ECE 222A – Fall 2016

Antennas and their System Applications


Latest Announcements

12-16: Final Average was 53.

12-5:   Due to popular demand, hwk 6 is now due on Friday Dec. 9 at 8am

12-3:   Review session is on Monday Dec. 5 at 7-8pm in Jacobs Hall 4309

12-3:   Final exam is on Wednesday 12/07/2016 at 11:30am-2:29pm in WLH 2115 (NOT our regular classroom). Closed book, closed notes. Bring at least two Blue Books. You can bring your one page double-sided cheat sheet. No programmable calculators allowed, but standard scientific calculators are OK. NO PENCIL is allowed, and only blue or black pens please.

11:29: ECE222A review will occur on Monday Dec. 5 at 7-8pm in 4309 Jacobs Hall

11:24:  For Problem 3, the quadratics phase-delay peaks at x=0,a, or x=+/-a/2 (depending on where you take your coordinates). Basically, it occurs at the edges of the aperture.

11-22:  HW6 is uploaded. HW5 is due next Tuesday.

11-20:  Makeup class on Monday Nov. 21 at 930-1050am in 4309 Jacobs Hall

11-15:  Midterm solution has been posted.

11-14:  There will be no TA office hour taking place today.

11-12:  HW5 is Uploaded.

11-7:   TA would be available on Monday 11-7 from 12:30-2:00 instead of regular office hours. For those who cannot attend and need assistance there will be another office hour provided upon request.

11-5:   There is no homework this week. Relax after the midterm (a bit). Midterm grades will be given on Tuesday Nov. 15.

11-2:   HW4 Solution is posted.

11-2:   HW4 submission will take place in TA office hours which is extended to 4:30 today.

11-1:   For the midterm, please bring your Blue Book. You can bring your One Page double sided cheat sheet. No programmable calculator. Normal calculators are allowed. NO PENCIL is Allowed. Bring your pens please.

10-29: HW3 Solution is uploaded.

10-28: Hw4 is uploaded.

10-27: HWs can be submitted on Friday 28th from 11AM - 2PM at Jacobs Hall Room 5101D (the back left cubicle of the Tutoring Center).

10-25: October 26 make-up lecture at 930-11am is in Jacobs Hall/Room4309

10-24: We will have two more make-up sessions and this will be it for the rest of the term: Wed. October 26 at 930-11am, and Monday Nov. 21 at 930-11am.

Put on your calendar that there is no class on Tuesday Nov. 8 and on Thursday Nov. 17. Prof. Rebeiz will be on travel.

10-22: HW2 Solutions are posted.

10:21: Hw2 solutions will be posted tomorrow.

10-21: Hw3 due is on Friday 28th according to the HW pdf document.

10-21: make-up lecture on Monday October 24 is cancelled. See you in class on Tuesday October 25.

10-20: HW3 is uploade. Due day is on Thursday 27th.

10-17: No classes on October 18 and 20.

Homework to be given on Friday to the TA, Omid, By 2 PM at Jacobs Hall Room 5101D (the back left cubicle of the Tutoring Center).

10-13: make-up sessions are scheduled on October 14th and 24th at 930-11am are now reserved in room 2315/Jacobs Hall

10-13: HW1 solution has been revised for Q4 and Q5. 

10-12: For HW2 Problem 3, Assume that one dipole is oriented towards x axis and the other one z axis with -l/2<z<l/2 instead of -l/2<y<l/2.

10-12: New Homework 2 with added corner reflector problem posted (see 6c)

10-10:The class has been moved to WLH 2115 (Warren lecture hall). See you there.

10-7:  HW2 is posted.

10-7:  homework will be posted late Friday.

10-6:  Prof. Rebeiz will not have OH on Thursday (today). He is on travel.

10-4:  There is no lecture on Thursday. Hw 1 submission will be taken place during the class in the hallway in front of Prof. Rebeiz office.

10-4:`Office hours today will be at 6-730pm in Prof. Rebeiz office.

10-1:  Please follow this link and download Matlab for your UCSD work.

9-30: make-up sessions are scheduled on October 14th and 24th at 930-11am are now reserved in room 2315/Jacobs Hall.

9:30: make-up sessions are scheduled on October 5 and 12th at 930-11am in room 4309/Jacobs Hall.

9-30: No pencils allowed. Homework written in pencil will be returned ungraded.

9-30:  Matlab is recommended for the homework assignments, and you can get a student version from the bookstore, or download a student version from the web (for a small fee). I am also working with JSOE to give you access to Matlab, but this may be on JSOE computers only. Will announce in class. (you can use other software if you wish, but Matlab is recommended).

9-29:  Homework 1 is uploaded and is due Thursday October 6, 2016.

9-28:    The hwk will be posted on Thursday late afternoon. Prof. Rebeiz wants to cover a few more things on Thursday before Hwk 1.
9-25:    Mid-term date, TA details and office hours updated.
9-22:    Welcome to ECE 222A - Fall 2016.

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:  Omid Erfani (

TA Offices Hours: TA office hours will be in Jacobs Hall Room 5101D (the back left cubicle of the Tutoring Center)

                          Mondays and Wednesdays at 2:30 - 4 pm


Lectures:    Tuesdays and Thursdays, 11:00 am - 12:20 pm, Sequoyah Hall 148


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 3 Nov 2016
                50%    Final Exam     Wednesday 7 Dec 2016,  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


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.