EEE 643: Advanced Topics in Electromagnetic Radiation
Fall 2017, Professor Constantine A. Balanis


Course information, announcements, problem sets, exams, etc. will be made available as the semester progresses.

This site will be updated throughout the semester.

  LAST UPDATE:  July 1, 2016. See Announcements for information.


 
 

Table of Contents

Syllabus
Announcements and Important Dates
Lectures & Homework, Tests and Final Exam Solutions
Homework Sets



Announcements and Important Dates:

Test #1: .................. Totally INDIVIDUAL Effort. Part In Class and Part Take Home.
1:  Covers material through Chapter 12.  

Test #2: ......................
1:  Covers material through Chapter 13.  
2:  Open Class Text Book and Class Website Notes ONLY; everything else is not allowed.  

Final Exam: .............................
1:  Covers material from Chapters  
2:  Open Class Text Book and Class Website Notes ONLY; everything else is not allowed.  


Homework Sets:

Homework #1: Due: Totally individual effort (at the beginning of the class).
1:  Starting with (12-121) derive (12-123) where R is given by (12-123a), showing all the details.

Homework #2: Due: ................... Totally individual effort (at the beginning of the class).
1:  Starting with (12-124) derive (12-126), showing all the details.

Homework #3: 40 Points. Due: ......................... Individual effort.
a:  Write a Matlab computer program, name it Line Strip, to solve the EFIE of (12-17a) of a line source above a finite PEC strip of width w. Use point matching-collocation method. The basis/expansion function should be rectangular pulses. The program should be interactive, whereby questions are asked sequentially about what is the the width of the strip (in wavelengths), then the height of the line source about the strip (in wavelengths), then the thickness of the strip (in wavelengths), and then the number of segments (N=integer).
b:  The output should be the normalized (relative to the wavelength) linear current distribution, both based on the EFIE and the Physical Optics (PO), and a plot of the normalized linear current distribution, like Figure 12-11 in the book.
c:  Once you have computed the normalized linear current distribution, both based on the EFIE and PO, the program should compute the normalized far-field amplitude radiation pattern of (12-22a) based both on the EFIE and PO, like Figure 12-12.
d:  You should submit a hard copy of the program output, including the figures replicating Figures 12-11 and 12-12.
e:  Send me electronically a copy of your program's source code so I can run it to see that it works.
P.S.:  The more user friendly you make your code, the higher the grade. Computational efficiency is also an important factor. The 40 points are reserved for the very best program(s). Use rectangular pulses for the basis/expansion functions. The program should be self contained; i.e., any subroutines should be included with the program.

Homework #4: Due: ........................................... Totally individual effort (at the beginning of the class).
1:  Starting with Equation 13-40(a) derive Equation 13-47, showing all the details.

Homework #5: 40 points. Due: ................... (before the beginning of the class). Individual effort.
  An electric line source is placed a height h above a 2-D PEC strip of width w, with exterior wedge angles (n=2) at edges #1 and #2 (the wedges angle WA1 and WA2 are both knife edges), similar to Figure 13-26.
a:  Write a user-friendly Matlab computer program to compute the normalized (in dB) amplitude patterns based GO and GO+UTD for the finite width strip, and GO for the infinite width strip, similar to those in Figure 13-27. The program should interactively ask for the width of the strip (in wavelengths), the height of the line source above the strip (in wavelengths), and the two wedge angles WA1 and WA2 (in degrees) (n=2).
b:  For a PEC strip with w = 2 x lambda, h = 0.25 x lambda, and WA1 = WA2 = 0 degrees (knife edges), compute and plot the normalized amplitude pattern based on GO and GO+UTD for the finite width strip, and GO for the infinite width strip, similar to those in Figure 13-27. Plot and compare, on the same figure with the others, the pattern based on EFIE/MoM of Homework #3.
c:  Repeat Part c for a PEC strip with w = 2 x lambda, h = 0.50 x lambda, and WA1 = WA2 = 0 degrees (knife edges). Place the plots for this case (h = 0.5 x lambda) on a separate figure.

Homework #6: 40 Points. Due: ........................... (before the beginning of the class). Individual effort.
a:  Write a Matlab computer program, name it Monopole, based on UTD formulation to computed the normalized (0 dB maximum) amplitude radiation pattern (in dB) of a quarter-wavelength monopole on a finite size ground plane; either square or circular.
b:  The program should be interactive and should ask what kind of ground plane (square or circular), size of the ground plane (entire side of the square GP; radius of the circular GP) (in wavelengths), frequency of operation (in GHz), and for the circular ground plane the angle thetao where the computations based on the two-point diffraction blend with those based on the 'ring-source radiator.'
c:  Using the developed Matlab computer programs, verify the patterns of Figures 13-33 and 13-39. However the program should be able to do any other sizes of ground planes; either square or circular.
  Since the formulations have already being covered in class and can be found either on the website class notes or in the book, it is not necessary to submit the formulations.

Homework #7: 40 Points. Due: ....................... Individual effort.
a:  Write a Matlab computer program, name it StripScatTM, to solve the EFIE of (12-63) for a plane wave incident on a finite PEC strip of width w. Use point matching-collocation method. The basis/expansion function should be rectangular pulses.
For each case, the program should be able to compute the linear current density (PO and EFIE) for any incidence angle, normalized bistatic SW (SW/lambda) and the normalized monostatic SW (SW/lambda)dB. The program should be interactive, whereby questions are asked sequentially about what is the the width of the strip (in wavelengths), the incidence angle phii (in degrees), then the thickness of the strip (in wavelengths), and then the number of segments (N=integer). Refer to Figure 12-13(a) for the geometry.
b:  The output should be the linear current density distribution (Amps/meter), both based on the EFIE and the Physical Optics (PO), and two plots, in two separate figures, w = 2 x lambda of the linear current density distribution, like Figure 12-15 in the book. One figure with two curves (one for EFIE and the other for PO) should be for an incidence angle phii=90 (in degrees). The other figure with two curves (one for EFIE and the other for PO) should be for an incidence angle of phii=120 degrees. However the program should be able to compute the linear current density for any incidence angle; i. e., (0 degrees < phii < 180 degrees), and thus any bistatic SW and the monostatic SW.
c:  Once you have computed the linear current distribution, both based on the EFIE and PO, the program should compute for w = 2 x lambda, in 2 separate figures, the far-field normalized Bistatic and Monostatic Scattering Widths (SW/lambda)dB. One figure should be for the normalized Monostatic SW and should have two curves; one based on the current density distribution obtained by the EFIE and the other on that of the PO. That figure should look like Figure 12-16. Another figure should be for the normalized Bistatic SW, with phii = 90 degrees, and it also should have two curves; one based on the current density distribution obtained by the EFIE and the other on that of the PO. That figure should look like Figure 11-5. The other figure should be for the normalized Bistatic SW, with phii = 120 degrees, and it also should have two curves; one based on the current density distribution obtained by the EFIE and the other on that of the PO. That figure should look like Figure 11-5.
Hint:  Because for this polarization you have only one electric field component (a z component), the most judicious definition of the SW will be that of (11-21b).
d:  You should submit a hard copy of the program output, including the figures replicating Figures 12-15, 12-16 and 11-5 for w = 2 x lambda, for both EFIE and PO .
e:  Send me and Alix, electronically, a copy of your program's source code so I can run it to see that it works.
P.S.:  The more user friendly you make your code, the higher the grade. Computational efficiency is also an important factor. The 40 points are reserved for the very best program(s). Use rectangular pulses for the basis/expansion functions. The program should be self contained; i.e., any subroutines should be included with the program.

Homework # SKIP: 40 Points. Due: ...........(before the beginning of the class). Individual effort.
a:  Write a Matlab computer program, name it Wire Charge, to solve the Poisson Integral Equation for the charge distribution of a general length, bend Perfect Electric Conductor (PEC) circular cross section wire of general bent angle alpha (greater than zero - alpha - less than 180 degrees), and of radius a. The program should be interactive, whereby questions are asked sequentially about what is the length (in meters), then the radius (in meters), the bent angle alpha (in degrees), and the number of segments (N=integer).
b:  The output should be the linear charge distribution and a plot of the charge distribution, like Figures 12-2 and 12-4 in the book. You should submit a hard copy of the program output, including the figures replicating Figures 12-2 (a,b) and (12-4) of the charge distribution.
c:  Send me electronically a copy of your program's source code so I can run it to see that it works.
P.S.:  The more user friendly you make your code, the higher the grade. The 40 points are reserved for the very best program(s). Use rectangular pulses for the basis/expansion functions. The program should be self contained; i.e., any subroutines should be included with the program.

Homework #: 40 Points. Due: ...................... Individual effort.
a:  Write a Matlab computer program, name it StripScatTE, to solve the EFIE of (12-74) for a plane wave incident on a finite PEC strip of width w. Use point matching-collocation method. The basis/expansion function should be rectangular pulses.
For each case, the program should be able to compute the linear current density (PO and EFIE) for any incidence angle, normalized bistatic SW (SW/lambda) and the normalized monostatic SW (SW/lambda)dB. The program should be interactive, whereby questions are asked sequentially about what is the the width of the strip (in wavelengths), the incidence angle phii (in degrees), then the thickness of the strip (in wavelengths), and then the number of segments (N=integer). Refer to Figure 12-13(b) for the geometry.
b:  The output should be the linear current density distribution (Amps/meter), both based on the EFIE and the Physical Optics (PO), and two plots, in two separate figures, w = 2 x lambda of the linear current density distribution, like Figure 12-15 in the book. One figure with two curves (one for EFIE and the other for PO) should be for an incidence angle phii=90 (in degrees). The other figure with two curves (one for EFIE and the other for PO) should be for an incidence angle of phii=120 degrees. However the program should be able to compute the linear current density for any incidence angle; i. e., (0 degrees < phii < 180 degrees),and thus any bistatic SW and the monostatic SW.
c:  Once you have computed the linear current distribution, both based on the EFIE and PO, the program should compute for w = 2 x lambda, in 2 separate figures, the far-field normalized Bistatic and Monostatic Scattering Widths (SW/lambda)dB. One figure should be for the normalized Monostatic SW and should have two curves; one based on the current density distribution obtained by the EFIE and the other on that of the PO. That figure should look like Figure 12-16. Another figure should be for the normalized Bistatic SW, with phii = 90 degrees, and it also should have two curves; one based on the current density distribution obtained by the EFIE and the other on that of the PO. That figure should look like Figure 11-6. The other figure should be for the normalized Bistatic SW, with phii = 120 degrees, and it also should have two curves; one based on the current density distribution obtained by the EFIE and the other on that of the PO. That figure should look like Figure 11-6.
Hint:  Because for this polarization you have only one magnetic field component (a z component), the most judicious definition of the SW will be that of (11-21c).
d:  You should submit a hard copy of the program output, including the figures replicating Figures 12-15, 12-16 and 11-6 for w = 2 x lambda, for both EFIE and PO .
e:  Send me electronically a copy of your program's source code so I can run it to see that it works.
P.S.:  The more user friendly you make your code, the higher the grade. Computational efficiency is also an important factor. The 40 points are reserved for the very best program(s). Use rectangular pulses for the basis/expansion functions. The program should be self contained; i.e., any subroutines should be included with the program.

Homework #: 40 points. Due: .............................. Individual effort.
A uniform plane wave, of a given polarization(TMz/soft; TEz/hard) is incident upon a PEC 2-D wedge, of any included angle WA, and of any incidence angle PHIP:
a:  Write a user-friendly Matlab computer program to compute the normalized amplitude pattern based on the exact solution and on GO+UTD. The program should interactively ask for the polarization of the incident wave (TMz/soft; TEz/hard), the interior angle WA of the wedge (in degrees), the incidence angle PHIP (in degrees) of the wave, and the observation distance RHO (in wavelengths) from the edge of the wedge.
b:  For a PEC wedge of 0 degrees included angle, incidence angle of 30 degrees, and an observation distance of 1 wavelength from the edge of the wedge, compute and plot the normalized total amplitude pattern, in polar form and on a dB scale. The figure should be similar to Figure 13-15. However the figure should have two curves; one curve based on the exact solution and the other based on GO+UTD.
c:  Compute and plot the normalized amplitude patterns, in rectangular form and on a linear scale (not in dB). The figure should like Figure 13-24 and should include ALL the curves of Figure 13-24(a). However, it should include two curves for the total field; one based on GO+UTD and one on the exact solution.
2:  Using the same computer program, repreat Problem 1 except for TEz (hard) polarization. The figures should be, respectively, the same as those of Figure 13-14 and 13-24(b).

Homework #: 40 points. Due: ...................... Individual effort.
a:  A hard-polarized uniform plane wave, whose magnetic field amplitude is Ho, is incident upon a two-dimensional PEC strip of width w. You can use Figure 13-27 as a guide. Formulate the problem, using GTD, for the backscattered/monostatic (phi=phi') magnetic field and its backscattering/monostatic scattering width SW.
b:  For a soft-polarized uniform plane wave incident upon a two-dimensional PEC strip, as shown in Figure 13-27, formulate the problem, using GTD, for the bistatic scattered electric field and its bistatic scattering width SW.
c:  Repeat Part b for a hard-polarized uniform plane wave.
d:  Write a user-friendly Matlab computer program to compute the normalized bistatic and bascattered/monostatic SWs (SW/lambda)dB and SW(dBm) for both soft and hard polarized uniform plane waves. The program should be interactive asking questions in sequence about the polarization (soft/hard) of the incident wave, the scattering width (monostatic or bistatic), the width of the strip (in wavelengths), the incidence angle (in degrees) of the wave, and the frequency of operation (in GHz). The angular space for both the backscattering/monostatic and bistatic patterns should be 0 < phi < 180 degrees and 0 < phi' <180 degrees.
e:  Plot the bistatic and backscattering/monostatic patterns for w = 2 x lambda, frequency = 10 GHz, and phi' = 120 degrees for both soft and hard polarized uniform plane waves. For each polarization (soft and hard), the backscattering/monostatic patterns should be in two separate figures; one figure for the soft and the other for the hard. Similarly, the bistatic cases should be in 2 separate figures; one figure for the soft and the other for the hard. In each of the 4 figures, plot and compare, for the respective polarisations, the patterns based on EFIE/MoM SW/lambda(dB) and SW(dBm). There should be a total of 4 figures; 2 figures for soft (monostatic and bistatic) and 2 figures for hard (monostatic and bistatic). Each one of these 4 figures should also include the respective EFIE/MoM scattering patterns (monostatic and bistatic) in SW/lambda(dB)and SW (dBm). For example, one figure should be for the monostatic, soft polarization, and it should have 4 plots [2 based on GTD, (SW/lambda)dB and (SW)dBm, and 2 based on EFIE/Mom, (SW/lambda)dB and (SW)dBm]. The same for the other 3 figures; bistatic (soft), monostatic (hard) and bistatic (hard).
f:  Submit a copy of your formulations (in word.doc format), Matlab computer programs, and the requested figures.

Homework #: 50 Points. Due: ..............(before the beginning of the class). Individual effort.
a:  Develop the formulations, showing all the details, for the program that follows.
b:  Write an interactive Matlab computer program, name it Aperture, based on UTD formulation to computed the normalized (0 dB maximum) amplitude radiation pattern (in dB and in polar form) of an aperture mounted on a finite size ground plane; either square or circular.
c:  The program should be interactive and should ask what kind of ground plane (square or circular), size of the ground plane (entire side of the square GP; radius of the circular GP) (in wavelengths), frequency of operation (in GHz), and for the circular ground plane angle thetao where the computations based on the two-point diffraction blend with those based on the 'ring-source radiator.'
d:  The program should be asking whether the aperture is rectangular (as shown in Table 12.1, columns 2 and 4 of the Antenna Theory book) or circular (as shown in Table 12.2, columns 2 and 3 of the Antenna Theory book). If it is rectangular, it should ask whether the field distribution is uniform (column 2 of Table 12.1) or that of the TE10 mode (column 4 of Table 12.1). If it is circular, it should ask whether the field distribution is uniform (column 2 of Table 12.2) or that of the TE11 mode (column 3 of Table 12.2).
e:  The program should be able to compute, taking into account the GO contribution and the regular diffractions from the edges of the ground plane, for both the E- and H-planes.
f:  Using the developed Matlab computer programs, verify the patterns of Figure 12.33 of the Antenna Theorybook. Place the patterns of this case in one figure of its own. Also perform computations for the cases that follow:
  1. A rectangular aperture, uniform distribution, a =3lambda, b=2lambda, square ground plane each side of 4lambda, E-plane and H-plane patterns; compare with the solution if the ground plane is infinite in size. Put the E-plane patterns in one figure and the H-plane in another figure.
  2. A rectangular aperture, with TE10 field distribution, a =3lambda, b=2lambda, square ground plane each side of 4lambda, E-plane and H-plane patterns; compare with the solution if the ground plane is infinite in size. Put the E-plane patterns in one figure and the H-plane in another figure.
  3. A circular aperture, with uniform field distribution, radius equal to 1.5lambda, square ground plane each side of 4lambda, E-plane and H-plane patterns; compare with the solution if the ground plane is infinite in size. Put the E-plane patterns in one figure and the H-plane in another figure.
  4. A circular aperture, with TE11 field distribution, radius equal to 1.5lambda, square ground plane each side of 4lambda, E-plane and H-plane patterns; compare with the solution if the ground plane is infinite in size. Put the E-plane patterns in one figure and the H-plane in another figure.
  However the program should be able to do any size aperture and/or ground plane; either square or circular aperture and/or ground plane. Also the units of the normalized amplitude patterns should be in dB in a scale of 0 to -40 dB
  If for any plane (E and/or H) there are no regular diffractions, then you should use slope diffractions. Do not use slope diffractions if there are regular diffractions.

Homework #: 40 Points. ...................(before the beginning of the class). Individual effort.
a:  For Homework #9 we assumed that for the circular ground plane, either for a rectangular or a circular aperture of any distribution, the ring radiator part of the pattern in the E-plane can be obtained by assuming the field diffracted at each point of the rim would be the same (uniform) as that diffracted in the E-plane diffraction point. As I had pointed out previously that is not correct but rather a simplification. Actually the field diffracted at each diffraction point of the rim of the circular ground plane consists of two different diffractions; one based on the diffraction of the Etheta component (hard polarization) and one based on the Ephi (soft polarization). Of course in the E-plane the Ephi is zero and you have only Etheta (hard polarization), and in the H-plane the Etheta is zero and you have only Ephi (soft polarization). Actually, for the apertures we considered, even the Ephi component was zero in the H-plane and that is why we need slope diffraction in that plane. Also the Ephi component is equal to zero along the surface of the ground plane for any observation angle phi. Therefore you do not have to account for any regular diffractions from the Ephi component. To make the problem more realistic, for this assignment I want you to revisit the ring radiator part of the circular ground plane and model it as nonuniform diffraction around the rim consisting only of the Etheta (hard polarization) regular diffraction; the Ephi (soft polarization) regular diffraction does not exist since the incident field of the Ephi component along the surface of the GP is zero. At any observation point in the ring-radiator part of the E-plane pattern, the total diffracted field will be sum of all the diffractions from all the points along the edge of the rim for the Etheta component only. This is only for the ring-radiator part of the E-plane pattern of any of the apertures (square or circular) and of any distribution. You do NOT have to do the same for the H-plane part of the pattern using a ring-radiator for the slope diffraction .
  P. S. You will have to use numerical integration to sum all the diffractions of the Etheta component from each point of the rim of the circular ground plane. You cannot assume uniform distribution, as we did before for the monopole on a circular ground plane which led to the Bessel function, because for the monopole we had symmetry; we do not have symmetry for the aperture; i.e., the fields radiated by the aperture are functions of the azimuthal angle phi. The fields radiated by the monopole had azimuthal symmetry; they were not function of phi. Also, in your computer program make the number of integration points variable (an option to select); i.e., you can start with 0.5 degree increments but make it as part of the input so we can change it to any other value.
b:  Therefore, reformulate and submit that part of the circular ground plane modeling for both the rectangular and circular apertures with distributions outlined in Homework #8. I want to see how you formulated the nonuniform part of the ring-radiator part of the circular ground plane for the E-plane of either aperture; rectangular or circular. Remember to take care of the proper normalization so that the ring-radiator part of the pattern blends with that of the two-point diffraction.
c:  Based on the new formulation of the ring-radiator for the circular ground plane, revise/update your previous, Homework #8, Matlab computer program to be able to model the nonuniform ring-radiator. Do NOT erase the uniform radiator part on your computer program. In fact, in each figure include, for comparison purposes, both patterns; one based on the uniform and the other on the nonuniform ring-radiators. Also in each figure, include the corresponding infinite ground plane pattern. Verify the computer program by comparing for the circular ground plane the patterns of all the previous aperture distributions for both rectangular and circular apertures.

Homework # : Due: .................................. (the beginning of the class).
1:  Problem 11.34. Also, assuming an Eo = 10^-3 v/m, plot on a linear plot, the current density on the upper part of the half-plane for 0.1 wavelengths < rho < 10 wavelengths. Assume an incident angle of 30 degrees.
2:  Repeat Problem 11.34 for the lower part of the half-plane. Also, assuming an Eo = 10^-3 v/m, plot on a linear plot, the current density on the lower part of the half-plane for 0.1 wavelengths < rho < 10 wavelengths. Assume an incident angle of 30 degrees.

Homework # : Due:........................... (at the beginning of the class).
1:  Problem 11.36. Also, assuming an Ho = 2.65 x 10^-6 a/m, plot on a linear plot, the current density on the upper part of the half-plane for 0.1 wavelengths < rho < 10 wavelengths. Assume an incident angle of 30 degrees.
2:  Repeat Problem 11.36 for the lower part of the half-plane. Also, assuming an Ho = 2.65 x 10^-6 a/m, plot on a linear plot, the current density on the lower part of the half-plane for 0.1 wavelengths < rho < 10 wavelengths. Assume an incident angle of 30 degrees.

Homework # : Due: ................................... (at the beginning of the class).
1:  A uniform plane wave of Soft Polarization is incident upon a PEC half-plane (n=2)at an incidence angle of 30 degrees. At a distance of rho = 1 wavelength from the edge of the wedge:
a:  Normalized field pattern using the exact solution.
b:  Magnitude of the Incident GO field.
c:  Magnitude of the Reflected GO field.
d:  Magnitude of the Incident GO + Reflected GO fields.
e:  Magnitude of the Incident Diffracted field.
f:  Magnitude of the Reflected Diffracted field.
  Compare the exact and the approximate solutions.
  P. S. The maximum scale should be 2.5.
2:  A uniform plane wave of Hard Polarization is incident upon a PEC half-plane (n=2)at an incidence angle of 30 degrees. At a distance of rho = 1 wavelength from the edge of the wedge:
a:  Normalized field pattern using the exact solution.
b:  Magnitude of the Incident GO field.
c:  Magnitude of the Reflected GO field.
d:  Magnitude of the Incident GO + Reflected GO fields.
e:  Magnitude of the Incident Diffracted field.
f:  Magnitude of the Reflected Diffracted field.
g:  Magnitude of the Incident GO + Reflected GO + Incident Diffracted + Reflected Diffracted fields.
  Compare the exact and the approximate solutions.
  P. S. The maximum scale should be 2.5.

Homework # : Due: ................................... (at the beginning of the class).
1:  Problem 13.5
2:  Problem 13.10
3:  A spherical wave, a distance s' from a scattering target, is incident upon a PEC sphere of radius a. For monostatic relections (reflections in the same direction as the incident field) at a distance s from the point of reflection at the surface of the sphere, reduce the amplitude spreading factor to its simplest form to get credit. It should be only a function of s, s' and a. Assume s>>rho1r, rho2r.

Homework # : Due: ................................(before the beginning of the class).
A:  Plot in one figure the magnitude of the incident diffracted field using GTD and UTD for rho = lambda and rho = 100 lambda.
B:  Plot in one figure the magnitude of the reflected diffracted field using GTD and UTD for rho = lambda and rho = 100 lambda.
C:  Plot in one figure the phase of the incident diffracted field using GTD and UTD for rho = lambda and rho = 100 lambda.
D:  Plot in one figure the phase of the reflected diffracted field using GTD and UTD for rho = lambda and rho = 100 lambda.
  Assume an incidence angle of 30 degrees. Follow Figure 13-20. Do not exceed a magnitude of unity. Use landscape format for each figure.

Homework # : Due: ......................... (at the beginning of the class).
  Using GO and UTD:
1:  Problem 13.16
2:  Problem 13.17
  For each polarization/graph for Part b of each problem, plot in rectangular plot, landscape format, two curves:
a.:  One curve representing the magnitued of the total GO field.
b.:  The other curve representing the magnitude of the (GO + UTD) field.

Homework : Due: ..........................(before the beginning of the class).
1:  Reproduce the solution to Example 13-4. Learn and show all the details/steps.
2:  Plot the normalized amplitude patterns, in polar plot and in dB (0 to -40 dB scale) when w = 2 lambda. Do this for:
a:  h = 0.5 lambda
b:  h = 0.25 lambda
  In each figure, plot three curves; one for GO, one for GO + GTD, and one for GO (when the width of the strip is infinite).

Homework# : Due: ..................................(before the beginning of the class).
1:  Problem 13.29
  In addtion to Parts a and b, do the following:
c:  Formulate the diffractions from edges #3 and #4 (H-Plane) of Figure P13-29.
d:  Plot the normalized total amplitude pattern (in decibels) for theta between 0 degrees and 180 degrees when w/2 = 14.825 lambda and a = 0.68 lambda.

Homework # : Due: .......................... (at the beginning of the class).
1:  Repeat, in detail, Example 13-5.
2:  Plot the 2-D RCS (SW) sigma (in dBm).
A:  In one figure plot two curves for w = 2 lambda, f = 10 GHz:
a:  Using GTD diffraction formulation.
b:  Using Physical Optics (PO).
B:  In one figure plot two curves for w = 10 lambda, f = 10 GHz:
a:  Using GTD diffraction formulation.
b:  Using Physical Optics (PO).
3:  Repeat, in detail, Example 13-5 for Hard Polarization.
4:  Plot the 2-D RCS (SW) sigma (in dBm).
A:  In one figure plot two curves for w = 10 lambda, f = 10 GHz:
a:  Using GTD diffraction formulation.
b:  Using Physical Optics (PO).
B:  In one figure plot two curves for w = 10 lambda, f = 10 GHz:
a:  Using GTD diffraction formulation.
b:  Using Physical Optics (PO).

Homework # : Due: ......................... (at the beginning of the class).
1:  A uniform plane wave is incident, at normal angle, on a 2-D PEC circular cylinder. Plot the normalized 2-D RCS/SW (sigma/lambda in dB), using a 0 to -60 dB scale, for radii between 0.1 lambda and 10 lambda. Do this for:
a.:  Soft Polarization: TMz
b.  Hard Polarization: TEz
2:  Repeat Problem 1 for the diffraction by a 2-D PEC wedge with included angles between 0 degrees and 60 degrees. First formulate the problem, and then do the plotting.
3:  Generate two more figures.
a.  One that has the Soft Polarization plots for the cylinder and wedge.
b.  The other that has the Soft Polarization plots for the cylinder and wedge.

Homework # : Due: ..............................(before the beginning of the class).
  Problem 13.33. Repeat Example 13-7.
a.  Show all the details of the formulation for diffractions from edges 1 and 2; not just what is in the book.
b.  Plot the normalized predicted polar pattern (in dB) shown in Figure 13-37 for theta between 30 - 180 degrees.

Homework #: Due: .........................(before the beginning of the class).
  A TEz (Hard Polarization) uniform plane wave is incident upon a 2-D strip of width w.
1:  Based on the single-order diffractions from the two edges and double-order diffractions between the two edges, plot, in a single graph (using a +30 to -40 dB scale), the normalized monostatic 2-D RCS/SW (sigma/lambda in dB) for w = 2 lambda using:
a:  Single diffractions from each of the two edges (same as Problem #10).
b:  Single diffractions from each of the two edges plus double diffractions between the two edges. I will give you the formulation for double diffractions.
c:  Physical Optics.
2:  Repeat Proble 1 for w = 10 lambda.

Homework #: Due: ................... (at the beginning of the class).
1:  Problem
2:  Problem
3:  Problem
4:  Problem

Homework #: Due: ...................(at the beginning of the class).
1:  Problem
2:  Problem
2:  Problem


 

Contact me!
 

Go back to top.
Part In Class and Part Take Home.
a:  Write a Matlab computer program, name it StripScatTE_MFIE_EFIE_PO, to solve the MFIE of (12-103a) and/or (12-107a) for a plane wave incident on a finite PEC strip of width and thickness w and t, respectively. Use point matching-collocation method. The basis/expansion function should be rectangular pulses.
b:  For each case, the program should be able to compute the linear current density (PO, MFIE and EFIE) for any incidence angle, normalized bistatic SW (SW/lambda) and the normalized monostatic SW (SW/lambda)dB. The program should be interactive, whereby questions are asked sequentially about what is the the width of the strip (in wavelengths), thickness of the strip (in wavelengths), the incidence angle phii (in degrees), and then the number of segments (N=integer). Refer to Figure 12-13(b) for the geometry.
c:  The output should be the linear current density distribution (Amps/meter), based on the MFIE, EFIE and the Physical Optics (PO), and two plots, in two separate figures, w = 2 x lambda, t = 0.1 x lambda of the linear current density distribution, like Figure 12-15 in the book. One figure with three curves (one for MFIE, one for the EFIE and the other for PO) should be for an incidence angle phii=90 (in degrees). The other figure with three curves (one for MFIE, one for the EFIE and the other for PO) should be for an incidence angle of phii=120 degrees. However the program should be able to compute the linear current density for any incidence angle; i. e., (0 degrees < phii < 180 degrees), and thus any bistatic SW and the monostatic SW.
d:  Once you have computed the linear current distribution, based on the MFIE, EFIE and PO, the program should compute for w = 2 x lambda, t = 0.1 x lambda, in 2 separate figures, the far-field normalized Bistatic and Monostatic Scattering Widths (SW/lambda)dB. One figure should be for the normalized Monostatic SW and should have three curves; one based on the current density distribution obtained by the MFIE, one by the EFIE, and the other on that of the PO. That figure should look like Figure 12-16. Another figure should be for the normalized Bistatic SW, with phii = 90 degrees, and it also should have three curves; one based on the current density distribution obtained by the MFIE, one by the EFIE, and the other on that of the PO. That figure should look like Figure 11-6. The other figure should be for the normalized Bistatic SW, with phii = 120 degrees, and it also should have three curves; one based on the current density distribution obtained by the MFIE, one by the EFIE, and the other on that of the PO. That figure should look like Figure 11-6.
Hint:  Because for this polarization you have only one magnetic field component (a z component), the most judicious definition of the SW will be that of (11-21c).
e:  You should submit a hard copy of the program output, with figures similar to Figures 12-15, 12-16 and 11-6 for w = 2 x lambda, t = 0.1 x lambda, and with each figure having three curves; one for MFIE, one for EFIE and one for PO .
f:  Send me electronically a copy of your program's source code so I can run it to see that it works.
P.S.:  The more user friendly you make your code, the higher the grade. Computational efficiency is also an important factor. The 25% of the final grade is reserved for the very best program(s). Use rectangular pulses for the basis/expansion functions. The program should be self contained; i.e., any subroutines should be included with the program.