Jacobs Hall (formerly EBU-1); Room 5608

                   Tel: 858-534-8001



Office Hours:    Tuesdays and Thursdays at 1.30-3:00 pm and by appointment,

                       Room 5608 Jacobs Hall



TA:  Yusheng Yin (


TA Offices Hours: Tutoring Center 5101, Jacobs Hall

                          Office Hours Mondays and Wednesdays, 3:30-5 pm


Lectures:    Tuesdays and Thursdays, 11:00 am - 12:20 pm, Warren Lecture Hall 2114


Lecture Notes:    Download on this website.  Lecture notes are required.


Textbook:    Not required.


Other books:    Antenna Theory: Analysis and Design, Balanis, Wiley, 2005

                      Antenna Theory and Design, Stutzman and Thiele, Wiley, 1998 (3rd edition, Wiley, 2013)

                      Antenna Theory and Design, Elliott, Wiley-IEEE, 2003

                      Antenna and Radiowave Propagation, Collin, McGraw Hill, 1985

                      Antennas for All Applications, Kraus and Marhefka, McGraw Hill, 2001


Software:    It is expected that you know Matlab, Mathematica, or Maple, etc.


Homework:    About 6-7 homeworks will be assigned.

                    Homework is due at the beginning of the lecture (not at the end).

                    Homework solutions will be posted about 12 hours after the due date.

                    Late homeworks will not be accepted except by permission from Prof. Rebeiz.


Grading:    15%    Homework

                35%    Mid-term       Thursday Nov. 2nd or Tuesday Nov. 7.
                50%    Final Exam    Wednesday 13 Dec 2017,  11:30 am - 2:30 pm, Location TBD

                All exams are open notes and open books.  Bring your class notes and any cheat-sheets that you wish to write, and any book that you wish.

                However, I do not recommend that you bring books with you.  You will not use them.



Decent math background in differential equations and complex numbers.

Undergraduate EM (Physics and ECE 107)

Knowledge of Maxwell Equations and Basic Waves.


Review material:

Review Maxwell's Equations and a Wave Chapter in any available undergraduate textbook.


Thoughts for the homework:

The homework will be graded very generally.  That is, we will assign 10, 8, 6, 4, 2, and 0 as grades with the following guidelines: 10 (Well done to mostly done), 6 (about half of it is done), and 0 (not much is done or homework is not given).  Late homework are not allowed unless by permission from instructor by email.



Course Outline

222A Antennas and Their System Applications

(Prerequisites: None, except a standard EM sequence at the undergraduate level. Communications people should be encouraged to take this course.)


- Introduction to Antennas: Gain, Directivity, Solid-angle, Impedance, Polarization, etc.

- Friis Transmission and Radar Equations: Some System Examples

- Review of Maxwell’s Equations, Reciprocity (important to antennas)

- Plane waves, Polarization, Wave Impedance, Poynting Vector

- Radiation and Free-Space Green’s function, Vector and Scalar Potentials

- Dipoles and Loops, Impedance of dipoles and loops

- Ground planes and Image Theory (introduce a bit arrays using image theory)

- Traveling-Wave Antennas (radio amateur antennas and near-horizon communications)

- Array Theory and Phased Arrays: Use signal processing techniques to analyze arrays (gain, tapered distribution, amplitude and phase error effects, 1-D and 2-D arrays, etc.)

- Mutual Impedance in Arrays: The emf method. Not a lot of coverage, but enough to understand it.

- Classic Antennas:  Dual-Dipole over a ground plane (symmetric pattern, array theory),

                             Dipole backed by a corner reflector (array theory),

                             Yagi-Uda (mutual coupling effect),

                             Log Periodic (endfire feeding),

                             Helical antennas (traveling waves on a circle and end-fire feeding arrangement),

                             Spiral antennas (wideband self-mapping),

                             Inverted F-Antennas (cell phones),

                             antennas for circular polarization (other than the helical antenna)

- Equivalence Principle and Slot Antennas (do not cover cavity backed slots)

- Microstrip Antennas: The two-slot model (do not cover cavity model), Microstrip antenna arrays.

- Miniature Antennas (Cell phone applications)

- System level applications of antennas (MIMO, Multi-Beam, Phased Arrays, etc.)




Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 4a

Lecture 5

Lecture 6

Lecture 7

Lecture 8

Lecture 9

Lecture 10

Lecture 11

More Antennas

Loop and Helix Antennas

Far field reflectors

RFID tutorial

Lecture 12

Slot antennas 1 2 3

Lecture 13

Horn antennas Square Circular

Lecture 14

Small Antennas 1 2

Miniature PIFAs 1 2 3

Multiband Antennas 1 2

Human Absorption of Radiation 1 2 3 4

Reflector and Lens Antennas 1 2


Additional Resources

Microstrip antenna and arrays:

Additional info on microstrip antennas

Planar 2-D microstrip arrays

Honest Miniature antennas by Mitsubishi Corp: GHz MHz

Picture of a 70-meter Deep Space Comm. Antenna at Goldstone, CA
A web-site with lots of nice information
Some Matlab codes:

Matlab codes for 2D radial pattern plotting

Matlab codes for 3D integration and plotting

Matlab codes for 3D pattern plotting


Some Matlab examples (very useful for homework):

An example for plotting 2D normalized pattern polar plots in dB

Matlab routine (polar_dB.m) for 2D normalized polar plots in dB


Homework 2B    Solutions

Homework 3        Solutions

Homework 4      Solutions

Homework 5       Solutions

Homework 6     

Midterm         Midterm_Solution

Final              Final_Solution

Fall 2012 
Fall 2011 


Fall 2010
Homework 6    


Academic dishonesty


Cheating, plagiarism and any other form of academic dishonesty will not be tolerated. This includes cheating on exams, using resources that are not allowed, copying lab reports or results, copying all or part of another group’s simulations or bread boards, lying to tutors/TAs or instructor, aiding in plagiarism or cheating, or any form of dishonesty. You may help each other with the homework (it does not need to be handed in). On the labs, you may consult each other. For example, you can ask how someone else went about solving the problem. You should not copy their solution or allow your solution to be copied. Once you have solved a problem yourself, you may compare and discuss. In short, you should do the work yourself and you can ask assistance from others. The TAs and tutors give you the same level of support (and this is a good yard stick for you to know what is allowed in terms of helping and what is not). Never claim work/ideas to be yours if they are not, and never assist others in cheating (e.g. by offering them your solutions). If you are not sure of what is allowed, ask the instructor. Wrong assumptions are never an excuse. There is a zero tolerance policy. Cheating on labs results on a zero credit on all labs; cheating on quizzes, the final exam or multiple labs will result in a possible F in the class. All cases of cheating will be reported to the department and your college. You risk possible suspension from UCSD.