CST天线例子 - 图文

Results Plot Properties... [Farfield Plot] General

The farfield is represented by two components (E?,E?) at spherical coordinates Theta and Phi. The coordinates Theta and Phi relate to the cartesian coordinate system, as can be seen in the 3D plot below. See Farfield View for help on the possible selections in the navigation tree.

All plots are scaled logarithmic in dB but can be changed to linear in the Farfield Plot Special Settings dialog (use the Specials... -button). Plot type frame

Polar: Plots the farfield with one coordinate varying and one fixed as a polar plot. Underneath the plot, secondary coefficients such as frequency, main lobe magnitude and direction, 3dB-angular width and side lobe suppression, will be shown.

Cartesian: Plots the farfield with one coordinate varying and one fixed as a cartesian plot. You can get exact field values by using the option Axis Marker from the Results menu.

2D: Plots the farfield with both coordinates varying as a 2D plot with each point colored according to its field value (see the color bar below the plot). Additionally, you will get the exact field value by moving

the

mouse

on

the

demanded position in the plot. The value will be shown in the plot’s lower right corner.

3D: Plots the farfield with both coordinates varying as a 3D plot.

Vary / Angle step width frame

Theta / Phi, Azimuth / Elevation, Alpha / Epsilon or Vertical / Horizontal: Select here which coordinate you want to be variable in your plot. These radio buttons are only active if you have selected Plot Type Polar or Cartesian.

Phi / Theta, Elevation / Azimuth, Epsilon / Alpha or Horizontal / Vertical: The title of this entry depends on your selection in the Vary frame and on the selected coordinate system in the Coordinate system frame. If you have selected Theta to be variable, you will have to set the constant value for Phi here. Else enter the constant value for Theta. You can enter decimal fractions using your keyboard. This entry is only active if you have selected Plot Type Polar or Cartesian.

Theta Step / Phi Step, Azimuth / Elevation Step, Alpha / Epsilon Step, Vertical / Horizontal Step or Step: The title of this entry depends on your selection in the frames Vary, Plot Type and Coordinate system. You may enter the angular step size in degrees for your plot here. In addition, 2D and 3D plots allow the independent specification of theta step and phi step. Select Lock steps to enforce a common step width. Small step sizes will result in a long time to calculate your plot. For Plot Type Polar or Cartesian, first try a step size of 5. For Plot Type 2D or 3D, much more points have to be calculated; therefore, it is better to first set a step size of at least 15.

The smallest allowed step size is 0.01 degree for Polar or Cartesian and 0.25 degree for 2D or 3D. To enter step sizes <1, please use your keyboard. Only certain step sizes are allowed. Your input will be set to the closest smaller allowed value. Farfield and Structure view frame

These settings are only active if the 3D-plot type has been chosen. With these settings it is possible to plot the farfield and the structure at the same time. It is very helpful to realize the spatial relation between the main or side lopes and the modelled antenna.

Show structure: Enables to plot the structure into the 3D-farfield plot:

Structure transparent: Only active if \Use this option in cases the antenna obscures most of the farfield plot.

Farfield size slider: Only active if \plot without zooming the structure Color Ramp ...

Opens the Color Ramp dialog box allowing you to set your preferred color mapping for the 2D/3D farfield plots. Color by value

In case of plot type 3D, use color ramp to map plot values to colors. Use the Color Ramp dialog to modify the mapping. Draw step lines

In case of plot type 3D, draw black lines at each angular step. The step size can be set in the farfield plot dialog box. Step lines are not very useful in unzoomed plots with step sizes of 1 degree or below. Draw iso longitude / latitude lines

Activates iso lines for the longitude and latitude of the currently active coordinate system. These lines will be displayed together with farfield 3D plots. Plot range for polar angles 0..360 degree

This settings extends the plot range of the polar angle (theta, elevation, alpha) to the full circle. The plot range of the corresponding lateral angle (phi, azimuth, epsilon) is reduced accordingly, depending on the active plot type. Plot range –180..180 degree

Choose the plot range of the lateral angles (phi, azimuth, epsilon) symmetric about the origin. This setting is also applied to the polar angles if possible. Angular range frame

These settings restrict a 2D or 3D farfield plot to a specified angular range. Plot angular range only: Activates the phi and theta plot range. ThetaStart / ThetaEnd: Sets the displayed theta range. PhiStart / PhiEnd: Sets the displayed phi range.

Please note that both angular ranges always refer to spherical coordinates. Frequency / Time

Sets the desired plot frequency or the plot time. Select Set time to toggle between farfield calculation and transient field display. These settings are only available for broadband farfields. Save As Source

Use this button to save the farfield to a file which can be used for setting up a farfield source. The angular step size of the plot will be used as step size in the saved ASCII file .Therefore it is recommended to set the step size to a rather small value (e.g. 1 degree) to ensure high accuracy of the simulation where the farfield source is used.

Please use the Origin page to set the origin to the center of the antenna in. In case this page is not available please use the VBA object FarfieldArray to set the origin first and save the resulting farfield as source (Example Farfield Origin VBA).

This button is disabled for the plot types Cartesian and Polar Plot . OK

Stores the current settings and closes the dialog box. Depending on the new settings a new plot of the farfields will be calculated. The calculation can be aborted by pressing the Abort button. Apply

Stores the current settings leaving the Farfield Plot tab sheet opened. Depending on the new settings a new plot of the farfields will be calculated. The calculation can be aborted by pressing the Abort button. FF View / Preview

Use this button to switch between farfield view and coordinate system preview. The latter hides the farfield and just shows the structure in respect to the defined coordinate system. Abort

Aborts the current calculation. Note that the last plot has been deleted. You will have to calculate a new plot by making the appropriate settings and pressing the OK or Apply button again. Close

Closes this dialog box without performing any further action. Help

Shows this help text. See also

Farfield Overview, Farfield View, Color Ramp, Farfield Plot, Farfield Source

Farfield Plot Dialog Pages: Plot Mode, Axes, Origin, Array, Decoupling Plane, Phase Center

二 FSS: Simulation of Resonator

Array Introduction Physical description

Frequency selective surfaces are increasingly used for the frequency filtering of plane waves in radar or communications systems. A one- or two-dimensional periodic array of resonant structures on a backing material, either apertures in a metallic sheet or metallic patches on a substrate, acts as a filter for a plane wave arriving from any angle of incidence. In this example an array of full wavelength resonant conducting rings on a dielectric substrate is simulated. Since the FSS would be used on curved structures like radomes, it is desirable that the FSS have the same resonant frequency for all incident plane wave angles. For a given polarisation, ring resonators are known to be stable with the scan angle. CST MICROWAVE STUDIO? (CST MWS) can be used to establish the angular dependence of the resonant frequency.

CST MICROWAVE STUDIO? Model: Parameter definition and preliminary settings

The simulation of an entire array of resonant rings would be prohibitively time and memory consuming. The use of CST MWS’s unit cell boundary conditions in the directions of periodicity allows a rapid but no less accurate simulation of large surfaces. Setting up the simulation may be greatly eased by using the “FSS – Unit Cell (FD)” template, which automatically applies unit cell boundary conditions in the x- and y-directions and sets up Floquet port excitations in the positive and negative z-directions. There is no need to define master and slave boundary conditions; the phase relation of the opposing boundaries is automatically set by specifying the incident angle of the inward travelling plane wave.

It is only necessary to construct a single ring on its backing substrate. Construction of the geometry itself is simple: a substrate is defined using a brick primitive object, and then a hollow cylinder can be used to create the ring. The conducting ring is a “lossy metal” type copper, and the substrate is Arlon AD 300 with a relative permittivity of 3.

Figure 1 - The “FSS - Unit Cell (FD)” template simplifies simulation set-up by automatically setting the

unit cell boundary conditions.

The incident angle of the incoming plane wave may be specified by setting angles Theta and Phi, both of which have already been parameterized by the template. The periodicity of the FSS is also freely configurable as shown below. Different periodicities can be assigned in the x- and y-directions, and the use of a skewed lattice is also possible by specifying the grid angle (this can be useful for simulating compact closely coupled arrays).

Figure 2 - The incident plane wave angle and unit cell periodicity of the FSS are freely configurable.

For off-normal incident angles the Floquet port modes ensure that the reflected wave is recorded in the direction of optical reflection, while the transmission is in the same direction as the incident wave. This is elucidated by the figure below.

Figure 3 - Incident and transmitted directions are automatically set by the Floquet modes.

The periodicity can also be specified, as in this example, by setting the size of the substrate to the desired periodicity, then checking the “Fit unit cell to bounding box” checkbox.

Figure 4 - Unit cell boundary conditions can be set to fit the bounding box.

The default Floquet port settings excite two plane waves with orthogonal electric fields as shown below (TE(0,0) and TM(0,0) modes), but higher order modes may also be specified in the port properties dialog (“Details”). Co-polar and cross-polar coupling between the modes, both reflection and transmission, are represented in terms of S-parameters. The co-polarised reflection of mode 1 at port Zmin would thus, for example, be named SZmin(1),Zmin(1), and the cross-polarised transmission between modes 2 and 1 SZmax(1),Zmin(2).

Figure 5 - Two orthogonal Floquet port modes are excited by default.

Figure 6 - Higher order or circularly polarised Floquet modes may be defined.

Once the geometry is constructed, the simulation conditions are set up, and some field monitors have been defined, the frequency solver can be started (with either a hexahedral or tetrahedral mesh).

Simulation results

Of primary interest in this case are the S-parameter results, which represent the reflection from and transmission through the FSS. The co-polar reflections and transmissions of both modes are almost identical due to the symmetrical circular rings (the slight difference is due to the tetrahedral mesh). The transmission is almost completely blocked at 15.02 GHz, as seen from the SZmin(1),Zmax(1) of about -63 dB, and the reflection is almost complete (SZmax(1),Zmax(1) ≈ -0.006 dB).

Figure 7 - Reflection from and transmission through the FSS.

A view of the electric field magnitudes at 15.02 GHz (which can be calculated after the simulation by using the “Calculate fields at axis marker” option) reveals the two full-wavelength resonances due to the two Floquet port modes.

Figure 8 - Electric fields at 15.02 GHz show the two Floquet port mode resonances.

Parameter sweep analysis

As mentioned previously, the dependence of the FSS resonant frequency on the angle of the incident plane wave is of interest. A parameter sweep can be set up to vary the incident angle, in this case

theta from 0 to 50 degrees, and the reflection and transmission coefficients can be investigated as an automated post-processing step.

Figure 9 - A parameter sweep can be set up to observe the effect of scan angle on the FSS transmission

characteristics.

The transmission coefficient of the TE mode shows greater dependence on variation of the scan angle in theta than the TM mode does. This is to be expected since the incident wave’s direction of incidence has not changed relative to the top and bottom of the rings (as oriented in the field plots above), only to the left and right.

Figure 10 - Effect of varying theta on transmission of the TE mode through the FSS.

Figure 11 - Effect of varying theta on transmission of the TM mode through the FSS.

Conclusion

This tutorial has described how CST MWS may be used for the simulation of frequency selective surfaces. The set up of the simulation may be greatly simplified by using a template which configures the simulation appropriately and generates Floquet port modes with parameterized incident angle of the plane wave. Once the geometry of a single cell has been constructed the periodicity can be set up very flexibly. Reflections from and transmissions through the FSS can be observed easily using the familiar S-parameter representation. Finally, a parameter sweep of the incident wave angle can be performed to investigate its effect on the performance of the FSS.

三 Antenna Tutorial

Single Antenna (Transient Solver):

Single Antenna (Frequency Domain Solver):

Antenna Array (Transient Solver):

Antenna Array Combine (Transient Solver):

Antenna Array Simultaneous (Transient Solver):

Contents

Geometric Constructions116 Introduction and Model Dimensions Geometric Construction Steps Common Solver Settings

S-Parameter and Farfield Calculation Transient Solver

Transient Solver Results Frequency Domain Solver Frequency Domain Solver Results Patch Antenna Array Antenna Array Calculation Geometric Construction Steps Combine Results Simultaneous Excitation Getting More Information

Geometric Constructions Introduction and Model Dimensions

In this tutorial you will learn how to simulate antenna devices. As a typical example you will analyze a circular patch antenna. The following explanations can be applied to other antennas as well.

Although, CST MICROWAVE STUDIO can provide a wide variety of results, this tutorial will concentrate mainly on the S-parameters and farfield results.

In addition, the single patch antenna will be extended to a rectangular 2x2 array pattern using three different methods. First, the farfield solution of the single patch antenna is applied to the antenna array feature, superimposing the results with different amplitudes and phase settings. Another possibility expands the patch model to a set of four identical antennas, each excitable with its own coaxial feed. Here, you have the option to calculate the antennas separately one after another and finally combine the results with arbitrary amplitudes and phase values, or to run the excitation simultaneously to produce the farfield result with only one solver cycle. The farfield distributions of all these possibilities will be compared.

We strongly suggest that you carefully read through the CST MICROWAVE STUDIO Getting Started manual before starting this tutorial.

?

?

The structure depicted above consists of two different materials: The Substrate and the Perfect Electric Conductor (PEC). There is no need to model the air above because it will be added automatically (according to the current background material setting) when the open boundary conditions are specified. This will be done automatically with an appropriate template. The feeding of the patch is realized with a coaxial line.

Geometric Construction Steps

This tutorial will take you step-by-step through the construction of your model, and relevant screen shots will be provided so that you can double-check your entries along the way.

Please remember the Edit construction step.

? Select a Template

After you have started CST DESIGN ENVIRONMENT? and have chosen to create a new CST MICROWAVE STUDIOproject, you are requested to select a template that best fits your current device. Here, the Antenna (on Planar Substrate) template should be chosen. If the following dialog box does not occur automatically, select File

Select template... from the main menu.

?

Undo facility in the event that you want to cancel the last

This template automatically sets the units to mm and GHz, defines the background material to vacuum

and

selects

appropriate

boundary

conditions

(see

chapter

Boundary

Conditions). Because the background material has been set to vacuum, the structure can be modeled just as it appears on your desk.

? Set the Working Planes Properties

The next step will usually be to set the working plane properties to make the drawing plane large enough for your device. Because the structure has a maximum extension of 60 mm along a coordinate direction, the working plane size should be set to at least 100 mm. These settings can be changed in a dialog box that opens after selecting Edit the Getting Started manual.

Working Plane Properties from the

main menu. Please note that we will use the same document conventions here as introduced in

In this dialog box, you should set the Size to 100 (the unit which has previously been set to mm by the chosen template is displayed in the status bar), the Raster width to 2 and the Snap width to 0.01 to obtain a reasonably spaced grid. Please confirm these settings by pressing the OK button.

? Draw the Substrate Brick

The first construction step for modeling a planar structure is usually to define the substrate layer. This can be easily achieved by creating a brick made of the substrates material. Please activate the brick creation mode now (Objects

Tab key that will open the following dialog box:

Basic Shapes

Brick,

).

When you are prompted to define the first point, enter the coordinates numerically by pressing the

In this example, you should enter a substrate block that has an extension of 60 mm in each of the transversal directions. The transversal coordinates can thus be described by X = -30, Y = -30 for the first corner and X = 30, Y = 30 for the opposite corner, assuming that the brick is modeled symmetrically to the origin. Thus, please enter the first points coordinates X = -30 and Y = -30 in the dialog box and press the OK button.

Afterwards, you can repeat these steps for the second point:

1. Press the Tab key

2. Enter X = 30, Y = 30 in the dialog box and press OK.

Now you will be requested to enter the height of the brick. This can also be numerically specified by pressing the Tab key again; entering the Height of -0.7 and pressing the OK button (it is convenient to define the substrate in the negative z-direction). Now the following dialog box will appear, displaying a summary of your previous input:

Please check all these settings carefully. If you encounter any mistakes, please change the value in the corresponding entry field.

You should now assign a meaningful name to the brick by entering e.g. substrate in the Name field, keep the Component default setting (component1).

Please note: The use of different components allows you to combine several solids into specific groups, independent of their material behavior. However, in this tutorial, it is convenient to construct the single patch antenna as a representation of one component that can then easily be extended into a patch antenna array.

Finally, you need to define the substrate material. Because no material has yet been defined for the substrate, you should open the New Material Parameters dialog box by selecting [New Material...] from the Material dropdown list:

In this dialog box, define a new Material name (e.g. Substrate) and set the Type to a Normal dielectric material. Afterwards, specify the material properties in the Epsilon and Mue fields. Here, you only need to change the dielectric constant Epsilon to 2.33. Finally, choose a color for the layer by pressing the Change button. Your dialog box should now look similar to the above picture before you press the OK button.

Please note: The defined material Substrate will now be available inside the current project for the further creation of other solids. However, if you want to also save this specific material definition 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 brick creation dialog box you can also press the OK button to finally create the substrate brick. Your screen should now look as follows (you can press the Space bar in order to zoom the structure to the maximum possible extent):

? Model the Ground Plane

The next step is to model the ground plane of the patch antenna. Because the antenna will be excited by a coaxial feed at the bottom face, the electric boundary at Zmin defined by the previously chosen template is not suitable as a ground plane. Consequently, a metallic brick must be additionally defined. First, the model has to be rotated by activating the rotation mode View Mode Rotate (). Then the bottom face has to be activated by the face pick tool (Objects Pick Pick Face, ), double-clicking on the substrates bottom face. The face selection should then be visualized as follows:

You can now extrude the selected face with the Extrude tool (

). Here, you must enter the

height and the material of the new shape to be created. In this example, the ground plane must have a non-zero thickness because of the coaxial feed that will be modeled later. In CST MICROWAVE STUDIO a port region must be homogeneous for at least three mesh lines in longitudinal direction. You can therefore choose a Height of 2.1 mm, representing three times the substrate thickness, as a sufficient dimension. Enter this value in the following dialog box and select PEC from the Material dropdown list as the metallic material property:

?

After entering a suitable name (e.g. ground) in the Name field and confirming your settings with the OK button, the current structure will look like this (rotated again to the see the top face):

? Model the Patch Antenna

After the ground plane has been defined, the patch antenna must be modeled as a cylindrical shape on the substrates top face. Please activate the cylinder creation mode (Objects Shapes

Cylinder,

coordinates numerically by pressing the Tab key to open the following dialog box:

Basic

). Similar to the construction of the substrates brick, enter the

Here, enter the center point of the cylinder with X = 0 and Y = 0 because the patch is located symmetrically on the substrate. Afterwards, please define the Radius with

23.2 mm and the Height with 0.07 mm in the shown dialog boxes that appear after you have pressed the Tab button:

Skipping the entry dialog for the inner radius by pressing the Esc button will lead to the following dialog box that provides a summary of your entered parameters:

Select PEC as the Material setting for the patch and assign a meaningful name to the brick by entering e.g. patch in the Name input field.

Again, please check the settings carefully and change any mistakes in the corresponding entry field. After you apply the settings with the OK button, your screen should show the following structure:

? Model the Coaxial Feed

The last modeling step is the construction of the coaxial feed as the excitation source for the patch antenna. This action introduces the working coordinate system (WCS). Because the feeding point is located asymmetrical to the circular patch it is advisable to activate the local coordinate system (WCS

To define the new center point for the coaxial feed the local coordinate system is moved along the positive v-direction (WCS Move Local Coordinates, 9.2 mm in the following dialog box:

). Therefore, please enter a value of

Local Coordinate System,

).

Now it is possible to design the coaxial feed by constructing two cylindrical shapes, similar to the previously defined circular patch.

Please activate the cylinder creation mode again (Objects Cylinder,

Basic Shapes

). First, enter the values for the coaxial substrate cylinder using the Tab key, again

skipping the input of the inner radius. The cylinder has an outer radius of 4 mm and an extension in the negative w-direction of 2.1+0.7=2.8 mm. Please check your settings against the following dialog box:

Select the previously defined Substrate material from the Material dropdown list and create the cylinder with the OK button.

As a result, the cylinder shape component1:solid1 intersects with two already existing shapes, the solid component1:substrate and the ground plane component1:ground. Here it is necessary to determine the type of intersection for the shapes. It is more convenient to combine the two substrate materials into a single shape, so please mark the radio button Add both shapes in the Shape Intersection dialog box as presented below and confirm with OK:

In the second case, the substrate cylinder must be inserted into the PEC material of the ground plane. Please mark the radio button Insert highlighted shape from the Shape Intersection dialog window as presented below and confirm again with OK:

The following screenshot allows you to double-check your model (please use Ctrl+w or toggle the wireframe visualization mode on and off):

to

The inner conductor is constructed by defining another cylinder made of PEC material. Please define the cylinder with an outer radius of 1.12 mm and again an extension of 2.8 mm in the negative w-direction. The cylinder creation dialog should appear as follows:

This time, select PEC from the Material dropdown list and define again a suitable name (e.g. feed) for the cylinder shape. Create the cylinder by pressing the OK button.

Please note: In this case no Shape intersection dialog window will appear, because the PEC shape is defined after the normal material shape (here: Substrate). This implies that the PEC shape is automatically inserted into the intersected shape. Refer to the Getting Started manual for more details.

After applying the OK button the final model will look like the below figure (again use Ctrl+w or

to toggle the wireframe visualization mode on and off):

Common Solver Settings

To this point, only the structure itself has been modeled. Now it is necessary to define some solver-specific elements. For an S-parameter calculation you must define input and output ports. Furthermore, the simulation needs to know how the calculation domain should be terminated at its bounds.

? Define the Waveguide Port

The next step is to add the excitation port to the patch antenna device, for which the reflection parameter will later be calculated. The port simulates an infinitely long coaxial waveguide structure that is connected to the structure at the ports plane.

A waveguide port extends the structure to infinity. Its transversal extension must be large enough to sufficiently cover the corresponding modes. In contrast to open port structures, the port range in this case is clearly defined by the outer shielding conductor of the coaxial waveguide.

Consequently, the easiest way to define the port range is to pick the face (Objects

Pick

Pick Face, ) of the coaxial feed (Substrate material) as demonstrated below (the model is rotated again to the bottom side first):

Please now open the waveguide dialog box (Solve

Waveguide Ports,

) to define the port:

Here, you have to choose how many modes should be considered by the port. For a simple coax port with only one inner conductor, usually only the fundamental TEM mode is of interest. Thus, you should simply keep the default setting of one mode.

Please confirm your port settings with the OK button to finally create the port. After rotating the model again to the top face, your model should now look as follows (please use again Ctrl+w or

to toggle the wireframe visualization mode on and off):

? Define the Frequency Range

The frequency range for the simulation should be chosen with care. Different considerations must be made when using a transient solver or a frequency domain solver (see next chapter for details).

In this example, the S-parameters are to be calculated for a frequency range between 2 and 3 GHz. Open the frequency range dialog box (Solve ? Frequency, the selected template and is displayed in the status bar):

) and enter the range from 2

to 3 (GHz) before pressing the OK button (the frequency unit has previously been set to GHz by

? Boundary Conditions

Because the calculation domain is only a limited volume it is necessary to define boundary conditions that incorporate the influences of the outer space. Please open the Boundary Conditions dialog box by selecting Solve

Boundary Conditions (

):

When the dialog box opens, all currently selected boundary conditions are simultaneously displayed in the main view:

When you selected the Antenna (on planar substrate) template at the beginning of this tutorial the boundary conditions were already properly set for this structure. At the ground plane, an electric boundary condition has been set that behaves like an infinite solid PEC brick. All other boundary planes are set to open or open (add space); they realize free space behind their boundary planes. Free space means that the electromagnetic fields are absorbed at these boundaries with virtually no reflections.

Please note: As a general rule, the open boundary conditions work best if they are at least 1/8 wavelength apart from the field source. Open (add space) already incorporates this rule and automatically adds the correct amount of background space to the structure.

Because the open (add space) boundary condition only adds background material to the structure, it should not be used if there is material that crosses the boundary plane and should practically extend to infinity (such as the substrate and ground solids in this example). In these cases, the open boundary condition must be invoked.

Please close this dialog box without any changes.

? Define Farfield Monitor

Besides the S-parameters, the main result of interest for antenna devices is the farfield distribution at a given frequency. The solvers in CST MICROWAVE STUDIOoffer the possibility of defining several field monitors to specify at which frequencies the field data shall be stored.

Please open the monitor definition dialog box by selecting Solve

Monitors (

):

?

In this dialog box, you should first select the Type Farfield/RCS before specifying the frequency for this monitor in the Frequency field. Afterwards, press the Apply button to store the monitors data. Please define a monitor at the frequency of 2.4 (with GHz being the currently active frequency unit). However, you may define additional monitors at other frequencies, each time

pressing the Apply button to confirm the setting and add the monitor in the Monitors folder in the navigation tree. After the monitor definition is complete, please close this dialog box by pressing the OK button.

S-Parameter and Farfield Calculation

A key feature of CST MICROWAVE STUDIOis the Method on Demand approach that allows specification of a simulator or mesh type that is best suited to a particular problem. Another benefit is the ability to compare the results from completely independent approaches. We demonstrate this strength in the following two paragraphs by calculating the S-parameters and the farfield of the constructed antenna device with both the transient and frequency domain solvers. The transient simulation uses a hexahedral mesh while the frequency domain calculation is performed with a tetrahedral mesh in this case. However, because both methods are self-contained, it is sufficient to work through only one of them. The chapter ends with a comparison of the two methods.

Please note that not all solvers may be available to you due to license restrictions. Please contact your sales office for more information.

?

Transient Solver

? Frequency Range Considerations for the Transient Solver

We recommend using reasonably large bandwidths of 20% to 100% for the transient simulation. In this example, the S-parameters are to be calculated for a frequency range between 2 and 3 GHz. With a center frequency of 2.5 GHz, the bandwidth (3 GHz 2 GHz = 1 GHz) is 40% of the center frequency, which is inside the recommended interval. Thus, you can simply choose the frequency range as desired between 2 and 3 GHz.

Please note: In a case where you just cover a bandwidth of less than 20%, you can increase the frequency range without losing accuracy. This extension of the frequency range could speed up your simulation by more than a factor of three!

In contrast to frequency domain solvers, the lower frequency can be set to zero without any problems! The calculation time can often be reduced by half if the lower frequency is set to zero rather than e.g. 0.01 GHz.

? Transient Solver Settings

The solvers parameters are specified in the Transient Solver Parameters dialog box that can be opened by selecting Solve corresponding icon (

Transient Solver from the main menu or pressing the

) in the toolbar:

You can accept the default settings and press the Start button to run the calculation. A progress bar appears at the bottom of the main window, displaying information about the calculations status:

This progress window disappears when the solver has successfully finished. During the simulation, the message window will display additional information:

Please note: If there are any warning or error messages during the simulation they will be written into the message window, as well.

Transient Solver Results

Congratulations, you have simulated the circular patch antenna using the transient solver! Lets review the results.

? 1D Results (Port Signals, S-Parameters)

First, observe the port signals. Open the 1D Results folder in the navigation tree and click on the Port signals folder.

Please note: It is possible to observe the progress of the results during the computation. In order to get the complete information, however, wait until the solver has finished.

This plot shows the incident and reflected wave amplitudes at the waveguide port versus time. The incident wave amplitude is called i1 (referring to the port name: 1) and the reflected wave amplitude is o1,1. As evident from the above time-signal plot, the patch antenna array has a strong resonance that leads to a slowly decreasing output signal.

A primary result for the antenna is the S11 parameter that will appear if you click on the 1D Results parameter:

|S| dB folder from the navigation tree. The following screenshot shows the reflection

It is possible to precisely determine the operational frequency for the patch antenna. Activate the axis marker by pressing the right mouse button and selecting the Show Axis Marker option from the context menu. Now you can move the marker to the S11 minimum and pinpoint a resonance frequency for the patch antenna of about 2.4 GHz.

The ripples that appear in the reflection parameters result from the time signal not sufficiently decaying (review again at the time signal plot). The amplitude of the ripples increases with the signal amplitude remaining at the end of the transient solver run. However, these ripples do not affect the location of the resonance frequency and therefore can be ignored for this example. More information about this type of numerical error is available in the Accuracy Considerations chapter.

? 2D and 3D Results (Port Modes and Farfield Monitors)

You should first inspect the port modes that can be easily displayed by opening the 2D/3D Results Port Modes

Port1 folder from the navigation tree. To visualize the electric field of the

fundamental port mode, click on the e1 folder. After properly rotating the view and tuning some settings in the plot properties dialog box, you should obtain a plot similar to the following picture (please refer to the Getting Started manual for more information on how to change the plots parameters):

The plot also shows some important properties of the coaxial mode such as TEM mode type, propagation constant and line impedance, etc.

In addition to the resonance frequency, the farfield is another important parameter in antenna design.

The farfield solution of the antenna device can be shown by selecting the corresponding monitor entry in the Farfields folder from the navigation tree. For example, the farfield at the frequency 2.4 GHz can be visualized by clicking on the Farfields directivity over the phi and theta angle:

farfield (f=2.4) [1] entry, showing the

Please note: You have the option to change the Results 5 degrees for a better angle accuracy of the plot.

As evident in the above figure, the maximum power is radiated in the positive z-direction. Note that there are several other options available to plot a farfield: the Polar plot, the Cartesian plot and the 2D plot.

? Accuracy Considerations

The transient S-parameter calculation is primarily affected by two sources of numerical inaccuracies:

1. Numerical truncation errors introduced by the finite simulation time interval. 2. Inaccuracies arising from the finite mesh resolution.

In the following section, we provide hints how to minimize these errors and achieve highly accurate results.

1. Numerical Truncation Errors Due to Finite Simulation Time Intervals

As a primary result, the transient solver calculates the time-varying field distribution that results from excitation with a Gaussian pulse at the input port. Thus the signals at ports are the fundamental results from which the S-parameters are derived using a Fourier Transform.

Even if the accuracy of the time signals is extremely high, numerical inaccuracies can be introduced by the Fourier Transform that assumes the time signals have completely decayed to zero at the end. If the latter is not the case, a ripple is introduced into the S-parameters that affects the accuracy of the results. The amplitude of the excitation signal at the end of the

Plot Properties

Step to

simulation time interval is called truncation error. The amplitude of the ripple increases with the truncation error.

Please note that this ripple does not move the location of minima or maxima in the S-parameter curves. Therefore, if you are only interested in the location of a peak, a larger truncation error is tolerable.

The level of the truncation error can be controlled with the Accuracy setting in the transient solver control dialog box. The default value of 30 dB will usually give sufficiently accurate results. However, to obtain highly accurate results for antenna structures, it is sometimes necessary to increase the accuracy to 40 dB or 50 dB.

Because increasing the accuracy requirement for the simulation limits the truncation error and increases the simulation time, the accuracy requirement should be specified with care. As a general rule, the following table can be used:

Desired Accuracy Level Accuracy Setting (Solver control dialog box) Moderate High Very high

The following rule may be useful, as well: If you find a large ripple in the S-parameters, increase the solvers accuracy setting.

2. Effect of the Mesh Resolution on the S-parameters Accuracy

Inaccuracies arising from the finite mesh resolution are usually more difficult to estimate. The only way to ensure the accuracy of the solution is to increase the mesh resolution and recalculate the S-parameters. When the results no longer significantly change when the mesh density is increased, then convergence has been achieved.

In the example above, you have used the default mesh that has been automatically generated by an expert system. The accuracy of the results is most easily tested with the full automatic mesh adaptation that can be switched on by checking the Adaptive mesh refinement option in the solver control dialog box (Solve

Transient Solver,

):

-30dB -40dB -50dB

Please note that the previously selected template has changed the default settings to the energy-based adaptive strategy that is more convenient for planar structures. Thus, you only have to activate the Adaptive mesh refinement tool in the Transient Solver Parameters dialog and start the solver again by pressing the Start button.

In this example, two adaptation passes are necessary to obtain a suitable result. This means that the maximum deviation of the S-parameters between the second and the third run is less than 2%.

The convergence process of the input reflection S1,1 during the mesh adaptation can be visualized by selecting 1D Results tree:

Adaptive Meshing

|S| dB

S1,1 from the navigation

You have the option of reducing the accuracy limit for the mesh adaptation or starting the adaptation with a finer starting mesh resolution to obtain even more accurate results. However, these options will certainly increase the simulation time and might be more recommendable after the basic design state of the antenna device is finished. Another possibility for obtaining an impression of the reliability of a solution is to perform a second simulation with a completely different solver and mesh type, as will be shown in the following chapter.

Please note: Refer to the Getting Started manual for more information on using Template Based Postprocessing for automated extraction and visualization of arbitrary results from various simulation runs.

Frequency Domain Solver

CST MICROWAVE STUDIOoffers a variety of frequency domain solvers that are specialized for different types of problems. They differ not only by their algorithms, but also by the type of grid on which they are based. The general purpose frequency domain solvers are available for hexahedral grids as well as tetrahedral grids.

The availability of a frequency domain solver within the same environment offers a very convenient method of cross-checking results produced by the time domain solver with minimal additional effort.

? Making a Copy of Transient Solver Results

Before performing a simulation with a frequency domain solver, you may want to keep the results of the transient solver to allow for an easy comparison of the two simulations. To obtain the copy

?

of the current results: Select, for example, the |S| dB folder in 1D Results, then press Ctrl+c and Ctrl+v. The copy of the result curve will be created in the selected folder. The name of the copy will be S1,1_1. You may rename it to S1,1_TD with the Rename command from the context menu. Use Add new tree folder from the context menu to create an extra folder. Please note that at the current time it is not possible to make a copy of 2D or 3D results.

? Optimize Structure for Tetrahedral Mesh

In the following section, the general purpose frequency domain solver is applied to the tetrahedral mesh. This solver is less efficient if there are PEC sheets with very small, but non zero thicknesses, as represented by the antenna patch in our example. Because this thickness has a rather small influence on the results compared to a zero thickness, we rebuild the patch as a PEC sheet, as shown in the following section.

First, select the patch in the navigation tree and then select the patchs bottom face using the face pick tool (Objects

Pick

Pick Face,

). Therefore rotate the structure as shown in the

picture below and double click on the patch.

A PEC sheet is easily created from the selected face by applying Objects Shape from Picked Faces,

):

Face Healing Tools

Enter a suitable name for the new shape (patch0) and confirm the creation by pressing the OK button. Finally, delete the old patch (component1 with zero height (component1

There may be old results present from the previous transient solver run that will be overwritten when changing the model. In this case, the following warning message appears:

patch0) remains.

patch) so that only the newly created patch

Press OK to acknowledge deletion of the previous results.

In order to allow a tetrahedral-based calculation, we change the Mesh type from hexahedral to tetrahedral in the Mesh Properties dialog box (Mesh

Global Mesh Properties,

). This

selection can also be performed directly in the Frequency Domain Solver Parameters dialog box when choosing the desired solver type, as demonstrated in the following chapter. Furthermore, regarding the circular geometry of the patch antenna and its coaxial feed, it is advisable to refine the default mesh settings. This ensures a homogenous size of the tetrahedra before starting the mesh adaptation. Therefore, please increase the Steps per wavelength to a value of 10 in the Mesh Properties dialog box:

Afterwards, open the Special Mesh Properties dialog box by pressing the Specials button. Please activate the Surface: General tab and reduce the Curvature refinement ratio to 0.03 and increase the Maximal number of steps from curvature refinement to 1000 to allow a better starting approximation of the circular elements. Press the Help button to obtain more information on the settings.

Please check the settings and confirm them by clicking the OK buttons in both dialog boxes.

? Frequency Domain Solver Settings

The Frequency Domain Solver Parameters dialog box is opened by selecting Solve Frequency Domain Solver from the main menu or by pressing the corresponding icon toolbar.

in the

There are three different methods to choose from. For the example here, please choose the General Purpose frequency domain solver. In the Mesh Type combo box you may choose between Hexahedral and Tetrahedral Mesh. Due to the previously made settings in the Mesh Properties dialog box, the Tetrahedral Mesh is already selected.

S-parameters in the frequency domain are obtained by solving the field problem at different frequency samples. These single S-parameter values are then used by the broadband frequency sweep to get the continuous S-parameter values. With the default settings in the Frequency samples frame, the number and position of the frequency samples are chosen automatically in order to fit the required accuracy limit throughout the entire frequency band.

Unlike the time domain solver, the tetrahedral frequency domain solver should always be used with the Adaptive tetrahedral mesh refinement. Otherwise, the initial mesh may lead to a poor accuracy. Therefore, the corresponding check box is activated by default.

Please note that it is necessary to choose a suitable Adaptation Frequency, correspondent to the assumed radiation behavior of the antenna. A good choice for an antenna structure is usually the center frequency of the calculation range, so in this example we enter the value of 2.5 GHz in the dialog box (see picture above) and deactivate the corresponding check box. Furthermore, to ensure that the adaptation will satisfy the desired accuracy limit, we increase the Maximum number of passes to 20 in the Adaptive Tetrahedral Mesh Refinement dialog box by pressing the Properties button of the mesh refinement:

After confirming this setting with the OK button, everything is now ready; you may press Start to start the calculation. A progress bar and abort button appear in the status bar, displaying some information about the solver stages:

After the desired accuracy for the S-parameter has been reached, the simulation stops. When the simulation has finished or has been aborted, both items disappear again. During the simulation, the Message Window will display details about the performed simulation.

Frequency Domain Solver Results

Congratulations, you have simulated the patch antenna using the general purpose tetrahedral frequency domain solver! Lets review the results.

? 1D Results (S-Parameters)

You can visualize the maximum difference of the S-parameters for two subsequent passes by selecting 1D Results

Adaptive Meshing

Delta S from the navigation tree:

As evident from the above diagram, several passes of the mesh refinement were required to obtain highly accurate results within the given accuracy level that is set to 1% by default.

You can view the S-parameters magnitude in dB by selecting 1D Results navigation tree:

|S| db in the

It is possible to precisely determine the operational frequency for the patch antenna. Activate the axis marker by pressing the right mouse button within the main window and selecting the Show axis marker option from the context menu. Now you can move the marker to the S11 minimum and pinpoint a resonance frequency for the patch antenna of about 2.4 GHz.

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