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1 Ansoft HFSS Advanced Training Exercise Radar Cross Section This exercise assumes that you already have some experience with Ansoft HFSS. Therefore, not every button click will be described. 1. Introduction In this exercise, we will model a trihedral corner reflector. It is depicted in figure 1. Fig. 1 Trihedral corner reflector It consists of three metal plates at right angles to eachother. Radiation entering the structure from the right in figure 1 will, after multiple bounces, reflect in the direction it came from. This is true for a large collection of incidence angles on the right-hand side of the reflector: radiation is reflected in the direction it came from. This makes the trihedral corner reflector an ideal calibration object in RCS experiments: it has a large cross section and one need not worry about alignment. Also, a combination of such reflectors is often used as add-on reflector on objects that should be visible to radar in all directions, like buoys or small yachts. The corner reflector is most useful when it is much larger than the wavelength of the radiation. When its size is comparable to a wavelength or smaller, picturing the waves as rays that undergo multiple bounces in the reflector no longer holds. For very short wavelengths, however, tolerances become an issue: if the plates are not exactly at 90 degree angles, the reflection will not be in the direction of incidence. In this exercise, the scattering object is several times larger than the wavelength.

2 In the high-frequency limit, the maximum RCS σ of this reflector is given by σ = πl 4 /(3λ 2 ), (1) where L is the length of each of the three edges that form the triangular aperture and λ is the wavelength. If one defines L as the distance between any corner of the aperture and the rear apex of the reflector, one has L = 2 L, and σ = 4πL 4 /(3λ 2 ). (2) 2. Draw In the Draw menu of HFSS, choose millimeters as the drawing units. Through Lines / Rectangle, construct three mm rectangles. Each one will have its first point in the origin. They will be lying in the three principal planes: one in XY, one in XZ, one in YZ. Make sure the three objects are covered sheet objects, not just polylines. These rectangles will be cut later to become the reflector. In order to create the air object, choose Solids / Box and make a box with the first point in (-8, -8, -8) and size (128, 128, 128). Call the new object airbox. About the size of the box: we will be performing a simulation at 10 GHz. At that frequency, the wavelength is 30 mm. We want the distance between the radiation boundary and the scattering object to be at least a quarter wavelength. We will perform two rotations to make the x-axis the center axis of the reflector. Select all objects and Arrange / Rotate them over 45 degrees around the z axis. Still having the objects selected, Arrange / Rotate them over 35.3 degrees around the y axis. Deselect all objects. Now that the plates have the correct orientation, we will cut off part of them. Measure the x coordinates of the vertices of the reflector. Three of them should be close to x=57.7, but not all three x coordinates are equal. This is because the ideal rotation angle is not exactly 35.3 degrees. We will cut at a convenient x coordinate near that of these three vertices. By editing the boxes in the upper-left part of the window, make the active point (57.7, 0, 0). Move the origin of the coordinate system to that point through Coordinates / Set Current CS / Move Origin. Use Solids / Split to cut the three plates along the yz plane, and keep the fragments below the plane.

3 We will also cut the air object. Having the coordinate system still at its new position, make the active point (8, 0, 0). We choose this value of 8 because we want the radiation boundary to be a quarter wavelength away from the reflector. With Coordinates / Set Current CS / Move Origin, or with the appropriate icon, move the coordinate system to that point. Use Solids / Split to cut the air object along the yz plane, and keep the fragment below the plane. Use Coordinates / Global to put the origin back to where it belongs. This completes the drawing. Your model should look like the one in figure 2. Fig. 2 The model of the trihedral corner reflector and the volume of air around it Choose File/Exit and Save the model. 3 Setup Materials In this menu, assign air to the air object. Then Exit and Save. Note: Since the corner reflector is a sheet object (no thickness), it doesn t get a material assigned to it, just a boundary condition. If you would have given the corner reflector a finite thickness, it would be a solid and you would assign a material (metal) to it.

4. Setup Boundaries / Sources Use Edit / Select / By Name / Object, or check Graphical Pick: Object (on the left) and select all surfaces of the air object at once. Assign a radiation boundary.

4 4. Setup Boundaries / Sources Use Edit / Select / By Name / Object, or check Graphical Pick: Object (on the left) and select all surfaces of the air object at once. Assign a radiation boundary. Use Edit / Select / By Name or to select all surfaces of the reflector at once. Assign a perfect_e boundary. Note: You can also perform this selection graphically, if you like. It requires the use of the right mouse button to select faces behind other faces, or making the air object temporarily invisible. Without selecting objects or faces, check Source and select Incident Wave from the list of sources. Check Spherical to set up an angular scan. Having more than one incident wave does not lead to a severe penalty in time and resources, due to the way the Finite Element Method works (excitations are in the right-hand side of the matrix equation). Take Theta Start=90, Stop=90, Points=1, and Phi Start=0, Stop=30, Points=4. Select a polarization. Click Refresh Arrows to display the directions of incidence (Figure 3). Give this excitation a name, e.g. inc_waves, and click Assign. Fig. 3 Setting up the incident waves

5. Setup solution and Solve In this menu, take a frequency of 10 GHz and request 3 adaptive passes. If you have a fast computer, request 4 adaptive passes.

5 5. Setup solution and Solve In this menu, take a frequency of 10 GHz and request 3 adaptive passes. If you have a fast computer, request 4 adaptive passes. Make the tet refinement 30% and the max_delta_e In many projects, more adaptive passes and a smaller tet refinement are better. In this project, since it s such a simple configuration, just three passes with an agressive refinement at the illuminated side will probably give the correct results a little quicker. Don t request a frequency sweep and start with initial mesh. When you hit OK, a warning comes up. Read it and say No. Click Solve. This simuation should take less than 20 minutes on most computers. 6. Post Process / Fields In the Fields Post Processor, access Data / Edit Sources first. Make sure you select the incident wave that comes in along the major axis of the trihedral corner reflector, and make sure that Scattered Fields is checked rather than Total Fields. Click OK. Fig. 4 Selecting the desired incident wave and selecting to view the scattered fields through Data / Edit Sources

6 Select Radiation / Compute / Far Field. Enter scans for phi and theta, e.g. for a scan in the positive x,z plane: phi start=0, stop=0, steps=0, theta start=0, stop=180, steps=180. In the Plot / Far Field window (which pops up automatically after Radiation / Compute / Far Field ), ignore the antenna-related options. HFSS allows you to access all these antenna-related options because a far-field solution is available, but we are just after RCS and Normalized RCS. Display the Radar Cross Section in square meters. The theoretical value for the high-frequency limit is 0.46 m 2. Notice that HFSS predicts a somewhat different value. That is because we are not very far into to the high-frequency region yet: the size of the trihedral corner reflector is just a few times the wavelength. Next, display the Normalized RCS, which is defined as RCS/λ 2 and hence is dimensionless. Check whether the values are what you expect, both absolute and in db. You can use the marker icon. Through Data / Edit Sources you can turn on other incident fields, preferably, but not necessarily, one at a time in this case. Compute the far field at theta=90 degrees and phi ranging from 0 to 360 degrees. Plot the RCS with theta as fixed variable. Notice that the beam always peaks in the direction where the incident field came from. Close the windows containing these plots with Window / Close. Next, turn the model until your point of view is on the z-axis, in other words, view the model from above. Use Plot / Field to display the Plot Quantity MagE On Geometry Volume airbox. Make it a Phase Animation with 30 divisions between 3 and 0. Notice that the field strength behind the corner is considerable, as if the incident wave goes right through the model. The reason for that is that we are observing scattered fields, not total fields. Remember total field = incident field + scattered field. The incident field is everywhere at all times. Behind the object, the scattered field is about as strong as the incident field but about 180 degrees out of phase, so that the total field will be small there. Only when we observe total fields, what we see coincides with our intuitive expectations. Use Data / Edit Sources to check Total Fields and click OK. Again, use Plot / Field to display the Plot Quantity MagE On Geometry Volume airbox in a Phase Animation with 30 divisions between 3 and 0. Now the field behind the corner is small. This completes this exercise on the trihedral corner reflector. 7. Other RCS experiments in HFSS

7 Another very simple RCS simulation is the following. Construct a square plate of x meter and illuminate it with a plane wave at GHz. Results for both horizontal and vertical polarization can be found in: R.A. Ross, Radar Cross Section of Rectangular Flat Plates as a Function of Aspect Angle, IEEE Transactions on Antennas and Propagation, Vol. AP 14, May 1966, pp , as well as in E.F. Knott, J.F. Shaeffer, M.T. Tuley: Radar Cross Section, 2 nd Edition, Artech House, ISBN , in the chapter on Phenomenological Examples of Radar Cross Section. From a graph in the latter reference, the maximum RCS seems to be 9 dbsm = 8 m 2. It is not known what the measurement accuracy was. Note that the graph in the reference is an angular scan of many angles of incidence. To reproduce the experiment, the Spherical option must be selected when defining the incident wave in HFSS. Also note that the size of this simulation is quite large: the plate measures about 5λx5λ. You need a computer with a lot of RAM to perform this simulation or.. make use of symmetry! With Solids / Split in the Draw menu, you can cut the plate twice, until you have just one-quarter model left. In Setup Boundaries / Sources, assign a Symmetry / Perfect_E boundary to the symmetry plane perpendicular to the electric field vector, and assign a Symmetry / Perfect_H boundary to the symmetry plane parallel to the electric field vector. Make sure the boundary type belongs to the Symmetry collection. Don t pick just Perfect_E or Perfect_H, as these will give you correct fields inside the model but wrong far-field results. We could have exploited symmetry in the trihedral corner reflector as well. A split along the xz plane would have cut the model in half. Having built the models for the trihedral corner reflector and the flat plate, you can cover the illuminated sides of the objects with lossy materials in HFSS, and observe how the RCS changes.

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