两腔窄带滤波器详述

CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial 163 The Narrow Band Filter Tutorial Geometric Construction and Solver Settings 164 Introduction and Model Dimensions 164 Geometric Construction Steps 165 Solver Settings and S-Parameter Calculation 182 Results 192 1D Results (S-Parameters) 192 2D and 3D Results (Port Modes and Three Dimensional Modes) 192 Accuracy Considerations 195 Alternative Solvers 200 The JD (lossfree) Eigenmode Solver 200 The Frequency Domain Solver 203 Getting More Information 206 164 CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial Geometric Construction and Solver Settings Introduction and Model Dimensions In this tutorial you will analyze a Narrow Band Filter. CST MICROWAVE STUDIO® can provide a wide variety of results. This tutorial however, concentrates solely on the S- parameters of the filter. We strongly suggest that you carefully read through the CST MICROWAVE STUDIO® Getting Started manual before starting this tutorial. The following two pictures show the structure and its dimensions in two different cross- section planes: All dimensions are given in mm 105 217 17.9 95 110 200 15 50 r = 2.9 r = 10 25 100 All dimensions are given in mm 105 217 17.9 95 110 200 15 50 r = 2.9 r = 10 25 100 100 100 The structure consists of two resonators, each formed by a perfect electrically conducting cylinder in a rectangular cavity. Both resonators are coupled via a rectangular iris. The CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial 165 two coaxial ports are capacitively coupled to the device by extending the coaxial cable’s inner conductor into the resonators. The following explanations on how to model and analyze this device can also be applied to other filter structures as well. Geometric Construction Steps This tutorial will take you step by step through the construction of the model, and relevant screen shots will be provided so that you can double-check your entries along the way. ! Select a Template Once you have started CST MICROWAVE STUDIO® and have chosen to create a new project, you are requested to select a template which fits best to your current device. Here the “Resonator” template should be chosen. The template automatically sets the units to mm and GHz, the background material to be perfect electrically conducting. Please select this template now and press the Ok button. ! Set the Working Plane’s Properties Once the units have been correctly set (which has been done by the template here), the modeling process usually starts with setting the working plane’s size large enough for the device. Since the structure has an extension of 200 mm along one coordinate direction, the working plane’s size should be set to 300 mm (or more). These settings can be changed in a dialog box, which opens after selecting Edit # Working Plane Properties 166 CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial from the main menu. Please note that we will use the same document conventions here as introduced in the Getting Started manual. In this dialog box you should set the Size to 300 (the unit which has been previously set to mm is displayed in the status bar), the Raster width to 10 and the Snap width to 5 to obtain a reasonably spaced grid. Please confirm these settings by pressing the Ok button. ! Draw the Filter’s Housing Due to the fact that the background material has been set to electric, you need to model the interior of the filter. The structure will then automatically be embedded within a perfect electric conducting enclosure. Therefore you should start the structure modeling by entering the filter’s housing which can easily be defined by creating an air-brick. Please activate the brick creation tool now by either selecting Objects # Basic Shapes # Brick or pressing the corresponding button in the toolbar ( ). Once you are prompted to enter the first point, you may enter the coordinates numerically by pressing the TAB key which will open the following dialog box: In this example you should create the housing with the transversal extension of 100 x 200 mm. In order to model the structure symmetrically to the origin, you should now enter the coordinates X = -50 and Y = -100 in the dialog box and press the Ok button (please remember that the geometric unit is currently set to mm). The next step is to enter the opposite corner of the brick’s base. Thus you should press the TAB key again and enter X = 50, Y = 100 in the coordinate fields before pressing Ok. CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial 167 Now you will be requested to enter the height of the brick. This can also be numerically achieved by pressing the TAB key, entering a Height of 110 and pressing the Ok button again. After the steps above have been completed, the following dialog box will appear showing you a summary of your input: Please check all entries carefully. When you encounter any mistakes, please change the value in the corresponding entry field. You should then give the shape a meaningful Name (e.g. “housing”). Since the housing consists of vacuum, you can keep the Material default setting (“Vacuum”) as well as the assignment to the default Component “component1”. Please note: The use of different components allows you to collect several solids into specific groups, independently of their material behavior. However, here it is convenient to construct the complete filter device as a representation of one component. Finally, confirm the creation by pressing Ok. Your screen should now look as follows (you can press the SPACE key in order to zoom the structure to the maximum possible extent): 168 CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial Since some structures will be inserted into this air brick in the following steps, it is advantageous to switch the display to wireframe mode because otherwise the newly created shapes may be hidden inside this brick. The easiest way to activate the wireframe visualization mode is to press the toolbar icon or to use the corresponding shortcut: Ctrl+W. Now the structure should look as follows: CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial 169 ! Create the Cylindrical Resonators The next step is to create the cylindrical resonators inside the air brick. Please activate the cylinder creation tool now by selecting either Objects # Basic Shapes # Cylinder from the main menu or by pressing the corresponding toolbar icon ( ). The first step in the cylinder creation process is to enter the center point coordinates. This can be achieved numerically by pressing the TAB key and entering the dimensions X = 0, Y = -50 in the dialog box before pressing the Ok button. In the following we will assume that you always confirm the settings in a dialog box by pressing the Ok button unless mentioned otherwise. The second step in the cylinder’s creation is to specify the outer radius. Similarly to the procedure above, you should now set the Radius to 17 after pressing the TAB key. After pressing the TAB key once more and setting the Height to 95, you may skip the definition of the cylinder’s inner radius by pressing the ESC key. Finally, the following dialog box will appear: Please check and correct all settings as necessary before you specify the cylinder’s Name to be “cylinder1”. So far, the cylinder consists of vacuum material. However, to specify the cylinder to be a perfect electric conductor (PEC), you need to change the Material assignment to “PEC”. Since the filter is constructed as one component, you can skip the Component setting and confirm the creation of the cylinder by pressing the Ok button. 170 CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial Your screen should then look as follows: After successfully creating the first cylinder you can now model the second cylinder in the same way: 1. Activate the cylinder tool: Objects # Basic Shapes # Cylinder, . 2. Press the TAB key and set the center’s coordinates to X = 0, Y = 50. 3. Press the TAB key and set the Radius to 17. 4. Press the TAB key and set the Height to 95. 5. Press the ESC key to skip the definition of the inner radius. 6. Set the Name of the cylinder to “cylinder2” 7. Change the Material assignment to “PEC” and press the Ok button. CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial 171 After the successful creation of the second cylinder, the screen should then look as follows: Please note: The creation of the second cylinder could also be achieved by applying a transformation to the first one. For the sake of simplicity, we simply recommended you to draw the cylinder twice. The application of transformations to copy shapes will be explained later in this tutorial. ! Create the Iris between the two Cavities The next step is to create the rectangular iris between the two cavities. This could easily be achieved by entering its dimensions numerically in the same way as the creation of the air brick above. However, since the iris should always extend across the entire width of the filter, we will now explain how this can be forced by using picked points. After activating the brick creation tool by selecting Objects # Basic Shapes # Brick or pressing the corresponding button in the toolbar ( ), you are requested to enter the first point. Instead of entering the point by double-clicking with the mouse or by entering the point numerically by pressing the TAB key, you should now activate the pick midpoint tool (Objects # Pick # Pick Edge Midpoint, ). Afterwards, all straight edges will be highlighted in the model: 172 CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial You should now double-click on the first edge shown in the picture above. By moving the mouse pointer you can now confirm that the first point of the brick is aligned with the mid- point of this edge. Even if the location of the midpoint may change (e.g. by parametrically editing the structure), the first point of the newly created brick will always be linked with the edge midpoint’s current position. You should now repeat the same steps (activate midpoint pick tool, double-click on the edge) with the second edge in order to specify the brick’s second point. Since now both points are located on a line, the brick creation tool prompts for the width of the brick. You should now press the TAB key and set the Width of the brick to 2. First Edge Second Edge CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial 173 In the last step of the interactive brick creation you are requested to enter the brick’s height. This can also be accomplished by pressing TAB and setting the Height to 105. Completing this step will now open the following dialog box: Some of the entry fields now contain expressions which reflect the relative construction of the brick. The expression xp(1), for instance, represents the x-coordinate of the initially picked edge’s midpoint. Please set the Name of the brick to “iris” now, change the Material assignment to “PEC” and press the Ok button. Your model should then look as follows: 174 CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial ! Create the Coaxial Couplings So far, you have modeled the filters internal structure. However, the next step is to model the coaxial couplings on both side walls of the filter. Before you start modeling the cylinders, you should firstly align the working coordinate system with one of the side walls of the filter. This will allow you to model the coupling structure in a much more convenient way. Please deactivate the wireframe plot mode by pressing the toolbar icon or using the shortcut Ctrl+W: You should then activate the face pick tool (Objects # Pick # Pick Face, ) and double-click on the top face as shown above. The selected face should then be highlighted in the model (see picture above). The next step is to align the working coordinate system with the picked face by selecting either WCS # Align WCS with Selected Face, pressing the toolbar button ( ) or by using the shortcut W (while the main view is active). After activating the wireframe drawing mode again (Ctrl+W), the model should look as follows: Top face Pick top face Top edge CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial 175 The location of the coaxial coupler’s center is located 17.9 mm below the top wall of the filter. Therefore the next step is to align the working coordinate system with the top wall of the filter which makes the definition of the coupler’s location more convenient. You should now again activate the midpoint pick tool (Objects # Pick # Pick Edge Midpoint, ) and double-click on the top edge shown in the picture above. Now the midpoint of this edge should become highlighted. You can then align the origin of the working coordinate system with this point by selecting WCS # Align WCS with Selected Point, pressing the toolbar button or just using the shortcut W. The following picture shows the new location of the working coordinate system: With the working coordinate system being aligned this way, the construction of the coaxial coupler is straightforward: 1. Activate the cylinder tool: Objects # Basic Shapes # Cylinder, . 2. Press the TAB key and set the center’s coordinates to U = 0, V = 17.9. 3. Press the TAB key and set the Radius to 10. 4. Press the TAB key and set the Height to 15. 5. Press the ESC key to skip the definition of the inner radius. 6. Set the Name of the cylinder to “coaxial substrate”. 176 CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial The cylinder creation dialog box should then look as follows: You still need to define the substrate material. Since no material has yet been defined for the substrate so far, you should open the material definition dialog box by selecting “[New Material…]” in the Material dropdown list: CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial 177 In this dialog box you should first of all define a new Material name (e.g. “Coaxial cable”) and set the Type to a “Normal” dielectric material. Then specify the material properties in the Epsilon and Mue fields. Here you only need to change the dielectric constant Epsilon to 2.2. Finally choose a nice color for the layer by pressing the Change button. Your dialog box should now look similar to the picture above before you press the Ok button. Please note: The defined material “Coaxial cable” will now be available inside the current project for the further creation of other solids. However, if you want to save this specific material definition also for other projects, you may check the button Add to material library. You will have access to this material database by clicking on Load from Material Library in the Materials context menu in the navigation tree. Back in the cylinder creation dialog box you can also press the Ok button to finally create the coaxial coupler’s substrate. Your model should now look as follows: The next step is to model the inner conductor of the coaxial coupler as a perfect electric conducting cylinder. Since both cylinders should always be coaxial, it is convenient to move the local coordinate system to the center of the substrate cylinder. Therefore please activate the circle center pick tool by either selecting Objects # Pick # Pick Circle Center from the main menu or by pressing the corresponding button in the toolbar ( ). Now double-click on the substrate cylinder’s upper edge as shown in the picture above which will highlight the circle center point. Finally you can align the working coordinate system with this point by selecting WCS # Align WCS with Selected Point or pressing the toolbar button . The following picture shows how your model should now look: Upper edge 178 CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial The inner conductor of the coaxial connector can now be easily modeled by performing the following operations to create a cylinder: 1. Activate the cylinder tool: Objects # Basic Shapes # Cylinder, . 2. Press the TAB key and set the center’s coordinates to U = 0, V = 0. 3. Press the TAB key and set the Radius to 2.9. 4. Press the TAB key and set the Height to -40. 5. Press the ESC key to skip the definition of the inner radius. 6. Set the Name of the cylinder to “conductor” 7. Change the Material to perfect electric conducting (“PEC”). 8. Press the Ok button to finally create the cylinder. The next step is to deactivate the working coordinate system by selecting WCS # Local Coordinate System or pressing the corresponding toolbar button . After all these steps, the model should now look as follows: CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial 179 So far, you have modeled one coaxial coupler but still need to create the second one. The most convenient way to achieve this is to create a mirrored copy by using an appropriate shape transformation. With help of multiple selection this only has to be done once for the complete coaxial coupler. Please select both parts of the connector (Components # component1 # coaxial substrate and Components # component1 # conductor ) while holding the SHIFT key. Afterwards please open the shape transformation dialog box (Objects # Transform or press the corresponding icon ( ) ): The first action in this dialog is to set the Operation to Mirror. Afterwards the parameters of the mirror plane are specified. Since this plane should be the X/Z plane of the global coordinate system, you only need to set the Y coordinate of the Mirror plane normal to 1. To create a mirrored copy of the existing multiple selected shape, please enable the option Copy. The new created solids will then also be grouped to the existing component “component1”. Confirm the settings by pressing Ok. In the “Shape Intersection” dialog you have to mark the radio button Trim highlighted shape in order to get the same coaxial connector as above. Confirm the setting by pressing Ok. 180 CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial You end up with the following picture: Original shape Mirrored copy CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial 181 And your screen should finally look as follows: 182 CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial Solver Settings and S-Parameter Calculation ! Define Ports The next step is to add the ports to the filter for which the S-parameters will be calculated. Each port will simulate an infinitely long waveguide (here a coaxial cable) which is connected to the structure at the port’s plane. Waveguide ports are the most accurate way to calculate the S-parameters of filters and should thus be used here. Since a waveguide port is based on the two dimensional mode patterns in the waveguide’s cross-section, it must be defined large enough to entirely cover these mode fields. In case of a coaxial cable, the port thus has to cover the coaxial cable’s substrate completely. Before you continue with the port definition, please deactivate the wireframe visualization by pressing the toolbar icon or using the shortcut Ctrl+W. The port’s extent can either be defined numerically or, which is more convenient here, by simply picking the face to be covered by the port. Therefore, please activate the pick face tool (Objects # Pick # Pick Face, ) and double-click on the substrate’s port face of one of the coaxial couplers as shown in the pictures below: Please open the waveguide dialog box now (Solve # Waveguide Ports, ) to define the first port 1: Pick substrate’s port face Substrate’s port face CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial 183 Whenever a face is picked before the port dialog is opened, the port’s location and size will automatically be defined by the picked face’s extent. Thus the port’s Position is initially set to Use picks for the coordiantes. You can simply accept this setting and go ahead. The next step is to choose how many modes should be considered by the port. For coaxial devices, we usually only have a single propagating mode. Thus you sh