EE351 homework info page

EE351 Homework Information

PE #1:

10.1: Fig. 10.4 isn't quite right. The wavelength is 3pi, but pi/4 is incorrect.
10.2
10.3
10.6: The conductivity of aluminum is given in Appendix B, p. 737, of the textbook.

PE #2 [Revised 2/9/03]:

10.10: Part (c) is really time average power density. (The author doesn't seem to distinguish between power density and power.)
10.11
Problem handed out in class (download problem). Answers: (a) d = 6.7196 m, (b) E_t = 15.7816*exp(-2.8092z)*cos(omega*t - 2.8106z + 0.7833) V/m, (c) E_r = 2988.84*cos(omega*t + 0.01048z + 3.1379) V/m . These were obtained using the general equations, but you can also use the special case (good conductor) equations. If you do, your answers will differ just a little (e.g., alpha_2=beta_2). To help you debug your problem, I got gamma = 0.9962793/179.7865 deg.

Prob. 1, 12.3: (a) There should be 23 propagating modes. (Or at least that's what Yanqiu and I both got.) The answer in the back of the book only give 18. (b) I got TE_15 and TM_15 for the highest propagating modes.
Prob. 2, 12.4: Aspect ratio means ratio of height to width (a x b).
Prob. 4, 12.6(b): Find the modes greater than TE_01 (i.e., whose cutoff frequencies are greater than 12 GHz).

PE #3:

Homework #4, Revised 3/10/03

Prob. 2 (13.4(a)): Be careful with this one. I had two false starts. Note that since I isn't constant but changes as a function of z, you have to integrate it. The integral is of the form int{I_0*(1-2|z|/l)dz} from -l/2 to l/2. You end up with an expression for the current that you then use in the formula for A_z_s (it replaces the constant I_0 we had before). The result is A_z_s = [(mu_0*I_0*l)/(8*pi*r)]*e^(-j*beta*r) Wb/m.
Prob. 3 (13.5): Since the current is constant, assume a Hertzian dipole.
Prob. 4 (13.11): TYPO in problem and answers at back of book!!! f = 100 MHz (and even so, it's really not the far field). However, use the far-field equations. Note that they don't give a theta (nor is a value implied by the problem), so assume E_max = 50 mV/m which occurs when theta = pi/2. Answers I got (no guarantees): (a) 90.7074 uA, (b) 250 uW.
Prob. 5: Delete.
Prob. 6: Delete parts (c) and (d). Clarification for part (b)--describe the 3-D radiation pattern.
Prob. 7 (13.12): The wording on this problem is confusing. What they mean is that you should plot the field patterns as opposed to the power patterns, but you should plot the E-plane and H-plane values of the fields.

Prob. 1 (13.18): Note that f(theta) is missing a factor of 1/2 (i.e., you need to divide the expression given by 2).
Prob. 2 (PE 13.3): To find the directivity, use the definition D = U_max/U_ave. Find U_max using P_ave and find U_ave by finding P_rad (i.e., you need to integrate).
Prob. 3 (13.23(a)): The answer for D should be 1.5.
Prob. 3 (13.23(c)): The answer for D should be 33.0233.
Prob. 4 (PE 13.6(b)): The answer for the group pattern should be |cos[(pi/4)cos(theta)-pi/4]|.
Prob. 6 (PE 13.8): The answers should be 107.4296 m^2 and 27.925 nW/m^2,

Prob. 1 (13.30): Note that the arrays are horizontal (i.e., in the x direction), so (assuming you use the equations for the vertical arrays given in the book), you need to measure theta from the positive x axis.
Prob. 4 (PE 14.1): Note the typos in the equation for s_0. S_11 should be replaced by S_22.
Prob. 6 (14.3(a)): The answer should be 0.33-j0.16. The answer to part (b) is a little different, but it's close enough.
Prob. 7 (14.8): Conductivities are given in Appendix B on p. 737. delta = 1/sqrt(pi*mu_0*f*sigma) for part (b).

Homework #8 Note that you must turn in your code for this assignment.

Homework #9 Revised 4/20/03 Note that you must turn in your code for this assignment.