## EE 135 Electromagnetic Fields and Waves - Winter 2007

### Instructor: Toshishige Yamada, Ph.D.(EE), Sr. Scientist, NASA Ames

### Teaching Assistant: Shirin Zarrabi

#### Handouts

- Course Syllabus
- Lecture Notes 1 & 2
- Lecture Notes 3
- Lecture Notes 4
- Lecture Notes 5
- Lecture Notes 6
- Lecture Notes 7
- Lecture Notes 8
- Lecture Notes 9
- Lecture Notes 10
- Lecture Notes 11

#### The Latest Messages

- Anybody can submit an extra credit report. If you are not sure, just prepare and submit. (March 14)
- For preparation for the Final, please check exam preparation memo . I will be updating this until the day before the Final. (March 15)
- Careful review of Midterms #1 and #2 will certainly be rewarding. (March 16)
- Final on 3/20 (Tu), 12:00-3:00 in the same room (#194). The starting time is 12:00, not 12:30. Closed textbook/notebook, no calculator, but two formula sheets allowed. (March 16)
- I have updated exam preparation memo . (March 19)
- In the Final, there was a lot of misunderstanding for the TML problem and the transformer problem. For the TML, all the textbook results are derived for z = -l and z = 0. If we label left-right differently, the equations need adjustments. For the transformer, the voltage relation, the power relation, and the Ohm's law are all valid. (March 28)
- There was inquiry for the lab grading. The average scores for Lab #1, 2, and 3 were 18.0, 19.4, and 17.2, respectively. The average total score was 54.6, and the median was 55. Based on the total score, A+ (60-57), A (56), A- (55), B+ (54), B (53), etc. were given. (March 28)
- The median scores for Lab #1, 2, and 3 were 18, 20, and 17, and the median total was 55. The score distribution had two sharp peaks at 56 and 54. (March 30)

#### Exams

- Midterm #1 on 2/6 (Tu), one formula sheet, closed notes, closed books, no calculators. (Jan 30)
- Chaps. 1 & 2, & vector math, complex numbers (initial quiz level) (Jan 30)
- The conceptual understanding of the following is critical: wave functions, longitudinal & transverse waves, attenuation, circuit analysis with phasor, TML general phasor solutions and BCs, standing waves and interference, voltage reflection coefficient, opencircuit, shortcircuit, and matching terminations for TML, vector analysis, complex number math, etc. (Jan 30)
- Midterm #1 is on 2/6 (Tu), 8:00-9:45, the same room. If you have a technical question, send me email. I will check email during the weekend, too. The reply will be posted on this web. (Feb 1)
**Check this memo for exam preparation. (Feb 1)**- Midterm #1 covers up to p.63 of the textbook. Check the memo for detail. (Feb 1)
- Midterm #1 solution and score weighting (Feb 6)
- There were growing concerns for Midterm #2 grading. As I have been stressing, the scores will be curved (the formula to be announced). I understand it was much tougher than Midterm #1. Technically, you want to be able to write down the starting equation correctly using a designated coordinate system. If you had trouble with the first question of each problem (writing down the starting equation with vector dl, vector dS, vector R in formulas in the given coordinate system), you want to review carefully. Now we can use even computers for calculations, but you absolutely need to know which equation to solve and which BC to use in advance. If a clear strategy is shown, partial credit has been given. Some are in fact benefitted by this. (March 7)
- Midterm #2 solution and score weighting (March 8)

#### Homework

- HW Assignment & Comments (Hints)
**Please check this peridically for any updates.** - For those who do not have a textbook yet, HW #1-1 HW #1-2 HW #1-3
- HW #1 solution
- HW #2 solution
- For those who did the old assignment of HW #2, please redo HW #3. They want to review undone problems in HW #2 by themselves using the solution. (Jan 31)
- HW #3 solution
- HW #4 solution
- HW #5 solution
- HW #6 solution

#### Laboratory Sessions

- The following is a planned schedule for the lab sessions. All
the sessions are from 4 pm - 6 pm. Attendance for the
**designated session**is critical for credit. If there is an uncontrollable conflict please let us know**in advance (by Friday)**. - Please check your designated sessions lab roster
- Please print out the relevant manual/report and attend the lab session.
- lab #1 manual/report lab dates on 1/22, 1/24, report due on 2/8
- lab #2 manual/report lab dates on 2/5, 2/7, report due on 2/22
- lab #3 (typo, this is #3, not #4) manual/report lab dates on 3/5, 3/7, report due on 3/15

#### Old Message Storage

- Textbook: F. T. Ulaby - Fundamentals of Applies Electromagnetism, 2004 Media Edition ISBN 0-13-185089-X. The bookstore will have copies in 3 days and the price is about $93. This is a little cheaper than the 2006 ed. If you want to buy the 2006 ed., probably the problems are added and renumbered, so you want to make sure you have the correct set of problems for each HW assignment. (Jan 4)
- You should be comfortable with Math Quiz today - inner product, outer product, divergence, and curl. If you know Gauss's theorem and Stokes's theorem, that is super. (Jan 4)
- Please send me an email if you need a permission code. You could choose either lab session temporarily. (Jan 9)
- On Jan 11, we will schedule the lab sessions. (Jan 9)
- We will look at the phasor technicque. Please review complex numbers, and the polar coordinate representation. (Jan 9)
- Lab session candidates: Fri 1-3, Tue 4-6, Wed 4-6. Tomorrow, you will indicate your preference. We will select two slots that are most popular according to the result tomorrow. Please email Yamada immediately if nothing works. (Jan 10)
- It tunrs out that Fri 1-3 is extremely unpopular, but some people can make only this slot. Tue 4-6 has been occupied by another course. We will conduct another sign-up on 1/16 (Tu) (Jan 11)
- You want to be comfortable with the phasor technique, because this will be used in the transmission lines in Chap. 2. (Jan 11)
- New time slot candidates are, Mon 2-4, Mon 3-5, Fri 3-5, Mon 4-6, & Fri 4-6, in addition to the previous Wed 4-6, Thu 4-6. On 1/16 (Tu), we will conduct a sign-up again and choose the most appropriate two time slots. FYI, Tue 4-6 and Wed 12-2 have already been taken by another course. (Jan 12)
- In the phasor technique, the inversion from the phasor to the time-dependent function may require some practice. This is the "price" we pay for very easy temporal differentiation and integration (no free lunch). Let us be familar with the procedure. (Jan 16)
- Please check the lab roster below and attend your designated session, because resources are limited and must be shared. (Jan 17)
- The first lab session is next week 1/22 & 24. Please check the roster and find out your date, and bring a printed manual/report #1 with you to BE 161. (Jan 19)
- We are studying the transmission line physics with an equivalent circuit model. We call exp(-gz)
a
**right-going (+)**wave because of exp(jwt) in the phasor (if we had adopted exp(-jwt) in the phasor, then exp(-gz) would have been a**left-going (-)**wave. Why?). It is a little awkward, but let us get used to this definition. (Jan 22) - After having a general wave solution y(x,t), what matters is the boundary condition. We will consider vanishing (y = 0), free (dy/dx = 0), & reflectionless (matching) conditions. (Jan 23)
- If you feel that you have trouble in understanding, do not wait until the exams are over.
Use the office hours earilier - it is a seminar style. Typically you will present
an issue you have trouble with. Then I will find a much simpler problem having the same elements
according to the KISS rule.
You will solve it in front of me (and other students), so you will never forget.
__Challenging__(e.g., the textbook is wrong) is of course welcome, too. (Jan 23) - There was a question for P2.5. In there , we need to find a square root of a complex number. The easiest way to do this is to use the polar representation. For example, z = x + jy = sqrt(x*x + y*y)*exp[j*arctan(y/x)] = r*exp(j*theta). Thus, sqrt(z) = sqrt(r)*exp(j*theta/2). Now arctan is a multi-valued function. We usually choose so that the value is between -pi/2 and pi/2. (Jan 24)
- Midterm #1 is on 2/6 (Tu), 8:00-9:45, in the same room. If you have a technical question, send me email. I will check email during the weekend, too. The reply will be posted on this web. (Feb 1)
- Check this memo for exam preparation. (Feb 1)
- Because of the midterm #1 on 2/6, there is no HW for this week. But lab #1 report is due on 2/8 (Th). (Feb 1)
- For those who did the old assignment of HW #2, please redo HW #3. They want to review undone problems in HW #2 by themselves using the solution. (Jan 31)
- Midterm #1 covers up to p.63 of the textbook. Check the memo for detail. (Feb 1)
- Regarding the midterm #1, there was a question regarding "no serious calculations." Basic calculations are of course necessary. You could interpret it as no serious numerical calculations (this is necessary because we do not use calculators). You want to be familiar with vectors, matrices, complex functions, and calculus at the prerequisite course level. (Feb 3)
- Doing a problem has two aspects: considering the algorithm to reach the final asnwer and considering the background of the problem - why is the problem possible, if we remove this condition, what happens, etc. Everybody does the first part, but doing the second part is quite rewarding, not only for the exams, but for ourselves. We can feel we understand something well. (Feb 3)
- Lab session #2 on 2/5 & 2/7. Please print out the manual/report #2 below. (Jan 30)
- Lab #1 report hints: 2.1.2 ar is a radial vector and is parallel to vector OP. If the field has this property, it is called a central force field. 2.3.3 The potential is proportional to |Q1|/(x+1)-|Q2|/(x-1) = |Q2|*[k/(x+1) -1/(x-1)] (Why?). In order to find a max, we need to differentiate this and set it to zero. Then, you should get the given result. (Feb 1)
- Midterm #1 solution and score weighting (Feb 6)
- There was confusion for the longitudinal/transverse issue. I should have used a different variable for y. Some people thought because y and z are perpendicular, the wave is transverse. As long as the wave displacement and the propagation are clearly mentioned, the answer is considered technically correct. (Feb 6)
- We will finish Ch.3 on Thursday (2/8), and finally move into EM fields and waves from the next week. (Feb 6)
- Lab report #1 due on 2/8 (Th). (Feb 6)
- There was confusion for left-going right-going waves in the textbook description. The best way is to fix the argument and see what happens to z if we increase t. If z increases, it is a right going wave. (Feb 8)
- Regarding midterm #1 grading, logical flow is evaluated for answers which did not reach the correct conclusion. So some may have received more points than expected, and vice versa. In the reasoning section, a discussion is necessary to support equations. (Feb 8)
- HW #4 posted HW #4 (Feb 8)
- 3.17 and 3.18 require to sketch the vector fields. An example of vector field representation is Fig. 3-25 at p.133. The purpose of doing this is to develop intuition for div and curl. (Feb 10)
- For those who visited EE 251 during the office hours last week and forgot something there, please go to the EE Department Service and pick it up. (Feb 12)
- Hints for HW #4. In the Cartesian coordinates, phi hat is (-sin(phi),cos(phi),0). Thus, r*(phi hat) = (-y,x,0). In the arrow representation of the vector field, you need to place a field vector using that point as a starting point of the vector. The direction and the magnitude of the field should be reasonably accurate (the results will be schematic). In the Gauss and Stokes problems, it is necessary to find out the magnitude of ds for each face or dl for each segment. For example, the face with x = 1, -1< y <1, -1< z <1 must have vector ds with the magnitude of dydz and the direction of x hat. The surface integratin will be performed for E dot ds with -1< y <1, and -1< z <1. Repeat a similar procedure for all other surfaces. Then add them up. This must be the same as the integration of divE with respect to dxdydz at -1< x <1, -1< y <1, and -1< z <1. (Feb 13)
- HW #5 due on 2/22 (Th) assigned. (Feb 15)
- Lab #2 report due on 2/22 (Th) (Feb 15)
- Midterm #2 will be on March 6. E-fileds with Coulomb's law and Gauss's law and B-fields with Biot-Savart's law and Stokes's law will be main topics. We are interested in highly symmetric cases, so that cylindrical (symmetric with respect to phi) or spherical (symmetric with respect to theta and phi) coordinates are important. (Feb 17)
- Midterm #2: If an integration is difficult, a formula will be given (this will be done in class as needed), but you want to be able to write down the starting equation correctly. The vector cross product appears everywhere. Make sure you are comfortable with it. There is confusion, but I grade all exams. (Feb 22)
- HW #6 due on 3/1 (Th) assigned. (Feb 22)
- HW Assignment & Comments (Hints)
- HW #5 solution posted below. (Feb 24)
- It is a good time for you to focus on understanding rather than memorizing. If we want to import results, we always have to cook them - converting variables and modifying details. Sometimes we try to use them for undue cases violating the initial assumptions. This is very painful. It is much easier to write a program from the beginning rather than fixing a program giving errors permanently. (Feb 27)
- No HW due on 3/8 (Th) because of Midterm #2. (March 1)
- One formular sheet allowed for Midterm #2. Two formula sheets allowed for Final. (March 1)
- Check this memo for exam preparation. (March 4)
- Do not memorize but understand with clear mental images. Exam questions are made so that you can comfortably answer if you understand well, but you will be confused if you memorize everything. If you plan to spend the same time for exam preparation, it is much more rewarding to spend it for understanding. (March 4)
- There was an inquiry on if Midterm 2006 problem set can be distributed. I did not, do not, and will not distribute it for the reason above (the question style/format will be drastically different). You may be able to find Midterms 2005 or before on the EE 135 web if you desparately want a previous example. But I do not know how rewarding it is. For Midterm #2 in 2007, I strongly recommend using exam preparation memo . I further added at 10 pm Sun, so even though you have seen this before, please check it again. (March 4)
- There was a question about (R hat) in Biot-Savart. (R hat) is a unit vector defined by (R arrow)/(R magnitude). What are the starting and ending points of (R arrow)? (March 4)
- Lab #3 on March 5 and 7. (Feb 24)
- You really do not have to worry about the absolute score. The scores are curved as needed. If you have a few strong subjects, then it is good. (March 5)
- There were growing concerns for Midterm #2 grading. As I have been stressing, the scores will be curved (the formula to be announced). I understand it was much tougher than Midterm #1. Technically, you want to be able to write down the starting equation correctly using a designated coordinate system. If you had trouble with the first question of each problem (writing down the starting equation with vector dl, vector dS, vector R in formulas in the given coordinate system), you want to review carefully. Now we can use even computers for calculations, but you absolutely need to know which equation to solve and which BC to use in advance. If a clear strategy is shown, partial credit has been given. Some are in fact benefitted by this. (March 7)
- I will talk about an extra credit project tomorrow (the purpose and the content to be announced tomorrow). (March 7)
- HW #6 solution posted. (March 7)
- Detailed review of Midterm #2 will be given tomorrow. (March 7)
- Midterm #2 solution and score weighting (March 8)
- Extra credit project due on 3/15 (Th). A report regarding an EM field topic would be appropriate. Must be typed single-space with a few pages. An example would be new solution using a different method for previous midterm problems or texbook problems. (March 8)
- We will finish Faraday's law and develop conceptual understanding of EM waves. (March 8)
- Because of the lab #3 report and Final (and extra credit project for those who are planning), there is no need to turn in HW 7 & 8, but please review by yourself. (March 8)
- HW Assignment & Comments (Hints)
**Please check this peridically for any updates.** - For final preparation, please check exam preparation memo . (March 12)
- Lab report #3 due on 3/15 (Th). Extra credit project (for those who are interested in) due on 3/15 (Th).

#### General Class Information

Class Newsgroup:- NEWSGROUP - for announcements, general discussion, and help

Instructor:- Name: Toshishige Yamada, Ph.D.(EE) (EMAIL)
- Phone: 459-3844
- Office: BE 251

Instructor Office Hours:- Tu & Th, 9:45 - 11:45 at BE 251

Teaching Assistant(s):

- Name: Shirin Zarrabi (EMAIL)
- Office: E2 244

Office Hours:- DAYS, TIMES