Plane wave in free space Exercise no. 1

Transcription

1 Plane wave in free space Exercise no. 1 The exercise is focused on numerical modeling of plane wave propagation in ANSYS HFSS. Following aims should be met: 1. A numerical model of a plane wave propagating in free space should be created. Parameters of free space are identical with vacuum. Frequency of wave is f = 9 GHz. Considering the computed field distribution, wavelength should be determined as the shortest distance of two points with the same phase, and the value should be verified: λ = c / f (1.1) where c is velocity of light and f denotes frequency. 2. Plane wave propagates in free space with the dielectric constant r = 4. What is the wavelength with respect to the propagation in vacuum? 3. Plane wave propagates in free space with the dielectric constant r = 1 and conductivity tan = 0.1. What is the field distribution with respect to the propagation in vacuum?

2 How to do it ANSYS HFSS numerically solves Maxwell equations in the differential form by finite element method (FEM). FEM decomposes an analyzed structure to tetrahedral elements (finite ones). In each element, electromagnetic field is approximated by a parametric function. In the next step, parameters are evaluated to minimize energy of the computed field. Today, we are aimed to create a simple model of plane wave propagation in HFSS. Plane wave will be formed by a special wave-guiding structure: The top wall and the bottom wall of the waveguide are created by perfect electric conductor (). Since electric field intensity has to be perpendicular to the wall, the plane wave will have E component oriented in a vertical direction. Side walls of the waveguide are created by perfect magnetic conductor (PMC). Since magnetic field intensity has to be perpendicular to the PMC wall, the plane wave will have H component oriented in a horizontal direction. Wave propagates in parallel to the longitudinal axis of the waveguide. Direction of propagation is perpendicular both to the electric field E and to the magnetic field H at the same time. H E k PMC PMC Fig. 1.1 Transversal cut (left) and longitudinal cut (right) of the analyzed waveguide. Now, attention is turned to modeling the described waveguide in ANSYS HFSS. Following steps have to be done: Menu: Project Insert HFSS Design We create a numerical model based on in finite elements in frequency domain (wave propagation is modeled in a harmonic steady state). Menu: Draw Box In the graphical editor, we click points creating vertexes of a block. In the list of objects, Box1 appears. Clicking the right button the CreateBox, dimensions of the box can be specified accurately. In our case, XSize = 22 mm, YSize = 200 mm and ZSize = 10 mm. If Position is set to (0 mm, 0 mm, 0 mm), the left back bottom vertex of the box appears in the origin of the coordinate system. User s interface of ANSYS HFSS version 15.0 is depicted in Fig. 1.2: On the top, we have a conventional toolbar with frequently used commands. The box can therefore be created via menu (Draw Box) or by a corresponding icon.

3 In the central-left part, Project Manager is available. The task to be computed is specified by a consecutive setting of all the items of the project (from Model to Radiation). On the right from Project Manager, the list of geometric objects is displayed. In our case, only Box1 is listed. In the window Properties, which is below Project Manager, parameters of objects are listed. Bottom windows display messages related to the status of modeling. Warnings and errors are shown in the left window, status of computations is given in the right window. Fig. 1.2 User s interface of ANSYS HFSS. Now, let us continue the preparation of the model: Key F + click on the face of the box the face is selected o Top and bottom face: HFSS Boundaries Assign Perfect E (perfect electric conductor) o Front and back face: HFSS Boundaries Assign Perfect H (perfect magnetic conductor) o Right face: HFSS Boundaries Assign Radiation Boundary (radiating face perfectly absorbing energy of a propagating wave; reflections are eliminated) o Left face: HFSS Excitation Assign Wave Port (field distribution on the input port is the source of the wave) Properties of the wave port have to be determined in several dialog boxes: 1. General. The port is named (the default name 1 can be used).

4 2. Modes. On the line Mode = 1, we click the column Integration line. In the center of the input face, we create an arrow from the top wall to the bottom wall. Center of the face is indicated by a triangle. 3. Post processing. Default settings are used. Menu: HFSS Analysis Setup Add solution setup On the first tab (General), we set frequency of analysis (Solution frequency) to 9 GHz. Other settings stay unchanged. Menu: HFSS Validation check A dialog for the verification of the correctness of the model is opened. If the model is correct (see fig. 1.3), analysis can be run. Menu: HFSS Analyze all Fig. 1.3 verification of the correctness of the created model. Before running the analysis, HFSS requires the model to be saved. Run of the analysis is indicated in the right bottom window. Finishing analysis, results can be displayed. Select: Box1 (in the box with objects), Field overlays (in Project Manager by right click), Menu: Plot fields H Vector H That way, magnetic component of the computed electromagnetic wave is displayed. H field (in Project Manager by right click) Menu: Modify attributes Spectrum: grey Color palette for a proper representation of computed fields can be selected. The described steps can be repeated for the electric field. That way, the complete field consisting of electric components (red arrows) and magnetic components (grey arrows) can be displayed (see Fig. 1.4). If filed distribution should be animated, we use: Menu: View Animate If output of analysis should be copied to clipboard, we use: Menu: Edit Copy image If distance of two points should be measured, we use: Menu: Modeler Measure Position

5 Fig. 1.4 Electric field intensity vector (red) and magnetic field intensity vector (grey) of wave propagating in a waveguide from Fig. 1.1.