antenna tutorial

T U T O R I A L S · V E R S I O N 4

C S T M I C R O W A V E S T U D I O ®

H F D E S I G N A N D A N A L Y S I S

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CST MICROWAVE STUDIO®

Tutorials

The Magic Tee Tutorial 3

The Coaxial Connector Tutorial 25

The Microstrip Phase Bridge Tutorial 63

The Patch Antenna Tutorial 91

The Cavity Tutorial 127

The Narrow Band Filter Tutorial 151

16.08.2002

The Magic Tee Tutorial

Geometric Construction and Solver Settings 4

Introduction and Model’s Dimensions 4Geometric Construction Steps 5

Results 15

1D Results (Port Signals, S-Parameters) 152D and 3D Results (Field Monitors and Port Modes) 17

Accuracy Considerations 19

Getting More Information 23

4 CST MICROWAVE STUDIO®

– Magic Tee Tutorial

Geometric Construction and Solver Settings

Introduction and Model’s Dimensions

In this tutorial you will analyze a well-known and commonly used high frequency device:the Magic Tee. The main idea behind the Magic Tee is to combine a TE and a TM waveguide splitter (see the figure below for an illustration and the dimensions). Although CSTMICROWAVE STUDIO® can provide a wide variety of results, this tutorial concentratessolely on the S-parameters and electric fields. In this particular case, port 1 and port 4are de-coupled, so one can expect S14 and S41 to be very small. Viewing the electricfields should give you a better insight into the Magic Tee.

Now let’s start the tutorial and try to understand the behavior of this “magic” waveguidedevice.

We strongly suggest that you carefully read through the CST MICROWAVE STUDIO®

Getting Started manual before starting this tutorial.


– Magic Tee Tutorial 5

Geometric Construction Steps

! Select a Template

Once you start CST MICROWAVE STUDIO® and choose to create a new project, youare requested to select a template which fits best to your current device. Here the“Waveguide Coupler” template should be chosen.

This template automatically sets the units to mm and GHz, the background material toPEC (which is the default anyway) and all boundaries to be perfect electric conducting.

Since the background material (which will automatically enclose the model) is specifiedas being a perfect electric conductor here, you only need to model the air filled parts ofthe waveguide device. In the case of the Magic Tee, a combination of three bricks issufficient to describe the whole device.

! Define Working Plane Properties

The next step will usually be to set the working plane properties in order to make thedrawing plane large enough for your device. Since the structure has a maximumextension of 100mm along a coordinate direction, the working plane size should be set to100mm (or more). These settings can be changed in a dialog box, which opens afterselecting Edit # Working Plane Properties from the main menu. Please note that we willuse the same document conventions here as they have been introduced in the GettingStarted manual.



Change the settings in the working plane properties window to the values given belowbefore pressing the Ok button.

Size 100Width 10Snap width 5

! Define the First Brick

Now you can go ahead and create the first brick:

The easiest way to do this is to click the “create a brick” icon or select Objects #Basic Shapes # Brick from the main menu.

CST MICROWAVE STUDIO® now asks you for the first point of the brick. The currentcoordinates of the mouse pointer are shown in the bottom right corner of the drawingwindow in an information box. After you double-click on the point x=50 and y=10, theinformation box will show the current mouse pointer’s coordinates and the distance (DXand DY) to the previously picked position. Drag the rectangle to the size DX=-100 andDY=-20 before you double-click to fix the dimensions. CST MICROWAVE STUDIO® nowswitches to the height mode. Drag the height to h=50 and double-click to finish theconstruction. You should now see both the brick, shown as a transparent model, and adialog box, where your input parameters are shown. If you have made a mistake duringthe mouse based input phase, you can correct it by editing the values numerically.Create the brick with the Ok button. Your brick’s mouse-based input parameters aresummarized in the table below.

Xcenter 50 = XmaxYcenter 10 = YmaxDX -100 (Xmin = -50)DY -20 (Ymin = -10)H 50 (Zmin=0, Zmax=50)



You have just created the waveguide connecting ports 2 and 3. Adding the waveguideconnection to port 1 will introduce another of CST MICROWAVE STUDIO®’s features,the Working Coordinate System (WCS). It allows you to avoid making calculationsduring the construction period. Let’s continue and discover this tool’s advantages.

! Align the WCS with the Front Face of the First Brick

To add the wave guide belonging to port 1 on the front face as shown in the pictureabove, activate the “Pick face” tool with one of these three options:

1. “Pick face” tool icon2. Objects # Pick # Pick Face3. Shortcut: F

Note: The shortcuts only work if the main drawing window is active. You can activateit by single-clicking into it.

Now simply double-click on the front face of the brick to complete the pick operation.

The working plane can now be aligned with the selected face by pressing the “align WCS

with face” icon . This action moves and rotates the WCS so that working plane (uvplane) coincides with the selected face.

Front face



! Define the Second Brick

With the WCS in the right place, it’s quite simple to create the second brick. Start thebrick creation mode with either the main menu’s Objects # Basic Shapes # Brick or the

corresponding icon . Please remember that all values used for shape constructionare relative to the uvw coordinate system as long as the WCS is active.

The new brick should be aligned with the edge mid-points of the first brick as shown inthe picture above. In a first step you should pick the lower edge’s mid point by simply

activating the appropriate pick tool (Objects # Pick # Pick Edge Mid Point or use theshortcut: M). Now all edges become highlighted and you simply double-click on the firstbrick’s lower edge as shown in the picture. Afterwards you should repeat the sameprocedure for the brick’s upper edge.

Since you have now selected two points, which are located on a line, you will berequested to enter the width of the brick. Please note that this step will be skipped if thepreviously picked two points already form a rectangle (not only a line). Now you shoulddrag the width of the brick to w=50 (watch the coordinate display in the lower right cornerof the drawing window) and double click at this location.

Finally you have to specify the brick’s height. Therefore you should drag the mouse tothe proper height h=30 and double-click at this location. Please note that instead ofspecifying coordinates with the mouse (as we have done here), you can also press theTAB key whenever a coordinate is requested. This will open a dialog box where you canspecify the coordinates numerically.

Lower edgemid point

Upper edge mid point



After finishing the brick’s interactive construction, a dialog box will again appear showinga summary of the brick’s parameters.

Some of the coordinate fields now contain mathematical expressions since some of thepoints were entered by using the pick tools. Here the functions xp(1), yp(1) represent thepoint coordinates of the firstly picked point (the mid point of the first brick’s lower edge).Analogously the functions xp(2) and yp(2) correspond to the upper edge’s mid point.

You should now confirm the brick’s creation by pressing the Ok button. Let’s go straightahead to construct the third brick.

First brick’s top face



! Align the WCS with the First Brick’s Top Face

The next brick should be aligned with the top face of the first brick. In order to align the

local coordinate system with this face you should first activate the Pick Face mode ( ,Objects # Pick # Pick Face or shortcut F) and double-click on the desired face.

Afterwards you should press the “align WCS with face” icon , select WCS # AlignWCS With Selected Face from the main menu or use the shortcut W.

! Construct the Third Brick

The brick creation mode for drawing the third brick should now be activated by selecting

either Objects # Basic Shapes # Brick or the “create a Brick” icon .

Once you are requested to enter the first point you should activate the mid point edgepick tool (as you already did for the previous brick) and double click on the top face’supper edge mid point (see picture above).

The next step is to drag the mouse in order to specify the extension of 50 along the –vdirection (hold down the Shift key while dragging the mouse to restrict the coordinatemovement to the v direction only) and double-click at this location. Afterwards you shouldspecify the width of the brick as being w=20 and the height being h=30 in the same wayor by entering these values numerically.

Top face’s upper edgemid point



Finally confirm these settings in the brick creation dialog box. Now the structure shouldlook as follows:

! Define Port 1

In the next step you will assign the first port to the front face of the Magic Tee (seepicture above). The easiest way to do this is to pick the port face first by activating the

face pick tool ( , Objects # Pick # Pick Face or shortcut F) and double-clicking at thedesired face.

Once the port’s face is selected you can open the wave guide port dialog box by eitherselecting Solve # Wave guide Ports from the main menu or by pressing on the “define

port” icon . The settings in the wave guide port dialog box will automatically specifythe extension and location of the port according to the bounding box of previously pickedelements (faces, edges or points).

Front face



In this case you can simply accept the default settings and press Ok to create the port.The next step is the definition of ports 2, 3 and 4.

! Define Ports 2, 3, 4

Repeat the last steps (pick face and create port) to define port 2, port 3 and port 4. Onceyou have completed this step your model should look as follows. Please double-checkyour input before you go ahead to the solver settings.

Port 3



! Define the Frequency Range

The frequency range for this example extends from 3.4 GHz to 4 GHz. Change Fmin andFmax to the desired values in the define frequency dialog box (opened by pressing the

“define frequency” icon or choosing Solve # Frequency) and store this settings bypressing the Ok button. The currently selected units are shown in the status bar.

! Define Field Monitors

Since the amount of data generated by a broadband time domain calculation is hugeeven for relatively small examples, it is necessary to define which field data should bestored before the simulation is started. CST MICROWAVE STUDIO® uses the concept ofso-called “monitors” in order to specify which types of field data to store. In addition to thetype, you also have to specify whether the field should be recorded at a fixed frequencyor at a sequence of time samples. You can define as many monitors as necessary inorder to get the fields at various frequencies. Please note that an excessive number offield monitors may significantly increase the memory space required for the simulation.

In order to add a field monitor click the “define monitor” icon or select Solve # FieldMonitors from the main menu.

In this example you should define an electric field monitor (Type = E-Field) at aFrequency of 3.6 GHz before pressing the Ok button to store the settings.



! Define the Solver’s Parameters and Start the Calculation

The solver’s parameters are specified in the solver control dialog box, which can beopened by selecting Solve # Transient Solver from the main menu or by pressing the

“transient solver” icon .

You should now specify whether the full S-matrix should be calculated or if a subset ofthis matrix is sufficient. For the Magic Tee device we are interested in the input reflectionat port 1 and in the transmission from port 1 to the other three ports 2, 3 and 4.

Thus we only need to calculate the S-parameters S1,1, S2,1, S3,1 and S4,1. All of themcan be derived by an excitation at port 1. Therefore you should change the Source typefield in the Stimulation settings frame to Port 1. If you left this setting at All Ports, the fullS-matrix would be calculated.

Finally press the Start solver button in order to start the calculation. A progress windowappears showing you some information about the calculation’s status.

This progress window disappears when the solver has successfully finished. Otherwise aDetails field will be shown to display error messages or warnings.



Results

Congratulations, you have simulated the Magic Tee. Let’s have a look at the results.

1D Results (Port Signals, S-Parameters)

Firstly, take a look at the port signals. Open the 1D results folder in the navigation treeand click on the Port signals folder.

This plot shows the incident and reflected or transmitted wave amplitudes at the portsversus time. The incident wave amplitude is called i1 and the reflected or transmittedwave amplitudes of the 4 ports are o1,1, o2,1, o3,1 and o4,1. You can see that thetransmitted wave amplitudes o2,1 and o3,1 are delayed and distorted. (o2,1 and o3,1 areidentical so don’t worry if you only see one curve).



The S-Parameters can be plotted by clicking on the 1D Results # SdB folder.

As expected previously, the transmission to port 4, S4,1 is extremely small (-150 dB isclose to the solver’s noise floor). It is obvious that this simple device is very poorlymatched so that the transmission to the ports 2 and 3 is in the same order of magnitudeas the input reflection at port 1.



2D and 3D Results (Field Monitors and Port Modes)

Finally we will have a look at the 2D and 3D field results. We will first inspect the portmodes, which 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 fundamentalport mode you should click on the e1 folder.

The plot also shows some important properties of the mode such as mode type, cut-offfrequency and propagation constant. The port modes at the other ports can be visualizedin the same way.

The full three-dimensional electric field distribution in the Magic Tee can be shown byselecting the 2D/3D Results # E-Field # efield (f=3.6) folder from the navigation tree andclicking on the Normal item. The field plot will then show a three dimensional contour plotof the electric field normal to the surface of the structure.



You can watch an animation of the fields by checking the Animate Fields option in thecontext menu. The appearance of the plot can be changed in the plot properties dialogbox, which can be opened by selecting Results # Scalar Plot from the main menu or PlotProperties from the context menu. Optionally you can also double-click on the plot inorder to open this dialog box.



Accuracy Considerations

The transient S-parameter calculation is mainly affected by two sources of numericalinaccuracies:

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

In the following we will give you some hints how to handle these errors and how toensure to achieve highly accurate results.

! Numerical Truncation Errors Due to Finite Simulation Time Intervals

The transient solver calculates the time varying field distribution in the device whichresults from excitation with a gaussian pulse at the input port as primary result. Thus thetime signals of the port mode amplitudes are the fundamental results from which the S-parameters are derived by using a Fourier Transform.

Even if the accuracy of the time signals themselves is extremely high, numericalinaccuracies can be introduced by the Fourier Transform which assumes that the timesignals have completely decayed to zero at the end. If the latter is not the case, a rippleis introduced in the S-parameters affecting the accuracy of the results. The amplitude ofthis ripple increases with the signal amplitude remaining at the end of the transient solverrun.

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

The level of the truncation error can be controlled by using the Accuracy setting in thetransient solver control dialog box. The default value of –30dB will usually givesufficiently accurate results for coupler devices. However, to obtain highly accurateresults for filter structures it is sometimes necessary to increase the accuracy to –40dBor –50dB.

Since increasing the accuracy requirement for the simulation limits the truncation errorand thus in turn increases the simulation time, it should be specified with care. As a ruleof thumb, the following table can be used:

Desired Accuracy Level Accuracy Setting(Solver control dialog box)

Moderate -30dBHigh -40dBVery high -50dB

The following general rule may be useful as well: If you find a large ripple in the S-parameters, it might be necessary to increase the solver’s accuracy setting.



! Effect of the Mesh Resolution on the S-parameter’s Accuracy

The inaccuracies arising from the finite mesh resolution are usually more difficult toestimate. The only way to ensure the accuracy of the solution is to increase the meshresolution and recalculate the S-parameters. If these results do not significantly changeanymore by increasing the mesh density, then convergence has been achieved.

In the example above, you have used the default mesh which has been automaticallygenerated by an expert system. The easiest way to prove the accuracy of the results is touse the fully automatic mesh adaption which can be switched on by checking theAdaptive mesh refinement option in the solver control dialog box (Solve # TransientSolver):

After activating the adaptive mesh refinement tool, you should now start the solver againby pressing the Start solver button. After a couple of minutes during which the solver isrunning through mesh adaption passes, the following dialog box will appear:



This dialog box tells you that the desired accuracy limit (2% by default) could be met bythe adaptive mesh refinement. Since the expert system’s settings have now beenadjusted such that this accuracy is achieved, you may switch off the adaption procedurefor subsequent calculations (e.g. parameter sweeps or optimizations).

You should now confirm the deactivation of the mesh adaption by pressing the Yesbutton.

After the mesh adaption procedure has completed, you can visualize the maximumdifference of the S-parameters for two subsequent passes by selecting 1D Results#Adaptive Meshing # Delta S from the navigation tree:

As you can see, the maximum deviation of the S-parameters is below 0.55% whichindicates that the expert system based meshing would have been fine for this exampleeven without running the mesh adaption procedure.



The convergence process of the input reflection S1,1 during the mesh adaption can bevisualized by selecting 1D Results# Adaptive Meshing# |S|linear# S1,1 from thenavigation tree:

The convergence process of the other S-parameters can be visualized in the same way.Please note that S4,1 is extremely small (<-120dB) in this example such that it’svariations are mainly due to the numerical noise and thus are disregarded by theautomatic mesh adaption procedure.

By inspecting the plots, you can confirm that the results are quite stable here.

The huge advantage of this expert system based mesh refinement procedure overtraditional adaptive schemes is that the mesh adaption needs to be carried out once foreach device only in order to determine the optimum settings for the expert system.Afterwards there is no need for time consuming mesh adaption cycles during parametersweeps or optimization.



Getting More Information

Congratulations! You have just completed the Magic Tee tutorial which should haveprovided you with a good working knowledge on how to use the transient solver tocalculate S-parameters. The following topics have been covered so far:

1. General modeling considerations, using templates, etc.2. Use picked points to define objects relatively to each other.3. Define ports.4. Define frequency ranges and boundary conditions.5. Define field monitors.6. Start the transient solver.7. Visualize port signals and S-parameters.8. Visualize port modes and field monitors.9. Check the truncation error of the time signals10. Ensure to obtain accurate and converged results by using the automatic expert

system based mesh adaption.

You can obtain more information for each particular step by using the online help systemwhich can be activated either by pressing the Help button in each dialog box or bypressing the F1 key at any time to obtain context sensitive information.

Sometimes we have referred to the Getting Started manual which is also a good sourceof information for general topics.

In addition to this tutorial you can find some more S-parameter calculation examples inthe examples folder in your installation directory. Each of these examples contains aReadme item in the navigation tree which will give you some more information about theparticular device.

Finally, you should refer to the Advanced Topics manual for more in depth information onissues such as the fundamental principles of the simulation method, mesh generation,usage of macros to automate common tasks, etc.

And last but not least: Please also visit one of the training classes being regularly held ata location near you. Thank you for using CST MICROWAVE STUDIO!

The Coaxial Connector Tutorial


Introduction and Model’s Dimensions 26Geometric Construction Steps 27Solver Settings and S-Parameter Calculation 45

Results 53




26 CST MICROWAVE STUDIO® – Coaxial Connector Tutorial



In this tutorial you will analyze a 90 degree coaxial connector. CST MICROWAVESTUDIO® can provide a wide variety of results. This tutorial, however, concentrates on S-parameters and surface currents.



All dimensions are given in mil

9070

60 180

310

100

390

39090510

190100

170

40

90°

600

130

140200

160

280

Por

t1

Port 2

Metal

Teflon

Rubber

200

Air

180

160

1

23

140

60

140

All dimensions are given in mil

9070

60 180

310

100

390

39090510

190100

170

40

90°

600

130

140200

160

280

Por

t1

Port 2

Metal

Teflon

Rubber

200

Air

180

160

1

23

140

60

140

The structure shown above consists of several coaxial sections. The inner conductor ofthe connector is made of perfect electrically conducting material and is embedded invacuum. This structure is mounted at three locations with rings made of teflon. One ofthese fixtures additionally contains a rubber ring.

The following explanations on how to model and analyze this device can also be appliedto other coaxial connector structures as well.

CST MICROWAVE STUDIO® – Coaxial Connector Tutorial 27


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

! Select a Template

Once you start CST MICROWAVE STUDIO® and choose to create a new project, youare requested to select a template which fits best to your current device. Here the“Coaxial Connector” template should be chosen.

This template automatically sets the units to mm and GHz, the background material andall boundaries to be perfect electrically conducting. Since the background material and allboundary conditions have been set to be perfect electric conductors, you only need tomodel the interior parts of the connector.


! Set the Units

The template has automatically set the geometrical units to mm. Since all geometricaldimensions are given in mil for this example, you have to change this setting manually.Therefore, please open the units dialog box by selecting Solve # Units from the mainmenu:

Here you should set the Dimensions to mil and press Ok.

! Set the Working Plane’s Properties

The next step will usually be to set the working plane properties in order to make thedrawing plane large enough for your device. Since the structure has a maximum extentof 1320 mil along a coordinate direction, the working plane size should be set to 1500 mil(or more). These settings can be changed in a dialog box, which opens after selectingEdit # Working Plane Properties from the main menu. Please note that we will use thesame document conventions here as they have been introduced in the Getting Startedmanual.

In this dialog box, you should set the Size to 1500 (the unit which has previously beenset to mil is displayed in the status bar), the raster width to 100 and the snap with to 50 toobtain a reasonably spaced grid. Please confirm these settings by pressing the Okbutton.


! Draw the Air Parts

In this structure, the air can be easily modeled by uniting two rotational symmetric parts(a figure of rotation and a cylinder) as shown in the picture below.

880

480510290

140

160

200Air

Air

xy

1,9

23

4567

8

140

Figure of rotation

Cylinder

160

180

880

480510290

140

160

200Air

Air

xy

1,9

23

4567

8

140

Figure of rotation

Cylinder

160

180

In the first step, you can now start drawing the figure of rotation. Since the cross sectionprofile is a simple polygon, you don’t need to use the curve modeling tools here (pleaserefer to the Getting Started manual for this more advanced functionality). For polygonalcross sections it is more convenient to use the figure of rotation tool, activated byselecting Objects # Rotate from the main menu or pressing the toolbar button .

Since no face has been previously picked, the tool will automatically enter a polygondefinition mode and request you to enter the polygon’s points. You could do this by eitherdouble-clicking at each point’s coordinates on the drawing plane by using the mouse oryou could also enter the values numerically. Since the latter approach may be moreconvenient here, we suggest pressing the TAB key and entering the coordinates in thedialog box. All polygon points can thus be entered step-by-step according to the followingtable (whenever you make a mistake, you can delete the most recently entered point bypressing the backspace key):

Point X Y1 0 02 0 1403 480 1404 480 2005 990 2006 990 1607 1280 1608 1280 09 0 0


After the last point has been entered, the polygon will then be closed. The “RotateProfile” dialog box will then automatically appear.

This dialog box allows you to review the coordinate settings in the list. If you encounterany mistakes you can easily change the values by simply double clicking at the incorrectcoordinate’s entry field.

The next step is to assign a material Layer to the shape. In this case, the default layer is“Vacuum” which practically is appropriate for this example.

Finally, please assign a proper Name (e.g. “Air1”) to the shape and press the Ok buttonto finish the creation of the solid. The picture below shows how your structure should looklike now (you may need to rotate the view as explained in the Getting Started manual inorder to obtain this plot).


The construction of the second air part by creating a cylinder can be simplified if a localcoordinate system is introduced first. You can now activate the local coordinate systemby selecting WCS # Local Coordinate System or pressing the corresponding toolbarbutton . Afterwards, the origin of this coordinate system should be moved by selectingWCS # Move Local Coordinates ( ). The following dialog box allows you to enter avector along which the origin of the working coordinate system (WCS) will be moved.

You should now shift the origin by 160 mil along the u direction and by 180 mil along thev direction in order to position the WCS at the center of the cylinder’s base. Afterwardsyou need to rotate the WCS along its u-axis by 90 degrees which can be easily achievedby selecting WCS # Rotate +90° around U axis or using the shortcut Shift+U. The modelshould then look as follows:

The second air part can now be created by using the cylinder tool: Objects # BasicShapes # Cylinder, . Once the cylinder creation mode is active you are requested topick the center of the cylinder. Since this is now the origin of the working coordinatesystem, you can simply press Shift+TAB to open the dialog box for numerically enteringthe coordinates and confirm the settings by pressing Ok (please note that holding downthe Shift key while pressing the TAB key opens the dialog box with the coordinate valuesinitially set to zero rather than the current mouse pointer’s location).


You are now requested to enter the radius of the cylinder. Please press the TAB keyagain and set the Radius to 140 before pressing the Ok button. The Height of thecylinder can then be set to 880 in the same way. Please skip the definition of the innerradius by pressing the ESC key (the air should be modeled as solid cylinder here) andcheck your settings in the following dialog box:

Finally, please set the Name of the cylinder to “air2” and verify that the solid is associatedwith the vacuum Layer. Confirm your settings by pressing Ok. Since the two air partsoverlap each other, the shape intersection dialog box will open automatically, asking youto select a Boolean operation to combine both shapes:


Please select the operation Add both shapes to unite both parts and press the Ok button.Your model should then finally look as follows:

! Model the Teflon and Rubber Cylinders

After successfully modeling the air parts, you can now go ahead and create the firstteflon cylinder. Therefore, it is advantageous to move the WCS to the middle of the tefloncylinder by selecting WCS # Move Local Coordinates ( ):

In this dialog box, you can enter the expression “390 + 310 / 2” in the DW field in order tomove the WCS along the w-axis by this amount. Please refer to the structure’s schematicdrawing earlier in this tutorial to confirm that the new origin of the WCS is located in thecenter of the first teflon cylinder.

Once the coordinate system is located properly, you can now easily model the tefloncylinder by selecting Objects # Basic Shapes # Cylinder, ( ). When you are requestedto enter the cylinder’s center, you can press Shift+TAB and check the coordinate valuesU=0, V=0 before clicking on the Ok button.


Afterwards, press the TAB key again to set the cylinder’s radius to 200. The height of thecylinder should then be set to “310 / 2” (you are currently modeling one half of thecylinder only) in the same way. After skipping the definition of the inner radius bypressing the ESC key, the cylinder creation dialog box should appear:

In this dialog you should first of all assign a proper Name (e.g. “teflon1”) to the shapebefore you enter the expression “–310 / 2” in the Wmin field in order to properly set thecylinder’s full length.

The cylinder’s material is currently set to vacuum by default. In order to change this, youneed to press the New button which will open the layer parameter dialog box:


In this dialog box you should set the Layer name to “teflon” and the Type to be a normaldielectric material. Afterwards, you can specify the dielectric constant of teflon byentering “2.04” in the Epsilon field. Please select the Change button and choose a nicecolor.Finally, you should check your settings in the dialog box again before pressing the Okbutton to store layer’s parameters.

Back in the cylinder creation dialog box, you can create the cylinder by pressing the Okbutton as well. Since the teflon cylinder overlaps with the previously modeled air parts,the shape intersection dialog box will appear again:

Here you should now choose to insert the new teflon cylinder into the air part by selectingInsert highlighted shape before pressing the Ok button. Please refer to the GettingStarted manual for more information on Boolean operations.

Afterwards, the rubber ring inside the first teflon cylinder can be modeled analogously:

1. Activate the cylinder creation tool (Objects # Basic Shapes # Cylinder, ).2. Press Shift+TAB and set the center point to U = 0, V = 0.3. Press TAB and set the Radius to 200.4. Press TAB and set the Height to 100/2.5. Press TAB and set the inner Radius to 140.6. Set the Name to “rubber” and enter “–100/2” in the Wmin field.7. Press the New button to create a new layer.8. In the layer properties dialog box set the Layer name to “rubber”, its Type to

“Normal” and its dielectric constant Epsilon to 2.75.9. Choose a nice color by pressing the Change button and confirm the layer creation

by pressing Ok.


10. Back in the cylinder creation dialog box, verify the layer assignment to “rubber” andpress the Ok button.

11. In the shape intersection dialog box, choose Insert highlighted shape and press Ok.

After successfully performing all these steps above, your model should look as follows:

Before you now continue with the construction of the two remaining teflon rings, theworking coordinate system should be aligned with the front face shown in the pictureabove.

Therefore, please activate the pick face tool by either selecting Objects # Pick # PickFace from the main menu, pressing the corresponding toolbar button or just using theshortcut F (while the main view is active). Afterwards, the front face should be selectedby double-clicking on it. The working coordinate system is aligned with the front face byselecting WCS # Align WCS With Selected Face ( or shortcut W):

Front face

Align WCS

with picked face


The next step is to move the WCS to the location of the second teflon cylinder’s base.Therefore select WCS # Move Local Coordinates ( ) to open the corresponding dialogbox:

Please enter –290 in the DW field before pressing Ok. Now you can straightforwardlymodel the second teflon cylinder as shown in the structure’s drawing.

1. Activate the cylinder creation tool (Objects # Basic Shapes # Cylinder, ).2. Press Shift+TAB and set the center point to U = 0, V = 0.3. Press TAB and set the Radius to 280.4. Press TAB and set the Height to 190.5. Press TAB and set the inner Radius to 90.6. In the cylinder creation dialog box set the Name to “teflon2” and change the Layer

assignment to “teflon” before pressing Ok.7. In the shape intersection dialog box, choose Insert highlighted shape and press Ok.

The model should then look as follows:


For the creation of the third teflon ring you should again move the WCS to the properlocation:

1. Select WCS # Move Local Coordinates ( ) to open the move WCS dialog box.2. Enter –600 in the DW field and press Ok.

The construction of the teflon ring can then be performed by following the steps below:

1. Activate the cylinder creation tool (Objects # Basic Shapes # Cylinder, ).2. Press Shift+TAB and set the center point to U = 0, V = 0.3. Press TAB and set the Radius to 200.4. Press TAB and set the Height to 90.5. Press ESC to skip the definition of the inner radius.6. In the cylinder creation dialog box set the Name to “teflon3” and change the Layer

assignment to “teflon” before pressing Ok.7. In the shape intersection dialog box, choose Insert highlighted shape and press Ok.

After successfully completing these steps, the model should look as follows:

! Model the Inner Conductor

The creation of the inner conductor of the coaxial cable can again be simplified byaligning the working coordinate system with the front face shown in the picture above:

1. Activate the pick face tool (Objects # Pick # Pick Face, )2. Double-click on the front face shown above.3. Align the WCS with the picked face (WCS # Align WCS With Selected Face, )

Front face


The new location of the working coordinate system is then shown as in the picture below:

In a next step, the WCS should be rotated such that its u axis points into the structure byinvoking the command WCS# Rotate +90° around V axis (Shift+V).

Now the first part of the inner conductor can be modeled by a figure of rotation which isshown in the schematic drawing below:

9070

60

220630170

40

90°

600

Rotate polygon

12

3

60

Rotate picked face around axis

Extrude face

v

1,9 2u

3

4

56

7

8

9070

60

220630170

40

90°

600

Rotate polygon

12

3

60

Rotate picked face around axis

Extrude face

v

1,9 2u

3

4

56

7

8

Since the construction of a figure of rotation has already been explained in detail earlierin this tutorial, we will now give a short list of steps only:

1. Activate the wireframe visualization mode by pressing the toolbar icon or usingthe shortcut Ctrl+W. This will allow you to follow the construction since otherwise theparts of the inner conductor will be hidden inside the previously created shapes.

2. Activate the figure of rotation tool (Objects # Rotate, ).3. Enter the points shown in the table below by pressing the TAB key and specifying

the coordinate values numerically:

Point U V1 0 02 1020 03 1020 604 800 60

Rotate WCS

Around V axis


5 800 906 170 907 170 708 0 709 0 0

4. Once the last point has been defined and the polygon is then closed, the rotateprofile creation dialog box will open. In this dialog box check the points’ coordinates,set the Name of the shape to “conductor1” and change the Layer assignment to“PEC” before pressing Ok.

After successfully performing these steps, the screen should look as follows:


Please select the inner conductor by either double-clicking on it in the view or byselecting PEC # conductor1 from the navigation tree. Once this is done, you maydeactivate the wireframe plot mode ( or Ctrl+W):

The next step is to align the working coordinate system with the inner conductor’s endface shown above. Therefore, please rotate the view to ensure that the end face is visible(select View # Mode # Rotate and drag the mouse while pressing the left button).Afterwards, please activate the face pick tools (Objects # Pick # Pick Face, ) anddouble-click on the desired face.

End face


Now align the WCS with this face by pressing WCS # Align WCS With Selected Face( ). The next step is to define a rotation axis by selecting Objects # Pick # Edge fromCoordinates ( ). Then enter the first point’s coordinates by pressing the TAB key(U = -100, V = 0) and the coordinates of the second point (U = -100, V = -100) in thesame way. Finally please check and confirm the settings in the dialog box.

Afterwards you need to select the previously picked face once again (Objects # Pick #Pick Face, + double-click on the face). Activate the figure of rotation mode byselecting Objects # Rotate, ( ). Since a face has been previously picked, the definitionof polygon points is skipped and a dialog box is opened immediately:

In this dialog box you should first assign a proper Name (e.g. “conductor2”) to the shape.Since the rotation axis is aligned with the negative v-axis direction and the rotation angleis specified in a right-handed system, the Angle must be set to 90 degrees here (therotation axis is visualized by a blue arrow while the dialog box is open). Finally check theLayer assignment to PEC and press the Ok button.


Due to the creation of the new conductor, the shape selection is cleared automaticallyand the conductors will thus be hidden inside the air and teflon parts. Therefore pleaseselect the PEC layer by clicking at Layers # PEC in the navigation tree to obtain thefollowing picture:

The last step in the model’s geometric construction process is to create the thirdconductor by extruding the end face of the figure of rotation defined above.

Please rotate the view in order to obtain a picture similar to the following:

Afterwards, pick the end face of the conductor as shown in the picture above (Objects #Pick # Pick Face, + double-clicking at the end face).

You can now open extrude face dialog box by selecting Objects # Extrude or pressingthe toolbar button . Similarly to the figure of rotation, a polygon definition mode wouldbe entered by the extrude tool if no face had been previously selected.

End face

Pick

end face


In this dialog box, please assign a proper Name (e.g. “conductor3”), set the Height to 600(mil) and check the Layer assignment to PEC before pressing the Ok button. Afterwardsyou need to select the PEC layer again by clicking at Layers # PEC in the navigationtree. Your screen should then finally look as follows:


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 becalculated. 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 mostaccurate 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 thewaveguide’s cross-section, it must be defined large enough to entirely cover these modefields. In case of a coaxial cable, the port thus has to cover the coaxial cable’s substratecompletely.

Before you continue with the port definition, please clear the selection by either double-clicking on the view’s background or by selecting the Layers item in the navigation tree.

The port’s extent can either be defined numerically or, which is more convenient here, bysimply picking the face to be covered by the port. Therefore, please activate the pick facetool (Objects # Pick # Pick Face, ) and double-click the substrate’s port face of thefirst port as shown in the pictures below:

Pick first port’s substrate face

First port’s substrate face


Please open the waveguide dialog box now (Solve # Waveguide Ports, ) to define thefirst port 1:

Whenever a face is picked before the port dialog is opened, the port’s location and sizewill automatically be defined by the picked face’s extent. Thus the port’s Transversalposition is initially set to Use picks. You can simply accept this setting and go ahead.

The next step is to choose how many modes should be considered by the port. Forcoaxial devices, we usually only have a single propagating mode. Thus you shouldsimply keep the default of one mode.


Please finally check the settings in the dialog box and press the Ok button to create theport:

Now you can repeat the same steps for the definition of the second port:

1. Pick the corresponding substrate’s port face (Objects # Pick # Pick Face, ).2. Open the waveguide dialog box (Solve #Waveguide Ports, ).3. Press Ok to store the port’s settings.

Your model including the ports should now look as follows:


! Define Boundary Conditions and Symmetries

Before you start the solver, you should always check the boundary and symmetryconditions. The easiest way to do this is to enter the boundary definition mode bypressing the tool bar item or selecting Solve # Boundary Conditions. The boundaryconditions will then become visualized in the main view as follows:

Here all boundary conditions are set to “electric” which just means that the structure isembedded in a perfect electric conducting housing. These defaults (which have been setby the template) are appropriate for this example.

Due to the structure’s symmetry to the X/Y plane and the fact that the magnetic field inthe coaxial cable is perpendicular to this plane, a symmetry condition can be used. Thissymmetry will reduce the time required for the simulation by a factor of two. You shouldalso refer to the example in the Getting Started manual for more information onsymmetry conditions.


Please enter the symmetry plane definition mode now by activating the Symmetry planestab in the dialog box. The screen should then look as follows:

By setting the symmetry plane X/Y to magnetic, you force the solver to calculate only themodes which have no tangential magnetic field component to these planes (thus forcingthe electric field to be tangential to these planes).

After these settings have been made, the structure should look as follows:


Please note that you also could double-click at the symmetry plane’s handle and choosethe proper symmetry condition from the context menu.

Finally press the Ok button to complete this step.

In general, you should always make use of symmetry conditions whenever possible inorder to reduce calculation times by a factor of two to eight.


The frequency range for the simulation should be chosen with care. In contrast tofrequency domain tools, the performance of a transient solver such as CSTMICROWAVE STUDIO can be degraded if the frequency range is chosen to be toosmall (the opposite is usually true for frequency domain solvers).

We recommend using reasonably large bandwidths of 20% to 100% for the transientsimulation. In this example, the S-parameters are to be calculated for a frequency rangebetween 0 and 8 GHz. With the center frequency being 4 GHz, the bandwidth (8 GHz –0 GHz = 8 GHz) is 200% of the center frequency, which is just fine. Thus you can simplychoose the frequency range as desired between 0 and 8 GHz.

Please note: Assuming that you are interested primarily in a frequency range ofe.g. 11.5 to 12.5 GHz (for a narrow band filter), then the bandwidth would onlybe about 8.3%. In this case it would make sense to increase the frequencyrange (without loosing accuracy) to a bandwidth of 30% which corresponds to afrequency range of 10.2 – 13.8 GHz. This extension of the frequency rangecould speed up your simulation by more than a factor of three!

In contrast to frequency domain solvers, the lower frequency can be set to zerowithout any problems! The calculation time can often be reduced by half if thelower frequency is set to zero rather than e.g. 0.01 GHz.


After the proper frequency band for this device has been chosen, you can simply openthe frequency range dialog box (Solve # Frequency, ) and enter the range from 0 to 8(GHz) before pressing the Ok button (the frequency unit has previously been set to GHzand is displayed in the status bar):

! Define Field Monitors

Since the amount of data generated by a broadband time domain calculation is hugeeven for relatively small examples, it is necessary to define which field data should bestored before the simulation is started. CST MICROWAVE STUDIO® uses the concept ofso-called “monitors” in order to specify which types of field data to store. In addition to thetype, you can also choose whether the field should be recorded at a fixed frequency or ata sequence of time samples. You may define as many monitors as necessary in order toget the fields at various frequencies from a single calculation run. Please note that anexcessive number of field monitors may significantly increase the memory spacerequired for the simulation.

Let’s assume that you are interested in the current distribution on the coaxial cable’sconductors at several frequencies (2, 4, 6 and 8 GHz).

In order to add field monitors, select Solve # Field Monitors from the main menu or pressthe corresponding icon in the toolbar .


In this dialog box you should firstly select the Type H-Field / Surface current before youspecify the frequency for the monitor in the Frequency field. Afterwards you should pressthe Apply button to store the monitor’s data. Please define monitors for the followingfrequencies now: 2, 4, 6, 8 (with GHz being the currently active frequency unit). Pleasemake sure that you press the Apply button for each monitor (the monitor definition is thenadded in the Monitors folder in the navigation tree).

After the monitor definition is completed, you can close this dialog box by pressing theOk button.


The solver’s parameters are specified in the solver control dialog box, which can beopened by selecting Solve # Transient Solver from the main menu or by pressing thecorresponding icon in the toolbar.

Since this two port structure is lossless, the transient solver will need to calculate a singleport only in order to obtain the full S-matrix even if you specify All Ports for the Sourcetype.


In this case you can thus keep the default settings and press the Start solver button tostart the calculation. A progress window appears showing you some information aboutthe calculation’s status.


Results

Congratulations, you have simulated the coaxial connector! Let’s have a look at theresults.




This plot shows the incident, reflected and transmitted wave amplitudes at the portsversus time. The incident wave amplitude is called i1 and the reflected or transmittedwave amplitudes of the two ports are o1,1 and o2,1. These curves show the delay in thetransition from the input port to the output port and a relatively small reflection at the inputport.

The S-Parameters magnitude in dB scale can be plotted by clicking on the 1D Results #SdB folder.

As expected previously, the input reflection S1,1 is quite small (less than –15 dB) acrossthe entire frequency range.



Finally you can have a look at the 2D and 3D field results. You should first inspect theport modes, which 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 port mode,please click on the e1 folder. After properly rotating the view and tuning some settings inthe 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 theplot’s parameters):

The plot also shows some important properties of the mode such as mode type,propagation constant and line impedance. The port mode at the second port can bevisualized in the same way.


The full three-dimensional surface current distribution on the conductors can be shownby selecting one of the entries in the 2D/3D Results # Surface Current folder from thenavigation tree. The surface current at a frequency of 4 GHz can thus be visualized byclicking at the 2D/3D Results # Surface Current # h-field (f=4) [1] entry (you may needto activate the transparent plotting option by selecting Results # All Transparent, )

You can toggle an animation of the currents on and off by selecting the Results #Animate Fields item. The surface currents for the other frequencies can be visualized inthe same way as shown above.








Even if the accuracy of the time signals themselves is extremely high, numericalinaccuracies can be introduced by the Fourier Transform which assumes that the timesignals have completely decayed to zero at the end. If the latter is not the case, a rippleis introduced into the S-parameters affecting the accuracy of the results. The amplitudeof this ripple increases with the signal amplitude remaining at the end of the transientsolver run.


The level of the truncation error can be controlled by using the Accuracy setting in thetransient solver control dialog box. The coaxial connector template has already set thedefault to –40dB since this is a good compromise between speed and accuracy for thiskind of devices. However, you may set the accuracy to –50 dB or even –60 dB withrelatively little increase in computation time.







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 resolutionand recalculate the S-parameters. If these results do not significantly change anymorewhen the mesh density is increased, then convergence has been achieved.

In the example above, you have used the default mesh which has been automaticallygenerated by an expert system. The easiest way to test the accuracy of the results is touse the fully automatic mesh adaption which can be switched on by checking theAdaptive mesh refinement option in the solver control dialog box (Solve # TransientSolver):





After the mesh adaption procedure has completed, you can visualize the maximumdifference of the S-parameters for two subsequent passes by selecting 1D Results #Adaptive Meshing # Delta S from the navigation tree:

As you can see, three passes of the mesh refinement were required to obtain highlyaccurate results within the given accuracy level, which is set to 2% by default.


The convergence process of the input reflection S1,1 during the mesh adaption can bevisualized by selecting 1D Results # Adaptive Meshing # |S| dB # S1,1 from thenavigation tree:

The convergence process of the other S-parameters magnitudes and phases can bevisualized in the same way.




Congratulations! You have just completed the coaxial connector tutorial which shouldhave provided you with a good working knowledge on how to use the transient solver tocalculate S-parameters. The following topics have been covered so far:

1. General modeling considerations, using templates, etc.2. Model a coaxial structure by using the rotate, cylinder and extrude tools and define

the substrates.3. Define ports.4. Define frequency range, boundary conditions and symmetry planes.5. Define field monitors for surface current distributions.6. Start the transient solver.7. Visualize port signals and S-parameters.8. Visualize port modes and surface currents.9. Check the truncation error of the time signals10. Ensure to obtain accurate and converged results by using the automatic expert




In addition to this tutorial you can find some more S-parameter calculation examples forplanar structures in the examples folder in your installation directory. Each of theseexamples contains a Readme item in the navigation tree which will give you some moreinformation about the particular device.



The Microstrip Phase BridgeTutorial



Results 82




64 CST MICROWAVE STUDIO® – Microstrip Phase Bridge Tutorial



In this tutorial you will analyze a Microstrip Phase Bridge. CST MICROWAVE STUDIO®

can provide a wide variety of results. This tutorial, however, concentrates solely on the S-parameters and surface currents.



24.58

4.90

25.0044.41

44.6830.00300.00

40.40

20.00

30.00

Port 2

Port 1

Substrate = Al2O3

Metallisation = PEC

All dimensions are given in milli-inches (mil).Thickness of the metallisation is 0.118 mil.

177.58

The structure depicted above consists of two different materials: The aluminiumoxidesubstrate (Al2O3) and the stripline metallisation. There is no need to model the groundplane since it can easily be described by using a perfect electric boundary condition.

The following explanations on how to model and analyze this device can also be appliedto other microstrip devices as well.

25.0

CST MICROWAVE STUDIO® – Microstrip Phase Bridge Tutorial 65



! Select a Template

Once you start CST MICROWAVE STUDIO® and choose to create a new project, youare requested to select a template which fits best to your current device. Here the “PlanarFilter” template should be chosen.

This template automatically sets the units to mm and GHz, the background material tovacuum and all boundaries to perfect electric conducting. Since the background materialhas been set to vacuum, the structure can be modeled just as it looks like on your desk.


! Set the Units

The template has automatically set the geometrical units to mm. Since all geometricaldimensions are given in mil for this example, you have to change this setting manually.Therefore please open the units dialog box by selecting Solve # Units from the mainmenu:

Here you should set the Dimensions to mil and press Ok.


The next step will usually be to set the working plane properties in order to make thedrawing plane large enough for your device. Since the structure has a maximumextension of 300 mil along a coordinate direction, the working plane size should be set to400 mil (or more). These settings can be changed in a dialog box, which opens afterselecting Edit # Working Plane Properties from the main menu. Please note that we willuse the same document conventions here as they have been introduced in the GettingStarted manual.

In this dialog box, you should set the Size to 400 (the unit which has previously been setto mil is displayed in the status bar), the raster width to 10 and the snap with to 5 toobtain a reasonably spaced grid. Please confirm these settings by pressing the Okbutton.

! Draw the Substrate Brick

The first construction step for modeling a planar structure is usually to define thesubstrate layer. This can be easily achieved by creating a brick made of the substrate’smaterial. Please activate the brick creation mode now (Objects # Basic Shapes # Brick,

).


When you then are prompted to define the first point, you can enter the coordinatesnumerically by pressing the TAB key which will open the following dialog box:

In this example you should enter a substrate block which has an extension of 300 mil ineach of the transversal directions. The transversal coordinates can thus be described byX = -150, Y = -150 for the first corner and X = 150, Y = 150 for the opposite corner,assuming that the brick is modeled symmetrically to the origin. Thus please enter the firstpoint’s coordinates X = -150 and Y = -150 in the dialog box and press the Ok button.

Afterwards you can repeat these steps for the second point:

1. Press the TAB key2. Enter X = 150, Y = 150 in the dialog box and press Ok.

Now you will be requested to enter the height of the brick. This can also be numericallyspecified by pressing the TAB key again, entering the Height of 25 and pressing the Okbutton. Now the following dialog box will appear showing you a summary of yourprevious input:

Please check all these settings carefully. When you encounter any mistake, pleasechange the value in the corresponding entry field.

You should now assign a meaningful name to the brick by entering e.g. “substrate” in theName field.


You still need to define the substrate material. Since no material layer has yet beendefined for the substrate, you should open the layer definition dialog box by pressing theNew button:

In this dialog box you should define a new Layer name (e.g. Al2O3) and set the layerType to a Normal dielectric material. Afterwards specify the material properties in theEpsilon and Mue fields. Here you only need to change the dielectric constant Epsilon to9.9. Finally choose a nice color for the layer by pressing the Change button. Your dialogbox should now look similar to the picture above before you press the Ok button.

Back in the brick creation dialog box you can also press the Ok button to finally createthe substrate brick. You screen should now look as follows (you can press the SPACEkey in order to zoom the structure to the maximum possible extent):

Substrate’stop face


! Model the Stripline Metallisation

The next step is to model the stripline metallisation on top of the substrate. Thus youfirstly should move the drawing plane on top of the substrate. This can be easilyachieved by activating the face pick tool (Objects # Pick # Pick Face, ) and doubleclicking on the substrate’s top face as shown above. The face selection should then bevisualized as in the following picture:

After the face has now been selected, you can align the working coordinate system withits plane. Therefore please either select WCS # Align WCS With Selected Face from themain menu, press the toolbar button or simply use the shortcut W. Now the drawingplane will be aligned with the top of the substrate (you may switch off the visualization ofthe global coordinate axes by pressing Ctrl+A):


The easiest way to draw the metallisation here is to use a polygonal extrusion. This toolcan be entered by selecting Objects # Extrude or pressing the toolbar button . Oncethe polygonal extrude mode is active, you are requested to enter the polygon’s points.For each of these points you should press the TAB key and enter the point coordinatesmanually according to the following table (you may either enter the expressions or theabsolute values given in brackets):

Point U coordinate V coordinate1 25 / 2 (=12.5) -1502 25 / 2 (=12.5) -177.58 / 2 (= -88.79)3 44.41 / 2 (=22.205) -177.58 / 2 (= -88.79)4 44.41 / 2 (=22.205) -4.9 / 2 (= -2.45)5 44.41 / 2 + 40.4 (=62.605) -4.9 / 2 (= -2.45)6 44.41 / 2 + 40.4 (=62.605) -30 / 2 (= -15)7 44.41 / 2 + 40.4 + 30 (=92.605) -30 / 2 (= -15)8 44.41 / 2 + 40.4 + 30 (=92.605) 09 -44.41 / 2 – 44.68 (= -66.885) 0

10 -44.41 / 2 – 44.68 (= -66.885) -4.9 / 2 (= -2.45)11 -44.41 / 2 (= -22.205) -4.9 / 2 (= -2.45)12 -44.41 / 2 (= -22.205) -177.58 / 2 (= -88.79)13 -25 / 2 (= -12.5) -177.58 / 2 (= -88.79)14 -25 / 2 (= -12.5) -15015 25 / 2 (=12.5) -150

Please note that we do not recommend to enter the points relatively to each other herebecause this would make the detection of mistakes during the coordinate input moredifficult. Once you entered the last point from the table and the polygon is thus closed,the extrusion tool requests you to enter the height. Please press the TAB key again andenter the height to be 0.118. Afterwards, your screen should look as follows:

1,15

2

34

56

7 8

910

1112

1314


If your polygon does not look like the one in the picture above, please double-check yourinput in the dialog’s point list. Afterwards, please assign a Name to the solid (e.g.stripline) and change the Layer assignment to be a perfect electric conductor (PEC).After finally pressing the Ok button, the structure should look as follows:


So far, you have modeled half of the stripline structure. The other half can be created bymirroring the structure at the U/W plane of the working coordinate system. Please selectthe stripline by double-clicking at it (the substrate will then become transparent) and openthe transform dialog box afterwards (Objects # Transform Shape, ) :

In this dialog box you should change the Operation to Mirror before you set the V-coordinate of the Mirror plane normal to 1. Afterwards please switch on the Multipleobjects and Group objects options in order to copy the existing shape before mirroring itand to unite the original shape with the mirrored copy. Finally press Ok to create the fullstripline. Your model should then look as follows:


! Model the Via

After successfully modeling the stripline structure, the next step is to model the via whichshould be located in the center of the square pad. The alignment between these twogeometric elements can be specified by moving the working coordinate system to thecenter of the pad.

Please activate the pick point tool (Objects # Pick # Pick Point, ) and double click atone of the corners of the pad. Repeat the same steps in order to pick the point from theopposite corner as well. The picture below shows an example how your structure couldlook like now:

Please note: Due to the finite thickness it could be difficult to pick theappropriate points on the drawing plane since they are very close to the pointsfrom the metallisation’s top face. In order to simplify this task, CSTMICROWAVE STUDIO® offers a so called “snap points to drawing plane”feature which is activated by default. This feature will automatically snap allpicked points onto the workplane if they are indistinguishably close to it in thecurrent view. Zooming into the structure would allow to pick points from themetallisation’s top face as soon as they are clearly distinguishable from thepoints belonging to the bottom face.

In this example, we make use of this feature to ensure that the picked points arelocated on the drawing plane.

If you made a mistake, please clear all picked points (Objects # Clear Picks) and tryagain. The next step is to replace both points by a point in the middle of both. This caneasily be achieved by invoking the command Objects # Pick # Mean Last Two Points.Now a single point should be selected in the middle of the pad.

Now the working coordinate system can be aligned with this point by selecting WCS#Align WCS With Selected Point or by pressing the toolbar button . Your structureshould then look like the following picture:


The via can now be created by using the cylinder tool: Objects # Basic Shapes #Cylinder, . Once the cylinder creation mode is active you are requested to pick thecenter of the cylinder. Since this is the origin of the working coordinate system now, youcan simply press Shift+TAB to open the dialog box for numerically entering thecoordinates and confirm the settings by pressing Ok (please note that holding down theShift key while pressing the TAB key opens the dialog box with the coordinate valuesinitially set to zero rather than the current mouse pointer’s location).

You are now requested to enter the radius of the via. Please press the TAB key againand set the Radius to 10 before pressing the Ok button. The Height of the cylinder canthen be set to –25 in the same way. Please skip the definition of the inner radius bypressing the ESC key (the via should be modeled as solid cylinder here) and check yoursettings in the following dialog box:


Finally set the Name of the cylinder to “via”, check the Layer assignment to PEC andpress the Ok button. The model should then finally look as follows (please use Ctrl+W totoggle the wireframe visualization mode on and off):

! Add Space on Top of the Stripline

Since the structure will be embedded into a perfect electric conducting box, some spaceis needed between the metallisation layer and the top wall of the enclosure.

This can be easily achieved by defining proper background material properties in thecorresponding dialog box which can be opened by selecting Solve#Background Material( ).


In most cases it is sufficient to add an additional space of about five times the height ofthe substrate on top of the metallisation. Thus you should now enter 125 (= 5 • 25) in theUpper Z distance field and press Ok.

The structure should then finally look as follows (the working coordinate system has beendeactivated by using WCS# Local Coordinate System, ):

! Define Ports

The next step is to add the ports to the microstrip device for which the S-parameters willlater be calculated. Each port will simulate an infinitely long waveguide (here stripline)structure which is connected to the structure at the port’s plane. Waveguide ports are themost accurate way to calculate the S-parameters of microstrip devices and should thusbe used here.

Since a waveguide port extends the structure to infinity its transversal extension must belarge enough to sufficiently cover the microstrip mode. On the other hand it should not bechosen excessively large in order to avoid higher order mode propagation in the port. Agood choice for the width of the port is roughly ten times the width of the stripline. Aproper height is about five times the height of the substrate.

Applying the port size rules to the example here, you find that the optimum port’s width isroughly 250 mil and its height should be about 125 mil. In this example the whole modelhas a width of 300 mil and a height of 150 mil. Since these dimensions are close to theoptimal port size you can simply take these dimensions and apply the port to the fullextension of the model.



Here you should set the Normal of the port’s plane to the Y-direction and its Location tothe lower Y-bound (Min) of the structure. Since the port should extend across the wholeboundary of the model, you can simply keep the Full plane setting for the transversalposition.

The next step is to choose how many modes should be considered by the port. Formicrostrip devices, usually a single mode is propagating along the line. Thus you shouldsimply keep the default setting of one mode.

Let’s assume that you are interested in the additional phase shift of the device comparedto a microstrip line of the same length. In this case you could move the phase referenceplane for both ports to the center of the structure as shown below:

Port 1 plane Port 2 plane

Common phasereference plane

150 mil


Therefore please enter the distance between the port’s plane and the phase referenceplane in the Dist. To ref plane field. Please note that you have to enter a negativenumber (-150) here in order to move the reference plane inwards. After entering thedistance you may press the TAB key in order to move the focus to the next dialogelement. Once a reference plane distance has been set, the location of this plane will bevisualized in the main view.


Now you can repeat the same steps for the definition of the opposite port 2.

1. Open the waveguide dialog box (Solve #Waveguide Ports, )2. Set the Normal to Y3. Set the Location to Max.4. Enter the reference plane distance of –150.5. Press Ok to store the port’s settings.


Your model should now finally look as follows:

! Define the Boundary Conditions

In this case, the structure is embedded within a perfect electrically conducting enclosure.Since this is the default set by the template for planar structures, you don’t need tochange anything here.


The frequency range for the simulation should be chosen with care. In contrast tofrequency domain tools, the performance of a transient solver such as CSTMICROWAVE STUDIO can be degraded if the frequency range is chosen too small (theopposite is usually true for frequency domain solvers).

We recommend to use reasonably large bandwidths of 20% to 100% for the transientsimulation. In this example, the S-parameters are to be calculated for a frequency rangebetween 6 and 18 GHz. With the center frequency being 12 GHz, the bandwidth (18 GHz– 6 GHz = 12 GHz) is 100% of the center frequency, which is quite large enough. Thusyou can simply choose the frequency range as desired between 6 and 18 GHz.

Please note: Assuming that you were interested primarily in a frequency rangeof e.g. 11.5 to 12.5 GHz (for a narrow band filter), then the bandwidth wouldonly be about 8.3%. In this case it would make sense to increase the frequencyrange (without loosing accuracy) to a bandwidth of 30% which corresponds to afrequency range of 10.2 – 13.8 GHz. This extension of the frequency rangecould speed up your simulation by more than a factor of three!



After the proper frequency band for this device has been chosen, you can simply openthe frequency range dialog box (Solve # Frequency, ) and enter the range from 6 to18 (GHz) before pressing the Ok button (the frequency unit has previously been set toGHz and is displayed in the status bar):

! Define Monitors for the Surface Current

Besides the S-parameters, an interesting result for microstrip devices is the currentdistribution as a function of frequency. The transient solver used in CST MICROWAVESTUDIO is able to obtain the surface current distribution for an arbitrary number offrequency samples from a single calculation run. The only thing you need to do is todefine so called “field monitors” to specify at which frequencies the field data shall bestored.

Please open the monitor definition dialog box now by selecting Solve # Field Monitors( ):

In this dialog box you should firstly select the Type H-Field / Surface current before youspecify the frequency for this monitor in the Frequency field. Afterwards you should pressthe Apply button to store the monitor’s data. Please define monitors for the followingfrequencies now: 6, 9, 12, 15, 18 (with GHz being the currently active frequency unit).Please make sure to press the Apply button for each monitor (the monitor definition isthen added in the Monitors folder in the navigation tree).


After the monitor definition is completed, you can close this dialog box by pressing theOk button.


The solver’s parameters are specified in the solver control dialog box, which can beopened by selecting Solve # Transient Solver from the main menu or by pressing thecorresponding icon in the toolbar.

Since the structure is fully symmetric, it is sufficient to calculate the S-parameters S1,1and S2,1 to get the whole information about the device. Both results can be obtained byexciting the structure at port 1 only, so change the Source type to Port 1.

Finally you can press the Start solver button to start the calculation. A progress windowappears showing you some information about the calculation’s status.



Results

Congratulations, you have simulated the microstrip phase bridge! Let’s have a look atthe results.



This plot shows the incident, reflected and transmitted wave amplitudes at the portsversus time. The incident wave amplitude is called i1 and the reflected or transmittedwave amplitudes of the two ports are o1,1 and o2,1. These curves already show that thereflection is quite small for this device.


The S-Parameters magnitude in dB scale can be plotted by clicking on the 1D Results #SdB folder.

As expected previously, the input reflection S1,1 is quite small (less than –20dB) for themajority of the frequency range.

Probably the most important S-parameter information for a phase shifter is thetransmission phase which can be visualized by clicking on the 1D Results # arg(S)folder. If you want to visualize the phase curve for S2,1 only, you can also select thesubitem 1D Results # arg(S)# S2,1:



Finally you will have a look at the 2D and 3D field results. You should first inspect theport modes, which 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 fundamentalport mode you should click on the e1 folder. After properly rotating the view and tuningsome settings in the plot properties dialog box, you should obtain a plot similar to thefollowing picture (please refer to the Getting Started manual for more information on howto change the plot’s parameters):

The plot also shows some important properties of the mode such as mode type,propagation constant and line impedance. The port mode at the second port can bevisualized in the same way.


The full three-dimensional surface current distribution on the conductors can be shownby selecting one of the entries in the 2D/3D Results # Surface Current folder from thenavigation tree. The surface current at a frequency of 15 GHz can thus be visualized byclicking at the 2D/3D Results # Surface Current # h-field (f=15) [1] entry:

You can toggle an animation of the currents on and off by selecting the Results #Animate Fields item. The surface currents for the other frequencies can be visualized inthe same way as shown above.








Even if the accuracy of the time signals themselves is extremely high, numericalinaccuracies can be introduced by the Fourier Tramsform which assumes that the timesignals have completely decayed to zero at the end. If the latter is not the case, a rippleis introduced into the S-parameters affecting the accuracy of the results. The amplitudeof this ripple increases with the signal amplitude remaining at the end of the transientsolver run.


The level of the truncation error can be controlled by using the Accuracy setting in thetransient solver control dialog box. The default value of –30dB will usually givesufficiently accurate results for coupler devices. However, to obtain highly accurateresults for filter structures it is sometimes necessary to increase the accuracy to –40dBor –50dB.







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 resolutionand recalculate the S-parameters. If these results do not significantly change anymore byincreasing the mesh density, then convergence has been achieved.

In the example above, you have used the default mesh which has been automaticallygenerated by an expert system. The easiest way to test the accuracy of the results is touse the fully automatic mesh adaption which can be switched on by checking theAdaptive mesh refinement option in the solver control dialog box (Solve # TransientSolver):





After the mesh adaption procedure has completed, you can visualize the maximumdifference of the S-parameters for two subsequent passes by selecting 1D Results #Adaptive Meshing # Delta S from the navigation tree:

As you can see, the maximum deviation of the S-parameters is almost 4% between thefirst and the second pass which indicates that the adaptive mesh refinement wasrequired here to obtain highly accurate results.

The convergence process of the input reflection S1,1 during the mesh adaption can bevisualized by selecting 1D Results # Adaptive Meshing # |S| dB # S1,1 from thenavigation tree:


The convergence process of the other S-parameters magnitudes and phases can bevisualized in the same way. By inspecting the plots, you can confirm that the importantresults for the transmission phase are quite stable here:




Congratulations! You have just completed the microstrip phase bridge tutorial whichshould have provided you with a good working knowledge on how to use the transientsolver to calculate S-parameters. The following topics have been covered so far:

1. General modeling considerations, using templates, etc.2. Model a planar structure by using the extrude tool, define the substrate and create a

via.3. Define ports.4. Define frequency range and boundary conditions.5. Define field monitors for surface current distributions.6. Start the transient solver.7. Visualize port signals and S-parameters.8. Visualize port modes and surface currents.9. Check the truncation error of the time signals10. Ensure to obtain accurate and converged results by using the automatic expert




In addition to this tutorial you can find some more S-parameter calculation examples forplanar structures in the examples folder in your installation directory. Each of theseexamples contains a Readme item in the navigation tree which will give you some moreinformation about the particular device.



The Patch Antenna Tutorial

Geometric Constructions and Solver Settings 92


Results 107

1D Results (Port Signals, S-Parameters) 1072D and 3D Results (Port Modes and Farfield Monitors) 109Antenna Array Calculation 110


Patch Antenna Array 116

Geometric Construction Steps 116Combine Results 119Simultaneous Excitation 122


92 CST MICROWAVE STUDIO® – Patch Antenna Tutorial

Geometric Constructions and Solver Settings


In this tutorial you will analyze a circular patch antenna. CST MICROWAVE STUDIO®

can provide a wide variety of results, this tutorial, however, concentrates mainly on the S-parameters and farfield results.

In addition the single patch antenna will be extended to a rectangular 2x2 array patternusing three different ways. First the farfield solution of the single patch antenna is appliedto the antenna array feature, superposing the result with different amplitudes and phasesettings. Another possibility expands the patch model to a set of four identical antennas,each excitable with an own coaxial feed. Here you have the option to calculate theantennas separately one after another and finally combine the results with arbitraryamplitudes and phase values or even run the excitation simultaneously to produce thefarfield result with only one solver cycle. The farfield distribution of all these possibilitieswill be compared.



The structure depicted above consists of two different materials: The “Substrate” and thePerfect Electric Conductor (PEC). There is no need to model the air above since it will beadded automatically (according to the current background material setting) whenspecifying the open boundary conditions. This will be done automatically by using anappropriate template. The feeding of the patch is realized with a coaxial line.

The following explanations on how to model and analyze this device can be applied toother patch antenna devices as well. Please remember the Edit # Undo facility in casethat you want to cancel the last construction step.

CST MICROWAVE STUDIO® – Patch Antenna Tutorial 93



! Select a Template

Once you start CST MICROWAVE STUDIO® and choose to create a new project, youare requested to select a template which fits best to your current device. Here the“Antenna (on Planar Substrate)” template should be chosen.

This template automatically sets the units to mm and GHz and the background materialto vacuum. The open boundary condition is selected, except Zmax is set to “open (addspace)”, offering some free space above the antenna patch and Zmin is set to “electric”,providing a perfect electric conducting ground plane. Since the background material hasbeen set to vacuum, the structure can be modeled just as it looks like on your desk.

Please note: Concerning the boundary conditions it is possible to specify asymmetry boundary condition at the yz-plane in the boundary dialog box

(Solve # Boundary Conditions, ). This would reduce the simulation time bya factor of two. However, since the simulation does not take too long, we skipthe symmetry condition here, so that we can straightforwardly extend thisexample to an antenna array later.


The next step will usually be to set the working plane properties in order to make thedrawing plane large enough for your device. Since the structure has a maximumextension of 60 mm along a coordinate direction, the working plane size should be set to100 mm (or more). These settings can be changed in a dialog box, which opens afterselecting Edit # Working Plane Properties… from the main menu. Please note that we


will use the same document conventions here as they have been introduced in theGetting Started manual.

In this dialog box, you should set the Size to 100 (the unit which has previously been setto mm by the chosen template is displayed in the status bar), the raster Width to 2 andthe Snap With to 0.01 to obtain a reasonably spaced grid. Please confirm these settingsby pressing the Ok button.

! Draw the Substrate Brick

The first construction step for modeling a planar structure is usually to define thesubstrate layer. This can be easily achieved by creating a brick made of the substrate’smaterial. Please activate the brick creation mode now (Objects # Basic Shapes #Brick…, ).

When you then are prompted to define the first point, you can enter the coordinatesnumerically by pressing the TAB key which will open the following dialog box:

In this example you should enter a substrate block which has an extension of 60 mm ineach of the transversal directions. The transversal coordinates can thus be described byX = -30, Y = -30 for the first corner and X = 30, Y = 30 for the opposite corner, assumingthat the brick is modeled symmetrically to the origin. Thus please enter the first point’scoordinates 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 key2. 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 numericallyspecified by pressing the TAB key again, entering the Height of -0.7 and pressing the Okbutton (regarding an easy construction of the patch antenna it is convenient to define thesubstrate in negative z-direction). Now the following dialog box will appear showing you asummary of your previous input:


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

You should now assign a meaningful name to the brick by entering e.g. “Substrate” in theName field.

You still need to define the substrate material. Since no material layer has yet beendefined for the substrate, you should open the layer definition dialog box by pressing theNew… button:

In this dialog box you should define a new Layer name (e.g. “Substrate”) and set thelayer Type to a Normal dielectric material. Afterwards specify the material properties inthe Epsilon and Mue fields. Here you only need to change the dielectric constant Epsilonto 2.33. Finally choose a nice color for the layer by pressing the Change button. Yourdialog box should now look similar to the picture above before you press the Ok button.


Back in the brick creation dialog box you can also press the Ok button to finally createthe substrate brick. Your screen should now look as follows (you can press the SPACEkey 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. Since the antenna willbe excited by a coaxial feed at the bottom face the electric boundary at Zmin defined bythe previously chosen template is not suitable as a ground plane. As a consequence ametallic brick has to be defined additionally. This can be easily achieved by activatingthe face pick tool (Objects # Pick # Pick Face, ) and double clicking on the substrate’sbottom face. The model is rotated by activating the rotation mode View # Mode #Rotate ( ). The face selection should then be visualized as in the following picture:

Now you can extrude the selected face with the “Extrude face” tool . Here you have toenter the height and the layer of the new shape to be created. In this example theground plane must have a non-zero thickness because of the coaxial feed which will bemodeled later on. In CST MICROWAVE STUDIO® a port region has to be homogeneousfor at least three mesh lines in longitudinal direction. Thus you can choose a height of 2.1


Substrate’sselected bottom face


mm representing three times the substrate thickness as a sufficient dimension. Enter thisvalue in the following dialog box and select PEC from the Layer drop-down list as themetallic material property:

After entering a suitable name (e.g. “Ground”) in the Name input field and confirmingyour settings with the Ok button the current structure will look like this (rotated again tothe see the top face):

! Model the Patch Antenna

After defining the ground plane the patch antenna has to be modeled as a cylindricalshape on the substrate’s top face. Please activate the cylinder creation mode now(Objects # Basic Shapes # Cylinder, ). Similar to the construction of the substrate’sbrick you can enter the coordinates numerically by pressing the TAB key to open thefollowing dialog box:



Here you enter the center point of the cylinder with X = 0 and Y = 0, since the patch islocated symmetrically on the substrate. After this please define the Outer Radius with23 mm and the Height with 0.07 mm in the shown dialog boxes, each appearing after youhave pressed the TAB button:

Skipping the entry dialog for the Inner Radius by pressing the ESC button will lead to thefollowing dialog box showing you again a summary of your previously made input:

Select the PEC layer for the patch material and assign a meaningful name to the brick byentering e.g. “Patch” in the Name input field.

Again, please check all these settings carefully and change any eventually occurringmistakes in the corresponding entry field. After applying with the Ok button, your screenshould show the following structure:


! Model the Coaxial Feed

The last modeling step is the construction of the coaxial feed as the excitation source forthe patch antenna. This action introduces the working coordinate system (WCS). Sincethe feeding point is located asymmetrical to the circular patch it is advisable to activatethe local coordinate system (WCS # Local Coordinate System, ).

In order to define the new center point for the coaxial feed the local coordinate system ismoved along the positive v-direction (WCS # Move Local Coordinates, ) . Thus pleaseenter the value of 9.2 mm in the following dialog box:

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

First enter the values for the coaxial substrate cylinder by using the TAB button facility,again skipping the input of the Inner Radius. The cylinder has a outer radius of 4 mm andan extension in negative w-direction of 2.1+0.7=2.8 mm. Please check your settingsreferring to the following dialog box:


Select the previously defined “Substrate” layer and create the cylinder with the Ok button.

As a result the cylinder shape Substrate:solid1 intersects with two already existingshapes, the solid “Substrate:Substrate” and the ground plane “PEC:Ground”. Here it isnecessary to determine the kind of intersection for the shapes. It is convenient tocombine the two substrate materials into one single shape, so please mark the radiobutton Add both shapes in the “Shape intersection” dialog box as presented below andconfirm with Ok:

In the second case the substrate cylinder has to be inserted into the PEC material of theground plane. So please mark the radio button Insert highlighted shape from the “Shapeintersection” dialog window as presented below and confirm again with Ok:


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

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 2.8mm in negative w-direction. The cylinder creation dialog should look like this:


This time select the PEC layer type, define again a suitable name (e.g. “Feed”) for thecylinder shape and apply the Ok button.

Please note: In this case no “Shape intersection” dialog window will appear,because the PEC shape is defined after the normal layer shape (here:“Substrate”). This implies that the PEC shape is automatically inserted into theintersected shape.

After applying the Ok button the final model will look like this (please use again Ctrl+W or

to toggle the wireframe visualization mode on and off):

! Define Waveguide Port

The next step is to add the excitation port to the patch antenna device, for which thereflection parameter will later be calculated. The port simulates an infinitely long coaxialwaveguide structure which is connected to the structure at the port’s plane.

Since a waveguide port extends the structure to infinity its transversal extension must belarge enough to sufficiently cover the corresponding modes. So, in contrast to open portstructures, here the port range is clearly defined by the outer shielding conductor of thecoaxial waveguide.


Consequently the easiest way to define the port range is to pick the face (Objects # Pick# Pick Face, ) of the coaxial feed (“Substrate” shape) as demonstrated below (themodel is rotated again to the bottom side first):

Please open now the waveguide dialog box (Solve #Waveguide Ports, ) to define theport:

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

Port


Please confirm your port settings with the Ok button to finally create the port. Afterrotating the model again to the top face your model should now look as follows (pleaseuse again Ctrl+W or to toggle the wireframe visualization mode on and off):


The frequency range for the simulation should be chosen with care. In contrast tofrequency domain tools, the performance of a transient solver such as CSTMICROWAVE STUDIO® can be degraded if the frequency range is chosen too small (theopposite is usually true for frequency domain solvers).

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

Please note: In case that you just cover a bandwidth of less than 20% you canincrease the frequency range without loosing accuracy. This extension of thefrequency range could speed up your simulation by more than a factor of three!


After the proper frequency band for this device has been chosen, you can simply openthe frequency range dialog box (Solve # Frequency, ) and enter the range from 2 to 3(GHz) before pressing the Ok button (the frequency unit has previously been set to GHzby the selected template and is displayed in the status bar):


! Define Farfield Monitor

Besides the S-parameters, the main interesting result for antenna devices is the farfielddistribution at a given frequency. The transient solver used in CST MICROWAVESTUDIO® is able to obtain the farfields for an arbitrary number of frequency samplesfrom a single calculation run. The only thing you need to do is to define so-called “fieldmonitors” to specify at which frequencies the field data shall be stored.

Please open the monitor definition dialog box now by selecting Solve # Monitors ( ):

In this dialog box you should firstly select the Type “Farfield/RCS” before you specify thefrequency for this monitor in the Frequency field. Afterwards you should press the Applybutton to store the monitor’s data. Please define a monitor at the frequency of 2.4 (withGHz being the currently active frequency unit). However, you can define some moremonitors at other frequencies, each time pressing Apply button to confirm the setting andto add the monitor in the Monitors folder in the navigation tree. After the monitor definitionis completed, please close this dialog box by pressing the Ok button.


The solver’s parameters are specified in the “Solver Parameters” dialog box, which canbe opened by selecting Solve # Transient Solver from the main menu or by pressing thecorresponding icon in the toolbar:


Finally you can press the Start solver button to start the calculation. A progress windowappears showing you some information about the calculation’s status:


Please note: Clicking the Details button during the calculation opens a textfield, where some solver relevant information is displayed, concerning the portof excitation, the numerical timestep and much more.


Results

Congratulations, you have simulated the circular patch antenna! Let’s have a look at theresults.


! Port Signals


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

This plot shows the incident and reflected wave amplitudes at the waveguide port versustime. The incident wave amplitude is called i1 (referring to the port name: 1) and thereflected wave amplitude is o1,1. As you can see in this time signal plot, the patchantenna array has a strong resonance that leads to a slowly decreasing output signal.

! S-Parameters

A primary result for the antenna is the S11 Parameter, that will appear if you click on the1D Results # |S| dB folder from the navigation tree. The following screenshot shows thereflection parameter:


It is possible to precisely work out the operational frequency for the patch antenna.Activate the axis marker by pressing the right mouse button and selecting the Show axismarker option from the context menu. Now you can move the marker to the S11minimum and point out a resonance frequency for the patch antenna of about 2.41 GHz.

In the following chapter “Accuracy Considerations” an adaptive mesh refinement will beapplied to the structure in order to examine the accuracy of the solution. This is a goodpossibility if no theoretical value is available, which is usually the case for more complexsimulation models. The good result presented above will be confirmed.

The ripples that can be seen in the reflecting parameters result from the fact that the timesignal has not sufficiently decayed (have a look again at the time signal plot). Theamplitude of the ripples increases with the signal amplitude remaining at the end of thetransient solver run. However, these ripples does not effect the location of the resonancefrequency and therefore can be ignored for this example. Please find some moreinformation about this kind of numerical error again in the chapter “AccuracyConsiderations”.


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

Finally you will have a look at the 2D and 3D field results.

! Port Modes

You should first inspect the port modes, which can be easily displayed by opening the2D/3D Results # Port Modes # Port1 folder from the navigation tree. To visualize theelectric field of the fundamental port mode you should click on the e1 folder. Afterproperly rotating the view and tuning some settings in the plot properties dialog box, youshould obtain a plot similar to the following picture (please refer to the Getting Startedmanual for more information on how to change the plot’s parameters):

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

! Farfield Monitors

Beside the resonance frequency, the farfield is another important parameter in antennadesign.

Please note: For this action you will need the farfield calculation feature. If it islocked please contact your CST MICROWAVE STUDIO® distribution partner.

The farfield solution of the antenna device can be shown by selecting the correpondingmonitor entry in the Farfields folder from the navigation tree. For example the farfield atthe frequency 2.4 GHz can thus be visualized by clicking on the Farfields # farfield(f=2.4) [1] entry, showing the directivity over the phi and theta angle (The position of thecolor ramp can be modified by clicking on the Results # Farfield Plot… # Color ramp…button):


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

You can see that the maximum power is radiated in positive z-direction. Note that thereare several other options available to plot a farfield: the Polar plot, the Cartesian plot andthe 2D plot.

Antenna Array Calculation

Using the farfield results of the so far simulated single patch antenna, it is possible tocalculate the farfield distribution for an arbitrary antenna array consisting of identicalantenna elements as a post processing step.

Later on we will expand the antenna example by constructing a 2x2 antenna arraypattern, so it is of interest to apply the mentioned array calculation feature to the samerectangular array dimension. Thus please open the corresponding dialog box by pressingResults # Farfield Plot... # Antenna Array # Properties… and insert the values to createthe rectangular 2x2 array pattern in the xy-plane with a spatial shift of 60 mm (due to thedimension of the antenna substrate) and a phase shift of +90 degrees:


By pressing the Update antenna list button the coordinates and their respectiveamplitudes and phase values are displayed in the Antenna list as can be seen in thedialog box above.

Please note: The Antenna list can be modified if the radio button Edit antennalist is activated. This means that not only rectangular arrays with constant spaceand phase shift can be calculated, but by adding and modifying single antennasany array pattern with arbitrary amplitude and phase values can be defined.

Please confirm with the Ok button to calculate the resulting farfield of the defined arraypattern. The following screenshot demonstrates that the array arrangement together withthe constant phase shift of +90 degrees produce on the one hand a constructivesuperposition increasing the directivity of 6.88 dBi to 10.97 dBi, but also a slight rotationof the main loop in negative x and y direction:


Please feel free to define some more array patterns to analyze the resulting changes inthe farfield distribution. Here you have a fast and efficient way to design various antennaarrays without the necessity to restart a transient calculation.

Regarding the following calculations the antenna array feature should be disabled bynow. Therefore please check the radio button Single antenna in the “Farfield Plot” dialogbox (Results # Farfield Plot...):





In the following we will give you some hints on how to handle these errors and how toensure to achieve highly accurate results.



Even if the accuracy of the time signals themselves is extremely high, numericalinaccuracies can be introduced by the Fourier Transform which assumes that the timesignals have completely decayed to zero at the end. If the latter is not the case, a rippleis introduced into the S-parameters affecting the accuracy of the results. The amplitudeof this ripple increases with the signal amplitude remaining at the end of the transientsolver run.


The level of the truncation error can be controlled by using the Accuracy setting in thetransient solver control dialog box. The default value of –30dB will usually givesufficiently accurate results, however, to obtain highly accurate results for filter structuresit is sometimes necessary to increase the accuracy to –40dB or –50dB.






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 resolutionand recalculate the S-parameters. If these results do not significantly change anymore byincreasing the mesh density, then convergence has been achieved.


In the example above, you have used the default mesh which has been automaticallygenerated by an expert system. The easiest way to test the accuracy of the results is touse the full automatic mesh adaption which can be switched on by checking the Adaptivemesh refinement option in the solver control dialog box (Solve # Transient Solver, ):

After activating the adaptive mesh refinement tool, you should now start the solver againby pressing the Start solver button. After the solver has performed all mesh adaptionpasses, the following dialog box will appear:



In this example only two adaption passes are necessary to obtain a suitable result. Thismeans that maximum deviation of the S-parameters between the first and the second run


is less than 2%. Obviously in this example the mesh created first by the expert systemwas already quite acceptable for an accurate solution.

The convergence process of the input reflection S1,1 during the mesh adaption can bevisualized by selecting 1D Results # Adaptive Meshing # |S| dB ⇒ S1,1 from thenavigation tree:

The huge advantage of this expert system based mesh refinement procedure overtraditional adaptive schemes is that the mesh adaption needs to be carried out only oncefor each device in order to determine the optimum settings for the expert system.Afterwards there is no need for time consuming mesh adaption cycles during parametersweeps or optimization.


Patch Antenna Array

Using the so far constructed single patch antenna in this chapter the extension to a fourelement antenna array is demonstrated. Here, we will concentrate purely on the farfieldcalculations. All other results can be analyzed in a similar way as in the first part of thistutorial.

In the following we will construct the rectangular 2x2 array pattern. Here we use a resultcombination of a sequential excitation as well as a simultaneous excitation to obtain theradiation characteristics.

Considering this tutorial as a demonstration it might be useful to obtain the followingarray results as quickly as possible. Thus regarding the very good solution of the firstadaption pass (see chapter ”Accuracy Considerations”) we will reset the mesh settings tothe initial values to calculate with less mesh nodes. So please open the “MeshProperties” dialog box by pressing Mesh # Mesh Properties..., insert a value of 20 forLines per wavelength and 10 for Lower mesh limit and confirm by pressing the Ok button(please refer to the Online Help for some more detailed information about setting themesh properties):


The construction of the array is based on the translation functionality for selected objects,which will be applied to the current structure of the single patch antenna. This procedureis also applicable to a complete layer, including all associated solids.

Therefore please select the PEC layer from the “Layers” folder in the navigation tree andperform a transformation of the selected layer (Press the toolbar icon or enter theObjects # Transform Shape... menu). Now choose the Translate function in theupcoming “Transform Selected Object” dialog box and enter the value of –60 (referring to


the previously defined units of mm) for the x-component of the translation vector,correspondent to the structure dimension. In order to combine the translated and the oldshapes please activate the Multiple objects and the Group objects check buttons andperform the translation operation with the Ok button (the local coordinate system waspreviously switched off by clicking again WCS # Local Coordinate System or the icon

):

Now CST MICROWAVE STUDIO® copies the selected layer to the coordinates of itstranslated position and groups the old with the new shapes.

The same procedure has to be performed for the “Substrate” layer. So please select thislayer type from the “Layers” folder in the navigation tree and activate again the“Transform Selected Object” dialog box. Here the same settings are made as for thePEC layer and the translation is confirmed by applying the Ok button. This time anintersection occurs concerning the new shape “Substrate:Substrate” and the old shape“PEC:Feed”. Since in this case no shape modification is wanted, you can solve theintersection during the transformation process by activating the None check button:


The resulting structure consisting of two identical patch antennas will then look like this:

Please repeat the described transformation in the negative y-direction, for both layers,the “Substrate” and the PEC layer, again with a space shift of 60 mm. The occurringintersection dialog box can be solved again by activating the None button, so that thefinal array pattern will be created as follows:

To complete the model the remaining ports of the new created patch antennas have tobe created. This is done similar to the definition of the first port by picking thecorresponding port area (in each case the bottom face of the respective substratecylinders) and defining a port, again with only one mode.


Combine Results

In order to receive farfield results where all patches are driven simultaneously, thepossibility of result combination as a post processing step is performed. This means thatat first each port is excited individually one after another, after which arbitrarycombinations of these excitations can be defined with respect to different amplitude andphase values.


As described earlier the solver’s parameters are specified in the solver control dialogbox, which can be opened by selecting Solve # Transient Solver from the main menu orby pressing the corresponding icon in the toolbar:

Port 4

Port 2

Ground side

Port 3


Since all ports should be calculated you have to be sure that “All Ports” is selected in theSource type drop-down list. Now you can press the Start solver button to start thecalculation. Again the progress window appears indicating, in addition to the calculation’sstatus, the current solver cycle:

After the transient solver has finished please take a look at the farfield of a single patchfrom the array. It looks quite similar to the farfield distribution of the previously calculatedsingle patch antenna. The following screenshot shows again the directivity over theangles theta and phi. Click on the Farfields # farfield (f=2.4) [1] folder to bring your plotinto view:

! Combine Results

The interesting results, however, are those where all patches are driven at one time anda pre-determined amplitude and phase variation is taken into account. This can beproduced by CST MICROWAVE STUDIO using the “Combine results” option. Press


Results # Combine Results... to bring the “Combine Calculation Results” window intoview.

Now you have the option to change each amplitude and phase excitation in the portmode list. In order to compare the farfield result with the previously demonstratedantenna array feature we define identical antenna settings, i.e. the first antenna receivesa phase shift of +90 degrees, the third antenna –90 degrees and the two remainingantennas 0 degree:

Please note: The corresponding monitor label will be generated automaticallydue to the settings of the port mode combination, however, by disabling theAutomatic labeling button you are able to enter a label of your own.

After confirming your settings with the Combine button, you will observe a new farfieldsubfolder farfield (f=2.4) [1[1,90]+2[1,0]+3[1,-90]+4[1,0]] in the navigation tree. By clickingon it you will see the following farfield distribution, which is quite similar to the result ofthe antenna array feature:


As you can see, the combining of results is time efficient, since you do not have to restartthe transient solver, just enter the amplitude and phase and watch the combinedgenerated farfield plot.

Simultaneous Excitation

Another possibility to obtain the farfield result of the array pattern is the excitation of allfour ports simultaneously. In contrast to the combine result facility, here only onetransient solver run is required. However, the phase shift relationship between theantenna elements has to be known before the solver is started.

Please note: The definition of a phase shift in connection with a simultaneousexcitation of different ports will be converted, by use of the defined referencefrequency into a constant time shift between the port excitation signals. So inorder to examine a farfield result, the reference frequency has to be identical tothe frequency of the farfield monitor.

In order to define the simultaneous excitation you have to choose the Selected Portsoption in the Source type drop-down list in the Solver Parameters dialog box (Solve #Transient Solver…, ):


Pressing the Port mode list… button opens the following dialog box, where the selectiveand simultaneous port excitation settings can be defined:

Since all four existing ports shall be excited please activate all available check buttons inthe port mode list. In order to enter the amplitude and phase values, you first have toactivate the Simultaneous excitation by checking the corresponding button. Please enterthe reference frequency of 2.4 GHz so that the result will be compatible to the combinedfarfield monitor in the previous chapter. Again all antennas are driven with an amplitude


value of one and phase values of 90, 0, -90, 0 degrees. Please double-check yoursettings with the dialog box above and confirm with the Ok button.

Finally you can press the Start solver button in the “Solver Parameters” dialog box (Solve# Transient Solver…, ) to start the simultaneous calculation. Again, the progresswindow appears indicating, in addition to the calculation’s status, the simultaneous solvercalculation:

Take a look at the input time signals (you can select specific curves in your 1D plot viewby choosing Port Signals # Select Curves… to open the corresponding dialog box). Inthe picture below you can see the time delay of the different input signals due to thedefined phase shifts of the ports:

After the transient solver has finished you will find the resulting farfield information in theFarfields # farfield (f=2.4) [1[1,90]+2[1,0]+3[1,-90]+4[1,0],[2.4]] folder. Clicking on it willshow the following farfield plot of the directivity over the angles theta and phi. As to beexpected the result is very similar to the one produced by combining the results of thefour single port excitations in the previous chapter:



Congratulations! You have just completed the circular patch antenna tutorial whichshould have provided you with a good working knowledge on how to use the transientsolver to calculate S-parameters and farfield results. The following topics have beencovered so far:

1. General modeling considerations, using templates, etc.2. Model a planar structure by using the extrude tool, creating the substrate, circular

patch antenna and a coaxial feed.3. Define waveguide ports.4. Define frequency range.5. Define farfield monitors.6. Start the transient solver.7. Visualize port signals and S-parameters.8. Visualize port modes and farfield results.9. Check the truncation error of the time signals10. Ensure to obtain accurate and converged results by using the automatic expert

system based mesh adaption.11. Application of the antenna array feature.12. Extend the single patch antenna to a four element antenna array and combine single

calculation results as well as perform a simultaneous excitation.



In addition to this tutorial you can find some more S-parameter calculation examples forplanar structures or various antenna models in the examples folder in your installationdirectory. Each of these examples contains a Readme item in the navigation tree whichwill give you some more information about the particular device.



The Cavity Tutorial


Introduction and Model’s Dimensions 128Geometric Construction Steps 129Solver Settings 135

Eigenmode Calculation 138

Eigenmode Visualization and Q-Factor Calculation 142



128 CST MICROWAVE STUDIO® – Cavity Tutorial



The cavity tutorial demonstrates how to calculate the eigenmodes of an air filled cavity.Due to its rotational symmetry, you can easily model the cavity by rotating a crosssection profile around an axis. Furthermore due to a second symmetry it is sufficient todraw half of the profile and mirror the structure afterwards to build the full model.

Once the model is constructed, the analysis process is quite simple. This tutorial willshow you how to calculate and visualize a number of eigenmodes for this resonator. Inaddition to this, the Q-factors will be calculated as well.

Please note: The CST MICROWAVE STUDIO (CST MWS) “Eigenmodesolver” license is required for this tutorial. If it is not available, please contactyour CST MWS distribution partner.

The cross section polygon is shown below. Please note than only half of the profileneeds to be drawn because of the depicted symmetry. The coordinates are given in mmfor each of the polygon’s points.

(0;0)(210; 0)

(210; 65)

(129; 65)

(179; 139)

(179; 190)

(148; 215)(0; 215)

x

y

x

y

All coordinates are given in mm

Sym

met

rypl

ane

Rotation Axis

CST MICROWAVE STUDIO® – Cavity Tutorial 129

The following sections will guide you through the construction of the cavity’s model.Please make sure that you carefully complete each step before you step over to the nextone.


! Select a Template

Once you have started CST MWS and selected create a new project, you will berequested to choose a template for your structure.

Even if there is no particular template for eigenmode calculations, you may still chooseone of the templates which is best suited to your device. In this case the “WaveguideFilter” template is favourable since both structures are highly resonant waveguidedevices filled with air. Please select this template now and press the Ok button.

The aim of these templates is to properly adjust default settings such that they fit well tothe particular type of structure. In this case, the template sets the drawing unit to mm, thefrequency unit to GHz and all boundaries to be perfect electric conducting walls.Furthermore, it sets the background material to be a perfect electric conductor such thatonly the air within the cavity needs to be modeled.

! Set Working Plane Properties

Before you start entering the cavity’s shape, you should set the working plane to be largeenough to contain the model’s dimensions. The dialog box can be accessed by selectingEdit # Working Plane Properties. You should already be familiar with this documentconvention after reading the Getting Started manual.


The largest coordinate value is 215 mm, so a working plane size of roughly 250 mm willbe sufficient. Please enter this value in the Size field and set the Raster Width to 10 mmin order to obtain a reasonably fine grid on the drawing plane. Please note that allgeometric settings are in mm, since the current geometry unit is set to mm (alsodisplayed in the status bar).

! Create Figure of Rotation

After these preparation steps have been completed, you can now start drawing the figureof rotation. Since the cross section profile is a simple polygon, you don’t need to use thecurve modeling tools here (please refer to the Getting Started manual for this moreadvanced functionality). For polygonal cross sections it is more convenient to use thefigure of rotation tool, activated by selecting Objects # Rotate from the main menu.

Since no face has been previously picked, the tool will automatically enter a polygondefinition mode and request you to enter the polygon’s points. You could do this by eitherdouble clicking at each point’s coordinates on the drawing plane by using the mouse oryou could also enter the values numerically. Since the latter approach may be moreconvenient here, we suggest pressing the TAB key and entering the coordinates in thedialog box. All polygon points can thus be entered step by step according to the followingtable (whenever you make a mistake, you may delete the most recently entered point bypressing the backspace key):

Point X Y1 0 02 210 03 210 654 129 655 179 1396 179 1907 148 2158 0 2159 0 0

After the last point has been entered, the polygon will then be closed. The “RotateProfile” dialog box will then automatically appear.


This dialog box allows you to review the coordinate settings in the list. If you encounterany mistakes you can easily change the values by simply double clicking at the incorrectcoordinate’s entry field.

The next step is to assign a material Layer to the shape. In this case, the default layer is“Vacuum” which practically is appropriate for this example.

Finally you should assign a proper Name (e.g. “Cavity”) to the shape and press the Okbutton in order to finally create the solid. The picture below shows how your structureshould look line now:

Inner edge


! Pick Edge and Blend Edge

Having sharp edges inside cavities is usually not a good idea since strong fieldsingularities will occur at these edges. Therefore the sharp inner edge (shown on thepicture above) should be blended now.

The first step for blending the edge is to pick the edge from the model by entering thepick edge mode with the toolbar icon , the Objects # Pick # Pick Edge menu entry orthe shortcut E in the main view window. Once this mode is active, which is indicated byhighlighting all edges in the model, you can easily double-click at the inner edge. If theedge is hidden, you can rotate the view by using the view changing tools as explained inthe Getting Started manual. Sometimes it is also advantageous to switch the drawingmode to Wireframe (View # View options).

Once the proper edge has been selected, the model should look as follows:

If you accidentally picked the wrong edge, you can delete all picks by using Objects #Clear Picks and try again.

The next step is to blend the selected edge. Therefore just press the toolbar icon orselect Objects # Blend Edges from the menu. Afterwards a dialog box will open whereyou can set the Radius of the blend to 15 mm.

Inner edge


Finally press the Ok button to apply the blend. The structure should then look as follows:

! Mirror the Structure to Model the Entire Cavity

So far, you have successfully modeled half of the cavity. The easiest way to obtain thefull model is to mirror this structure to the planar back face.

The first step to achieve this is to define the mirror plane by picking the correspondingface from the model. Therefore, enter the face pick mode by pressing the toolbar itemor selecting Objects # Pick # Pick Face or just using the shortcut F in the main viewwindow.

Once the face pick mode is active you should simply double click at the planar back faceas shown in the picture above. If the face is hidden by the structure you can use the viewchanging tools as explained in the Getting Started manual. After the face has beenselected, the model should look as follows:

Back face

Back face


If this is not the case, then please delete all picks by selecting Objects ⇒ Clear Picks andtry again.

Now you should select the cavity’s solid by double-clicking it. Please check that its namebecomes highlighted in the navigation tree.

The next step is to use the transform tool to create the mirrored shape by pressing thetoolbar item or selecting Objects # Transform Shape.

In the upcoming dialog box you should firstly select the Operation Mirror. The mirrorplane’s coordinates will then be automatically set according to the previously-picked backface of the cavity, so you don’t need to change anything here.

Since the transformation should create a new shape by mirroring the existing one ratherthan just modifying it, you have to select the Multiple objects option. Furthermore theoriginal shape should also be combined with the mirrored one to form a single shape.Thus the Group objects option must be switched on as well.


Finally you should press the Ok button to create the entire cavity shown below:

In this picture, the cavity has been sliced for visualization purposes by using the View #Cutting plane tool.

Solver Settings

After you have successfully modeled the cavity’s geometry, all you need to do is tospecify some solver settings such as frequency range and boundary conditions beforeyou can finally start the solver to calculate the eigenmodes.


For this device the first five resonance frequencies are estimated to be below 1.5 GHz.Please open the frequency range dialog box by either pressing the icon from thetoolbar or selecting Solve ⇒ Frequency. In this dialog box you should set the upperfrequency limit to 1.5 (please remember that the frequency unit has been set to GHz asshown in the status bar).

Finally press the Ok button to store this setting.




Here all boundary conditions are set to electric which just means that the structure isembedded in a perfect electric conducting housing. These defaults (which have been setby the template) are appropriate for this example.

Assume that you are only interested in those modes which have longitudinal electric fieldcomponents along the (x-)axis of the device in this example. This a priori knowledgeabout the fields could be used to speed up the calculation by a factor of eight byinforming the solver about these symmetry conditions.



By setting the symmetry planes X/Y and X/Z to magnetic, you force the solver to onlycalculate fields which have no magnetic field tangential to these planes (and thus forcingthe electric field to be tangential to these planes). In addition to this you can set the Y/Zsymmetry plane to be an electric wall which implies that the electric field is forced to benormal to this plane.



Please note that you also could double-click at the symmetry planes’ handles andchoose the proper symmetry condition from the context menu.



Eigenmode Calculation

! Calculating the Eigenmodes by Using Fully Automatic Solver Settings

After completing all steps above you are now ready to start the eigenmode calculation.Therefore, you should open the eigenmode solver control dialog box by pressing thecorresponding toolbar icon or selecting Solve # Eigenmode Solver from the mainmenu.

The only setting which commonly needs to be specified here is the number of Modes tobe calculated. The solver will then calculate these number of modes starting from thelowest resonance frequency. It is usually advantageous to specify more modes tocalculate than you are actually searching for. Thus, assuming that you want to calculatethe first five modes in this example, you should advise the eigenmode solver to calculate10 modes, which is also the default. You, therefore, do not need to change anything hereand can just press the Start solver button right away.


Now a few progress bars will appear, keeping you informed about the current status ofyour calculation (e.g. matrix calculation, eigenmode analysis).

Due to the Perfect Boundary Approximation™, the number of mesh cells required fordiscretizing this example is quite small (roughly 9000). This in fact corresponds to asystem of equations consisting of about 27,000 unknowns. Calculating eigenmodes forsuch a system takes only a few minutes to complete on a modern PC.

After the solver has finished its work, a dialog box will be shown displaying theresonance frequencies of the first ten modes:

The accuracy for the mode solution is excellent for all these modes. A mode with anaccuracy of less than 1e-3 can usually be considered as being sufficiently accurate. Thisdialog box can be dismissed by pressing the Ok button.

In order to review the solver time required to achieve these results, you can display thesolver log-file by selecting Results # View Logfiles # Solver Logfile from the main menu.Please scroll down the text to obtain the following timing information (the actual valuesmay vary depending on the speed of your computer):

--------------------------------------------------------------Solver Statistics:

Mesh generation time: 0 days, 00 hours, 00 mins, 07 secsSolver time: 0 days, 00 hours, 03 mins, 05 secs

Total time: 0 days, 00 hours, 03 mins, 12 secs

--------------------------------------------------------------


! Optimizing the Performance for Subsequent Calculations

So far, you have successfully calculated the eigenmodes for this device in a reasonableamount of time. However, if you are going to make parametric studies it may beadvantageous to speed up the solver for subsequent runs.

This performance tuning step actually turns out to be quite simple: The eigenmode solvercan make use of a guess for the highest eigenmode frequency you are looking for. Theeigenmode solver automatically determines this guess from a previous calculation andprints the result in the log-file. This information is shown right below the timinginformation:

--------------------------------------------------------------

Optimum guess for the highest eigenfrequency would be: 1.732

--------------------------------------------------------------

In order to demonstrate how this information can be used for improving the solver’sspeed, you should now recalculate the eigenmodes once again to compare the timerequired for the simulation. Please enter the eigenmode solver control dialog box onceagain by pressing the corresponding toolbar icon or selecting Solve # EigenmodeSolver from the main menu.


In this dialog box just press the Specials button in order to open a dialog box for moreadvanced settings:

Once you know a guess for the highest eigenfrequency of interest (here 1.732 GHz), youcan enter this value in the Guess field. If you don’t know this value, just enter zero inorder to let the solver estimate this value automatically. After pressing the Ok button inthis dialog box you can restart the eigenmode solver by pressing the Start solver button.

Again, a progress bar will appear informing you about the status of your calculation.Please note that there is no need for recalculating the matrix since the structure has notbeen changed.

The solver will finish its work after a short time giving the same results as before for theeigenfrequencies. The timing information in the logfile should look similar to the databelow:

--------------------------------------------------------------Solver Statistics:



--------------------------------------------------------------

If you now compare the solver time only, you can see that specifying the guess for thehighest eigenfrequency could speed up the solution process by more than a factor of 2.5.

Please remember that these steps are only made here in order to illustrate how to speedup the solver for parametric sweeps or optimizations. The accuracy of the solution willalso be excellent by using the fully automatic procedure without this additional setting.For a single analysis of a particular device, this performance tuning step does not makesense, of course.


Eigenmode Visualization and Q-Factor Calculation

! Eigenmode Visualization

The eigenmode results can be accessed by selecting the corresponding item in thenavigation tree from the 2D/3D Results # Modes folder. The field patterns for each modewill be collected in subfolders named Mode N where N stands for the mode number.

To visualize the electric field of the first mode you can simply select the correspondingitem from the navigation bar: 2D/3D Results # Modes # Mode 1# e. The result data willthen be visualized in a three dimensional vector plot as shown in the picture above.

Please note that the field amplitudes of the modes will always be normalized such thateach mode contains a total energy of 1 joule.

In many cases, it is more important to visualize the fields in a cross section plane.Therefore, please switch to the 2D field visualization mode by pressing the icon or byselecting Results # 3D Fields on a 2D Plane. The field data should then be visualizedsimilar to the picture below. Please refer to the Getting Started manual or press the F1key for online help to obtain more information on field visualization options.


Besides the graphical field visualization, some information text containing maximum fieldstrength values and resonance frequencies will also be shown in the main window.

! Q Factor Calculation

The eigenmode’s Q-factors, which are an important quantity for cavity design, can beeasily derived from the field patterns. Please open the loss and Q-factor calculationdialog box by selecting Results # Loss and Q Calculation.


The only setting which needs to be specified here is the conductivity of the enclosingmetal. By default the conductivity of the Cond. Enclosure is set to copper (5e7 S/m).

You may change this setting by double-clicking on the Cond. Enclosure line in the listwhich opens the following dialog box:

In this example you can set the Conductivity value to silver (6.16e7 S/m) and press theOk button.

Back in the loss and Q factor calculation dialog box you should now select the desiredMode from the H-Field data list, e.g. the fundamental mode Mode 1. Finally you shouldpress the Calculate button to obtain the Q factor value.

The Q-factor is calculated to be 4.3553•104 for the fundamental mode. The Q-factors forthe other modes can be calculated in the same way.



The eigenmode calculation is mainly affected by two sources of numerical inaccuracies:

1. Numerical errors introduced by the iterative eigenmode solver.2. Inaccuracies arising from the finite mesh resolution.

In the following sections we will give you some hints how to handle these errors and howto ensure to achieve highly accurate results.

! Accuracy of the Numerical Eigenmode Solver

The first type of error is always quantified as Accuracy for each mode after thecalculation has finished. The modes can usually be considered sufficiently accurate formost practical applications if the mode accuracy is below 1e-3.

The results can be improved by specifying a proper guess for the highest eigenmodefrequency of interest and by increasing the number of iterations for the eigenmodesolver. Specifying more than five iterations does not usually improve the results anyfurther.

Sometimes higher modes are calculated with a lower accuracy than lower ones. In manycases it may be advantageous to calculate more modes than you are actually looking for,in order to improve the accuracy of the desired (lower) ones.

! Effect of the Mesh Resolution on the Eigenmode Accuracy

The inaccuracies arising from the finite mesh resolution are usually more difficult toestimate. The only way to ensure the accuracy of the solution is to increase the meshresolution and recalculate the eigenmodes. If the desired results (e.g. eigenmodefrequencies, Q-factors) do not significantly change anymore by increasing the meshdensity, then convergence has been achieved.

In the example above, you have used the default mesh which has been automaticallygenerated by an expert system. The easiest way to test the accuracy of the results is touse the fully automatic mesh adaption which can be switched on by checking theAdaptive mesh refinement option in the solver control dialog box (Solve # EigenmodeSolver):


After activating the adaptive mesh refinement tool, the Properties button becomes active.You should now press this button to open the mesh refinement properties dialog box:

Since you are actually interested in the first five modes of this structure only, you shouldchange the Number of modes to check to 5 in order to focus the mesh refinementprocedure on these modes. Afterwards you can close this dialog box by pressing the Okbutton.


Back in the solver dialog box, you can now start the eigenmode solver again by pressingthe Start solver button. After a couple of minutes during which the solver is runningthrough mesh adaption passes, the following dialog box will appear:


You should now confirm the deactivation of the mesh adaption by pressing the Yesbutton. The converged results for the eigenmode frequencies will then be shown in theupcoming dialog box:


After the mesh adaption procedure has completed, you can visualize the maximumrelative difference of the eigenmode frequencies for two subsequent passes by selecting1D Results # Adaptive Meshing # Error from the navigation tree:

As you can see, the maximum deviation of the eigenmode’s frequencies is below 0.14%which indicates that the expert system based meshing would have been fine for thisexample even without running the mesh adaption procedure.

The eigenmode solver accuracies achieved for the modes during the mesh adaption canbe visualized by selecting 1D Results # Adaptive Meshing # Mode Accuracies from thenavigation tree:


The plot shows that all mode accuracies for both passes are fine (even better than 2.5e-9). Finally, you can visualize the convergence process of the mode frequencies byclicking at 1D Results # Adaptive Meshing # Mode Frequencies:

By inspecting the plot above, you can confirm that the results are quite stable here.




Congratulations! You have just completed the Cavity tutorial which should have providedyou with a good working knowledge on how to use the eigenmode solver. The followingtopics have been covered so far:

1. General modeling considerations, using templates, etc.2. Use a figure of rotation and a mirror transformation to model the cavity.3. Define the frequency range, boundary conditions and symmetries.4. Run the eigenmode solver and display eigenmode frequencies and field patterns.5. Optimize the performance of the eigenmode solver for subsequent runs.6. Calculate the Q-factors of the eigenmodes.7. Check and if necessary improve the accuracy of the eigenmode solver.8. Ensure to obtain accurate and converged results by using the automatic expert



Sometimes we have referred to the Getting Started manual, which is also a good sourceof information for general topics.

In addition to this tutorial, you can find some more eigenmode solver examples in theexamples folder in your installation directory. Each of these examples contains aReadme item in the navigation tree which will give you some more information about theparticular device.


And last but not least: Please also visit one of the training classes which are regularlyheld at a location near you. Thank you for using CST MICROWAVE STUDIO!

The Narrow Band Filter Tutorial


Introduction and Model’s Dimensions 152Geometric Construction Steps 153Solver Settings and S-Parameter Calculation 167

Results 177

1D Results (S-Parameters) 1772D and 3D Results (Port Modes and Three Dimensional Modes) 177



152 CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial



In this tutorial you will analyze a Narrow Band Filter. CST MICROWAVE STUDIO®

canprovide a wide variety of results. This tutorial however, concentrates solely on the S-parameters of the filter.



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 = 1025

100

All dimensions are given in mm

105

217

17.9

95

110

200

15

50

r = 2.9

r = 1025

100

100100

The structure consists of two resonators, each of which build by a perfect electricallyconducting cylinder in a rectangular cavity. Both resonators are coupled with a

CST MICROWAVE STUDIO® – Narrow Band Filter Tutorial 153

rectangular iris. The two coaxial ports are capacitively coupled to the device by extendingthe coaxial cable’s inner conductor into the resonators.

The following explanations on how to model and analyze this device can also be appliedto other filter structures as well.


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

! Select a Template

Once you start CST MICROWAVE STUDIO®

and choose to create a new project, youare requested to select a template which fits best to your current device. Here the“Waveguide Filter” template should be chosen.

The template automatically sets the units to mm and GHz, the background material to beperfect electrically conducting.


Once the units have been correctly set (which has been done by the template here), themodeling process usually starts with setting the working plane’s size large enough for thedevice. 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 bechanged in a dialog box, which opens after selecting Edit # Working Plane Propertiesfrom the main menu. Please note that we will use the same document conventions hereas they have been introduced in the Getting Started manual.


In this dialog box you should set the size to 300 (the unit which has been previously setto mm is displayed in the status bar), the raster width to 10 and the snap width to 5 toobtain a reasonably spaced grid. Please confirm these settings by pressing the Okbutton.

! Draw the Filter’s Housing

Due to the fact that the background material has been set to electric, you need to modelthe interior of the filter. The structure will then be automatically embedded within aperfect electric conducting enclosure.

Thus you should start the structure modeling by entering the filter’s housing which caneasily be defined by creating an air-brick. Please activate the brick creation tool now byeither selecting Objects # Basic Shapes # Brick or pressing the corresponding button inthe toolbar ( ).

Once you are prompted to enter the first point, you may request to enter the coordinatesnumerically 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 x200 mm. In order to model the structure symmetrically to the origin, you should now enterthe coordinates X = -50 and Y = -100 in the dialog box and press the Ok button (pleaseremember 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 pressthe TAB key again and enter X = 50, Y = 100 in the coordinate fields before pressing Ok.

Now you will be requested to enter the height of the brick. This can also be numericallyachieved by pressing the TAB key, entering a Height of 110 and pressing the Ok buttonagain.After the steps above have been completed, the following dialog box will appear showingyou a summary of your input:


Please check all entries carefully. When you encounter any mistakes, please change thevalue in the corresponding entry field.

After naming the shape in a meaningful way (e.g. “housing”), verify that the brick isassigned to the vacuum layer and confirm the creation by pressing Ok.

Your screen should now look as follows (you can press the SPACE key in order to zoomthe structure to the maximum possible extent):


Since some structures will be inserted into this air brick in the following steps, it isadvantageous to switch the display to wireframe mode because otherwise the newlycreated shapes may be hidden inside this brick. The easiest way to activate thewireframe visualization mode is to press the toolbar icon or to use the correspondingshortcut: Ctrl+W. Now the structure should look as follows:

! Create the Cylindrical Resonators

The next step is to create the cylindrical resonators inside the air brick. Please activatethe cylinder creation tool now by selecting either Objects # Basic Shapes # Cylinderfrom the main menu or by pressing the toolbar icon ( ).

The first step in the cylinder creation process is to enter the center point’s coordinates.This can be achieved numerically by pressing the TAB key and entering the dimensionsX = 0, Y = -50 in the dialog box before pressing the Ok button. In the following we willassume that you always confirm the settings in a dialog box by pressing the Ok buttonunless mentioned otherwise.

The second step in the cylinder’s creation is to specify the radius. Similarly to theprocedure above, you should now set the Radius to 17 after pressing the TAB key.


After once more pressing the TAB key and setting the Height to 95, you may skip thedefinition of the cylinder’s inner radius by pressing the ESC key. Finally, the followingdialog box will appear:

Please check and correct all settings as necessary before you specify the cylinder’sName to be “cylinder1”. So far, the cylinder consists of vacuum material. However, tospecify the cylinder to be a perfect electric conductor (PEC), you need to change theLayer assignment to PEC before pressing the Ok button.

Your screen should then look as follows:


After successfully creating the first cylinder you can now model the second cylinder in thesame 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 Layer assignment to PEC and press the Ok button.

After the successful creation of the second cylinder, the screen should then look asfollows:

Please note: The creation of the second cylinder could also be achieved byapplying a transformation to the first one. For the sake of simplicity, we simplyrecommended you to draw the cylinder twice. The usage of transformations tocopy 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 easilybe achieved by entering its dimensions numerically as it has been done for the creationof the air brick above. However, since the iris should always extend across the entirewidth 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 orpressing the corresponding button in the toolbar ( ) you are requested to enter the firstpoint. 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 midpointtool (Objects # Pick # Pick Edge Midpoint, ). Afterwards, all straight edges will behighlighted in the model:

You should now double-click on the first edge shown in the picture above. By moving themouse pointer you can now confirm that the first point of the brick is aligned with the midpoint of this edge. Even if the location of the midpoint may change (e.g. by parametricallyediting the structure), the first point of the newly created brick will always be linked withthe edge midpoint’s current position.

You should now repeat the same steps (activate midpoint pick tool, double-click at theedge) 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 requests the width ofthe brick. You should now press the TAB key and set the Width of the brick to 2.

First Edge Second Edge


In the last step of the interactive brick creation you are requested to enter the brick’sheight. 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 constructionof the brick. The expression xp(1), for instance, represents the x-coordinate of the firstlypicked edge’s midpoint.

Please set the Name of the brick to “iris” now, change the Layer assignment to PEC andpress the Ok button. You model should then look as follows:


! Create the Coaxial Couplings

So far, you have modeled the filters internal structure. However, the next step is to modelthe coaxial couplings to both side walls of the filter.

Before you start modeling the cylinders, you should firstly align the working coordinatesystem with one of the side walls of the filter. This will allow you to model the couplingstructure in a much more convenient way. Please deactivate the wireframe plot mode bypressing the toolbar icon or using the shortcut Ctrl+W:

Afterwards you should activate the face pick tool (Objects # Pick # Pick Face, ) anddouble-click on the top face as shown above. The selected face should then behighlighted in the model (see picture above).

The next step is to align the working coordinate system with the picked face by selectingeither WCS # Align WCS With Selected Face, pressing the toolbar button ( ) or usingthe shortcut W (while the main view is active).

After activating the wireframe drawing mode again (Ctrl+W), the model should look asfollows:

Top face

Pick top face

Top edge


The location of the coaxial coupler’s center is located 17.9 mm below the top wall of thefilter. Therefore the next step is to align the working coordinate system with the top wallof 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 EdgeMidpoint, ) 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 theworking coordinate system with this point by selecting WCS # Align WCS With SelectedPoint, pressing the toolbar button or just using the shortcut W. The following pictureshows the new location of the working coordinate system:

With the working coordinate system being aligned this way, the construction of thecoaxial 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”


The cylinder creation dialog box should then look as follows:

You still need to define the substrate material. Since no material layer has yet beendefined for the substrate, you should open the layer definition dialog box by pressing theNew button:

In this dialog box you should first of all define a new Layer name (e.g. “coaxial cable”)and set the layer type to a Normal dielectric material. Afterwards specify the materialproperties in the Epsilon and Mue fields. Here you only need to change the dielectricconstant Epsilon to 2.2. Finally choose a nice color for the layer by pressing the Changebutton. Your dialog box should now look similar to the picture above before you press theOk button.


Back in the cylinder creation dialog box you can also press the Ok button to finally createthe coaxial coupler’s substrate. You model should now look as follows:

The next step is to model the inner conductor of the coaxial coupler as a perfect electricconducting cylinder. Since both cylinders should always be coaxial, it is convenient tomove 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 thetoolbar ( ). Now double-click on the substrate cylinder’s upper edge as shown in thepicture above which will highlight the circle center point. Finally you can align the workingcoordinate system with this point by selecting WCS # Align WCS With Selected Point orpressing the toolbar button . The following picture shows how your model should nowlook:

Upper edge


The inner conductor of the coaxial connector can now be easily modeled by performingthe 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 “coaxial inner conductor”7. Change the Layer 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 # LocalCoordinate System or pressing the corresponding toolbar button . After all these steps,the model should now look as follows:

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 anappropriate shape transformation. Firstly, you should now select the dielectric part of thecoaxial coupler by either double-clicking at it in the view or by selecting thecorresponding navigation tree entry (Layers # coaxial cable # coaxial substrate).


Afterwards please open the shape transformation dialog box (Objects # TransformShape or ):

The first action in this dialog is to set the Operation to Mirror. Afterwards the parametersof the mirror plane are specified. Since this plane should be the X/Z plane of the globalcoordinate system, you only need to set the Y coordinate of the Mirror plane normal to 1.To create a mirrored copy of the existing shape, please enable the option Multipleobjects. Confirm the settings by pressing Ok.

Original shape

Mirrored copy


The modeling stage is finished by copying the inner conductor of the coaxial coupler inthe same way as demonstrated for the substrate above:

1. Select the first coaxial coupler’s inner conductor by double-clicking at it in the view orby selecting Layers # PEC# coaxial inner conductor.

2. Open the shape transformation dialog box: Objects # Transform Shape or .3. Select the Operation Mirror.4. Set the Y coordinate of the Mirror plane normal to 1.5. Activate the Multiple objects option.6. Press the Ok button to create the mirrored copy.

Your screen should finally look as follows:

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 becalculated. 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 mostaccurate 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 thewaveguide’s cross-section, it must be defined large enough to entirely cover these modefields. In case of a coaxial cable, the port thus has to cover the coaxial cable’s substratecompletely.


Before you continue with the port definition, please deactivate the wireframe visualizationby 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, bysimply picking the face to be covered by the port. Therefore, please activate the pick facetool (Objects # Pick # Pick Face, ) and double-click at the substrate’s port face of oneof the coaxial couplers as shown in the pictures below:


Whenever a face is picked before the port dialog is opened, the port’s location and sizewill automatically be defined by the picked face’s extent. Thus the port’s Transversalposition is initially set to Use picks. You can simply accept this setting and go ahead.

The next step is to choose how many modes should be considered by the port. Forcoaxial devices, we usually only have a single propagating mode. Thus you shouldsimply keep the default of one mode.

Pick substrate’s

port face

Substrate’s port face



Now you can repeat the same steps for the definition of the opposite port 2.

1. Pick the corresponding substrate’s port face (Objects # Pick # Pick Face, ).2. Open the waveguide dialog box (Solve #Waveguide Ports, ).3. Press Ok to store the port’s settings.

Your model should now finally look as follows:




Here all boundary conditions are set to electric which just means that the structure isembedded into a perfect electric conducting housing. These defaults (which have beenset by the template) are appropriate for this example.

Due to the structure’s symmetry to the Y/Z plane and the fact that the magnetic field inthe coaxial cable is perpendicular to this plane, a symmetry condition can be used. Thissymmetry will reduce the time required for the simulation by a factor of two. You shouldalso refer to the example in the Getting Started manual for more information onsymmetry conditions.



By setting the symmetry plane Y/Z to magnetic, you force the solver to calculate only themodes which have no tangential magnetic field component to these planes (thus forcingthe electric field to be tangential to these planes).


Please note that you also could double-click at the symmetry plane’s handle and choosethe proper symmetry condition from the context menu.





The frequency range for this example extends from 0.58 GHz to 0.62 GHz. Change Fminand Fmax to the desired values in the define frequency range dialog box (opened bypressing the toolbar icon or choosing Solve # Frequency) and store these settings bypressing the Ok button (the frequency unit which has previously been set to GHz isshown in the status bar).


After completing all steps above you are now ready to start the S-parametercomputation. The filter device analyzed here is a narrow band filter for which two differentsolution methods can be used:

1. Transient solver2. Modal analysis solver (based on eigenmode solver)

The transient solver is definitely the most versatile tool to solve any kind of S-parameterproblem. However, for strongly resonant structures (such as the filter here), the modalanalysis solver is an interesting alternative which can be more computationally efficientthan the transient solver. Thus we are going to demonstrate how to use this highlyspecialized solver here. Please refer to the Getting Started manual and the other tutorialson how to utilize the transient solver for S-parameter problems.


For S-parameter calculations by using the modal analysis tool you should open theeigenmode solver control dialog box by pressing the corresponding toolbar icon orselecting Solve # Eigenmode Solver from the main menu.

The first important setting which commonly needs to be specified here is the number ofModes to be calculated. The solver will then calculate these number of modes startingfrom the lowest resonance frequency. The modal analysis solver usually requires areasonably large number of modes to be calculated, e.g. 20 for accurate results. Thusyou should set the number of Modes to 20 whenever you are going to calculate S-parameters.

The next important setting is the maximum number of iterations for the eigenmodesolver. Since the highly accurate calculation of 20 modes is a quite demanding task, youshould increase this number by entering 5 in the Iterations field for S-parametercalculations.

Afterwards, you need to activate the modal S-parameter calculation by selecting theCalculate modal coefficients option.

Please check your settings in the dialog box before pressing the Start solver button.

Now a few progress bars will appear, keeping you informed about the current status ofyour calculation (e.g. matrix calculation, eigenmode analysis).


After the solver has finished its work, a dialog box will be shown displaying theresonance frequencies of the first 20 modes:

The accuracy for the mode solution is excellent for all these modes. A mode with anaccuracy of less than 1e-3 can usually be considered as being sufficiently accurate. Thisdialog box can be dismissed by pressing the Ok button.

In order to review the solver time required to achieve these results, you can display thesolver log-file by selecting Results # View Logfiles # Solver Logfile from the main menu.Please scroll down the text to obtain the following timing information (the actual valuesmay vary depending on the speed of your computer):

-----------------------------------------------------------------Solver Statistics:



-----------------------------------------------------------------

The computation time required for the modal analysis S-parameter calculation once theeigenmodes have been obtained is only a few seconds and is also shown in the log-file:

-----------------------------------------------------------------

Total time needed for modal analysis: 0 hours 00 mins 03 secs

-----------------------------------------------------------------

! Optimizing the Performance for Subsequent Calculations

So far, you have successfully calculated the eigenmodes for this device in a reasonableamount of time. However, if you are going to make parametric studies it may beadvantageous to speed up the solver for subsequent runs.

This performance tuning step actually turns out to be quite simple: The eigenmode solvercan make use of a guess for the highest eigenmode frequency you are looking for. Agood choice for this guess is automatically obtained from the previous eigenmode resultsand shown in the log-file:

Optimum guess for the highest eigenfrequency would be: 3.479


In order to demonstrate how this information could be used for improving the solver’sspeed, you should now recalculate the eigenmodes once again to compare the timerequired for the simulation. Please enter the eigenmode solver control dialog box onceagain by pressing the corresponding toolbar icon or selecting Solve # EigenmodeSolver from the main menu.

In this dialog box just press the Specials button in order to open a dialog box for moreadvanced settings:

Once you know a guess for the highest eigenfrequency of interest (here 3.479 GHz), youcan enter this value in the Guess field. If you don’t know this value, just enter zero inorder to let the solver estimate this value automatically. After pressing the Ok button inthis dialog box you can restart the eigenmode solver by pressing the Start solver button.


Again, a progress bar will appear informing you about the status of your calculation.Please note that there is no need to recalculate the matrix since the structure has notbeen changed.

The solver will finish its work after a short time giving the same results as before for theeigenfrequencies. The timing information in the log-file should look similar to the databelow:

------------------------------------------------------------------Solver Statistics:



------------------------------------------------------------------

If you now compare the solver time only, you can see that specifying the guess for thehighest eigenfrequency could speed up the solution process by more than a factor ofthree.

Please remember that these steps are only made here in order to illustrate how to speedup the solver for parametric sweeps or optimizations. The accuracy of the solution willalso be excellent by using the fully automatic procedure without this additional setting.For a single analysis of a particular device, this performance tuning step does not makesense, of course.


Results

Congratulations, you have simulated the Narrow Band Filter. Let’s have a look at theresults.

1D Results (S-Parameters)

The S-Parameter magnitude in dB scaling can be plotted by clicking on the 1D Results #SdB folder.

As expected, the bandwidth of the transmission S2,1 is quite small. It is also obvious thatthis filter is somehow detuned.

2D and 3D Results (Port Modes and Three Dimensional Modes)

After inspecting the S-parameters you can have a look at the 2D and 3D field results.You should first inspect the port modes, which can be easily displayed by opening the2D/3D Results # Port Modes # Port1 folder from the navigation tree. To visualize theelectric field of the fundamental port mode you should click on the e1 folder.


The plot also shows some important properties of the mode such as mode type,propagation constant and line impedance. The port modes at the second port can bevisualized in the same way.

The three dimensional eigenmode results can be accessed by selecting thecorresponding item in the navigation tree from the 2D/3D Results # Modes folder. Thefield patterns for each mode will be collected in subfolders named Mode N where Nstands for the mode number.


To visualize the electric field of the first mode you can simply select the correspondingitem from the navigation bar: 2D/3D Results # Modes # Mode 1 # e. The result datawill then be visualized in a three dimensional vector plot as shown in the picture above.You may need to increase the number of arrows in the plot properties to obtain thepicture above. Please refer to the Getting Started manual for more information on how totune the plot options.

Please note that the field amplitudes of the modes will always be normalized such thateach mode contains a total energy of 1 joule.

In many cases, it is more important to visualize the fields in a cross-section of the device.Therefore, please switch to the 2D field visualization mode by pressing the icon or byselecting Results # 3D Fields on 2D Plane. The field data should then be displayed as inthe picture below. Again, you will need to increase the number of arrows to obtain thisplot. Please refer to the Getting Started manual or press the F1 key for online help toobtain more information on field visualization options.

Besides the graphical field visualization, also some information text containing maximumfield strength values and resonance frequencies will be shown in the main window.



The eigenmode calculation and thus the modal analysis is mainly affected by twosources of numerical inaccuracies:

1. Numerical errors introduced by the iterative eigenmode solver.2. Inaccuracies arising from the finite mesh resolution.

In the following sections we will give you some hints how to handle these errors and howto ensure to achieve highly accurate results.

! Accuracy of the Numerical Eigenmode Solver

The first type of error is always quantified as Accuracy for each mode after thecalculation has finished. The modes can usually be considered sufficiently accurate formost practical applications if the mode accuracy is below 1e-3.

The results can be improved by specifying a proper guess for the highest eigenmodefrequency of interest and by increasing the number of iterations for the eigenmodesolver.

Sometimes higher modes are calculated with a lower accuracy than lower ones. In manycases it may be advantageous to calculate more modes than you are actually looking forin order to improve the accuracy of the desired (lower) ones. Setting the number ofmodes to calculate to 20 should yield sufficiently accurate modal analysis S-parameterresults in most cases.

! Effect of the Mesh Resolution on the Eigenmode Accuracy

The inaccuracies arising from the finite mesh resolution are usually more difficult toestimate. The only way to ensure the accuracy of the solution is to increase the meshresolution and recalculate the eigenmodes. If the desired results (e.g. eigenmodefrequencies) do not significantly change anymore by increasing the mesh density, thenconvergence is achieved.

In the example above, you have used the default mesh which has been automaticallygenerated by an expert system. The easiest way to prove the accuracy of the results is touse the fully automatic mesh adaption which can be switched on by checking theAdaptive mesh refinement option in the solver control dialog box (Solve # EigenmodeSolver):



This dialog box tells you that the desired accuracy limit on the eigenmode’s frequencies(1% by default) could be met by the adaptive mesh refinement. Since the expert system’ssettings have now been adjusted such that this accuracy is achieved, you may switch offthe adaption procedure for subsequent calculations (e.g. parameter sweeps oroptimizations).


You should now confirm the deactivation of the mesh adaption by pressing the Yesbutton. The converged results for the eigenmode frequencies will then be shown in theupcoming dialog box:

After the mesh adaption procedure has completed, you can visualize the maximumrelative difference of the eigenmode frequencies for two subsequent passes by selecting1D Results # Adaptive Meshing # Error from the navigation tree:

As you can see, the automatic mesh adaption procedure requires four passes to achieveconvergence for this challenging filter structure. This indicates that it is necessary to runthe mesh adaption for this example in order to achieve highly accurate results.


The eigenmode solver accuracies achieved for the modes during the mesh adaption canbe visualized by selecting 1D Results # Adaptive Meshing # Mode Accuracies from thenavigation tree:

The plot shows that all mode accuracies for all four passes are fine (even better than 8e-12). Finally, you can visualize the convergence process of the mode frequencies byclicking at 1D Results # Adaptive Meshing # Mode Frequencies:


Finally, the most interesting result are the converged S-parameters shown below:

The final S-parameters changed quite significantly from the first results obtained by usingthe start mesh created by the expert system. In general, it can be stated that accurate S-parameter results for filter structures can only be obtained by mesh convergence studies.These studies can be carried out either by manually changing the settings of the expertsystem or, as demonstrated here, by running the automatic mesh adaption tool.




Congratulations! You have just completed the Narrow Band Filter tutorial which shouldhave provided you with a good working knowledge on how to use the modal analysissolver to calculate S-parameters of filter structures. The following topics have beencovered so far:

1. General modeling considerations, using templates, etc.2. Define basic structure elements such as bricks and cylinders.3. Use the working coordinate system to simplify the shape creation.4. Create copies of existing shapes by using transformations.5. Define the frequency range, boundary conditions and symmetries.6. Run the modal analysis solver and display S-parameters, eigenmode frequencies

and field patterns.7. Optimize the performance of the eigenmode solver for subsequent runs.8. Check and if necessary improve the accuracy of the modal analysis solver.9. Ensure to obtain accurate and converged results by using the automatic expert



Sometimes we have referred to the Getting Started manual, which is also a good sourceof information for general topics.

In addition to this tutorial, you can find some more eigenmode and modal analysis solverexamples in the examples folder in your installation directory. Each of these examplescontains a Readme item in the navigation tree which will give you some more informationabout the particular device.

You should also consider using the transient solver to calculate the S-parameters forfilter structures. Please check out the other tutorials and the transient solver examples inthe examples folder for more information.


And last but not least: Please also visit one of the training classes which are regularlyheld at a location near you. Thank you for using CST MICROWAVE STUDIO!

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