Radar cross-section of a sphere coated by a dielectric material 1. Project Description : This is a class project performed by graduate student Alper Ugur. under the supervision of Prof. Dr. Ercument Arvas at Syracuse University, RF/Microwave Lab (SURF). The commercial software, Ansoft HFSS is used to simulate the design. This project is intended to find the radar cross-section of a sphere coated with a dielctric material. Purpose of doing this simulation is to compare RCS results with analytic results and to implement and use the some superior characteristics of software such as symmetry property and manual mesh option. H-field symmetry is used to solve the question. Therefore Solution of the half of the structure is enough. By doing this both computing time is decreased and the number of meshes increased. That means, RCS is much more close to the theoretical RCS than that of the solution without symmetry used. Another advantage of using symmetry and manual mesh option is that; user does not need to simulate same structure four times which is done by other students. A plane electromagnetic wave is incident on a conducting sphere of radius 0.333 lambda coated with a dielectric of thickness 0.067. The direction of propagation of the incident plane wave is in -z direction and the E field is in -x direction. Dielectric constant of the coating material is 4. Wavelength is arbitrary. 2. Drawing the circuit using HFSS: Drawing is the first step of every simulation software packages. Ansoft HFSS7.0 has its own drawing tool. Complex solid body, surface, and line can be made by using the drawing tool. It also has ability to share the CAD model with other drawing packages such as such as AutoCAD or Pro/ENGINEER using ACIS format, developed by Spatial Technology Inc. ACIS is called SAT file because its file name has "sat" extension. SAT file is widely used in the manufacturing industry. The model of the combline filter has been exported to ACIS format by using HFSS. The figure below is the drawing window for HFSS. To make drawing easier, there are four windows, 3 for 3 planes (xy, yz, xz) and one for the 3D view. For more information about drawing using HFSS tool, please refer to the manual of HFSS. 3. Material Assignment After the model has been generated by using the drawing tool, the next step is to assign physical properties of each object in the model. Ansoft HFSS provides a material library, which contains typical metals and dielectric materials. If your material is not on the list, you can add it by putting its parameters. Anisotropic material and nonlinear material can be added. The material setup window will pop up after you click "Setup Materials…" on the main window. Only the objects, which have visibility attribute, will be shown in this window. All objects are assigned as UNASSIGNED material at the first time. All objects must be assigned before beginning the next step. The steps for setting up material are the following. 1) Click the object name or click the object on the display window. The color of object will change to confirm if it is a right object. 2) Select the material. If the material is a metal, only surface of the object will be used in the simulation. It assumes that there is no field inside metal. If the object is thinner than skin depth, the object must be assigned as a lossy dielectric. 3) Click assign. The material will change from UNASSIGNED to the selected material. In this application, there are 3 objects. radiation should be assigned as vacuum. conductor should be assigned as perfect conductor and dielslab should be assigned as a dielectric material with relative dielectric constant 4 4. Setting-Up Boundaries and Sources Maxwell equations are a set of differential equations. To solve these equations, the initial values and the boundary conditions must be given. Ansoft HFSS has SOURCE as the initial values and BOUNDARY as the boundary conditions. SOURCE and BOUNDARY of the problem must be set before starting the solver. The 3D Boundary/Source Manager will pop up after you click "Setup Boundaries/Sources…" on the main window. Symmetry boundary Radiation boundary There are 5 types of sources as the following. 1) Port 2) Incident wave 3) Voltage drop 4) Current 5) Magnetic bias Type 1 and 2 are commonly used. Port is used when the desired outputs are the responses of N-port device. Port is assigned by selecting a surface, which covers the whole excitation region. It assumes that the edges of the surface are connected to perfect conductor. One side of the surface must be metal so that the excited power can only propagate to one direction. The solver will find modes, which can exist on the cross-section. These modes are excitation modes. The S-parameters for each mode can be obtained. Incident wave is used in a scattering problem. Incident wave is defined by its propagation vector and its magnitude. To obtain bi-static radar cross-section, the boundary of the workspace must be set to radiation boundary. The other types of SOURCE can be used for exciting the problem but it is not physical. It is a better idea to excite the problem with its physical excitation. If a device is fed by a coax, a coax should be included in the simulation. The coax should be set up as a port so that the S- parameters can be obtained. The detail of SOURCE can be found in Ansoft HFSS online manual. There are 8 types of boundary as the following. 1) Perfect E 2) Perfect H/Natural 3) Finite conductivity 4) Impedance 5) Radiation 6) Symmetry 7) Master 8) Slave Perfect E can be used for a zero-thickness perfect conductor. It should be used in the area, which has zero tangential electric fields. Perfect H can be used at the surface of the aperture on the ground plane. It should be used in the area, which has zero tangential magnetic fields. Metal loss can be defined by using finite conductivity or impedance boundary. Radiation boundary is used for terminating the workspace in scattering problem. The tangential component of electric and magnetic fields on the surface of the workspace will be used for computing far field by using equivalence principle. Symmetry boundary is used when the problem has symmetry. For the N-port device problem, the symmetry plane must pass through all ports in the problem. The detail of BOUNDARY can be found in Ansoft HFSS online manual. In this RCS application there is a magnetic symmetry. Only half of the filter needs to be simulated. We can split the sphere structure in half by using the drawing tool. The symmetry plane is assigned by selecting the surfaces on that plane. Care must be taken that the whole plane is selected and magnetic symmetry is chosen. The ports are defined by selecting the surfaces at the location of ports. One side of the surfaces must be metal so that excited wave will propagate into one direction. If both side of the surface are medium, the simulation will fail to start. 5. Solution Setup HFSS has all information of the problem at this point. It is ready to solve the Maxwell's equations. Two more things must be given before HFSS can start solving the problem. The information of mesh size must be given since numerical method will be used. The interested frequency band must be given. The picture below shows HFSS Solution Setup Windows. The top and bottom windows are for the mesh information. For the beginner, the bottom window should be kept as the default. The blanks on the top window must be filled. The frequency filled in Single Frequency blank is used for the initial mesh size. This number should be larger than the maximum frequency of the interested band. In the high Q problem, like combline filter, the initial mesh size is not small enough to capture the change of fields in some areas. Adaptive Mesh must be used. When Adaptive Mesh is selected, HFSS reduces the mesh size at the critical areas after each simulation. The adaptive growth is controlled by Tet. Refinement. The adaptive process repeats until the difference between S-parameters of two consecutive passes is less than specific number, Max delta S. The adaptive process is also terminated, when the number of requested passes is reached. The interested frequency band is specified by sweep option. After adaptive process is terminated, the mesh information will be used to simulation each frequency point. There are two types of sweep. Discrete sweep is for solving each frequency point separately. Fast sweep is for using an algorithm to solve all frequencies at once. For more information about Solution Setup, please refer to the manual of HFSS. In this example manual mesh is defined to solve the structure Therefore most of the solution time wasted in adaptive pass is saved. By doing manual mesh, Number of tetrahedras increase enormously compared to the adaptive mesh solution, which means solution results obtained from manual mesh is closer to the actual results than the other type of solution. After Solution Setup is done, Solve button on the main window will be active. Click Solve button to start HFSS simulation. The simulation may take several hours. 6. Post Process After the problem has been solved, the results can be viewed and manipulated by using Post Process. There are three options in the Post Process menu as shown below. 3D fields including, radiation pattern, can be viewed by "Fields.." option. "Matrix Data ..." is for manipulated S-parameters obtained from the simulation. "Matrix Plot..." is for view responses of the device. Window below appears when "Fields..." option is selected. This window allows user to compute radiation pattern. Mesh, Fields, Far Field, and Near Field can be plotted. To find the radar cross section of the structure click to the normalized RCS on the left window below then click to polarization type as total then click ok button to see the normalized RCS in dB scale as shown below. Obtained result is shown below. 7. Comparison In this application, HFSS ver7 is used to find RCS of a given structure. Software's manual mesh generation and the symmetry properties are employed. Therefore solution time is decreased. And because of the huge increase in the number of tetrahedra enabled, results are much closer to the theoretical rcs values than that of the rcs when the same software is used without any property. Theoretical radar cross-section of the same structure is below. Figure in below, NO symmetry property and manual mesh generation is applied. This is done by other student.