Ansoft HFSS Training Example:

Aperture-Coupled Patch Antenna This exercise assumes you have already had a little exposure to Ansoft HFSS, e.g. through one or two previous exercises. Therefore, it will no longer describe every single button click. Still, it will guide you in sufficient detail. In this exercise, you will model an aperture-coupled patch antenna. The model is shown in Figure 1. It has a ground plane sandwiched between two layers of dielectric. There is a signal trace on the bottom and a patch antenna on the top. A slot in the ground plane between the trace and the patch allows electromagnetic coupling. The structure is resonant: it will only radiate in a narrow frequency band. Around the structure is a volume of air.

Fig. 1 Aperture-coupled patch antenna

1. Draw the geomtry of the model Start Maxwell by typing maxwell & on the command line if you work on a UNIX workstation, or by choosing the appropriate icon if you work on a PC. The “Maxwell Toolbar” will come up. In the Maxwell Toolbar, choose Projects. This brings up the Maxwell Control Panel or Project Manager. In that window, create a New project in the directory of your choice. Call the project patchant. Make sure the type is High-Frequency Structure Simulator. If the project doesn’t open upon creation, click the Open button to open this new project. A new window comes up: the Executive Commands window or Main Menu that belongs to this project. In the new window, click on Draw to bring up the 3D modeler, which is the drawing package. In the 3D modeler, select centimeters as the unit to work in. If you feel very comfortable with the 3D modeler, you can build the model from the following list of objects with their points of smallest (x,y,z) and their sizes. Then you can read the comments in this chapter on the air box and the slab, and move on to the part where you cut the model in half to take advantage of symmetry. Otherwise, skip the list and follow the instructions in the remainder of this chapter. Object name Object type Min. x,y,z Size air solid, box -9, -9, -4 18, 18, 10 dielbot solid, box -5, -5, -0.16 10, 10, 0.16 dieltop solid, box -5, -5, 0 10, 10, 0.16 ground sheet, rectangle -5, -5, 0 10, 10 (x,y) trace sheet, rectangle -5, -0.2475, -0.16 7, 0.495 (x,y) slot sheet, rectangle -0.0775, -0.7, 0 0.155, 1.4 (x,y) patch sheet, rectangle -2, -1.5, 0.16 4, 3 (x,y) slab solid, box -5.1, -1.5, -0.8 0.1, 3, 0.8 Let’s start with the two layers of dielectric. Choose Solids➜ Box to create the bottom layer. This layer stretches from (x,y,z) = (-5, -5, -0.16) to (x,y,z) = (5, 5, 0). Hence, the size is (10, 10, 0.16). Activate coordinates in the left-hand part of the window if necessary by checking the boxes in front of them. Call the new object dielbot. Once it has been created, use View➜ Fit All or the corresponding icon or the “hotkey” f if desired to improve the visibility. You can create the top dielectric by duplicating the bottom one. First select the bottom dielectric by clicking the SEL icon, then clicking on the object in one of the windows or in the list (note that it changes color), and clicking OK. Choose Edit➜ Duplicate➜ Along Line. Enter the vector (0, 0, 0.16) and take a total number of 2. Click OK. HFSS creates a second object, offset from the first one by (0, 0, 0.16) and hence lying right on top of it,

and calls it dielbot1. Let’s change that name. Choose Edit➜ Attributes➜ By Clicking and select the object dielbot1. Click OK, change the name to dieltop, and click OK. Finally click Cancel to get out of the “edit attributes mode”.

Fig. 2 The objects dielbot and dieltop. Note that they are symmetrical with respect to the x,z and y,z

planes. Let’s create the ground, the trace, the slot, and the patch. Choose Lines➜ Rectangle for each object. For each object, enter the coordinates of the first point in the x,y,z boxes on the left, click Enter, make sure the xy plane is checked since the rectangle will be horizontal, give the object a size and a name and a color, etc. Obtain the names and the coordinates from the table above. Make sure that covered is checked, since this simulation requires sheet objects rather than just lines with nothing in between. Once all four sheet objects are there, create the next solid box, the air around the objects. How large should the air box be? Important is that the absorbing boundary or radiation boundary that you will place on the outer surface of the air box be not too

close to radiating objects. The rule of thumb is that that boundary needs to be a quarter wavelength away if you want to obtain an accurate antenna pattern. This antenna is expected to radiate near 2 GHz, so the faces of the air box should be 4 cm away from radiating objects. You could measure this 4 cm from the edges of the patch or from the edges of the ground plane. Whether you measure from the edges of the ground plane or not depends on your engineering judgement of how significant radiation from those edges will be, relative to radiation from the patch itself. For large ground planes, you may want to put the air box on top of the ground plane rather than making it go all the way around it. In this case, let’s be prudent and make the air box at least 4 cm larger than the ground plane in all directions, and even a little more in the upward direction, where we expect most of the radiation to go. Use Solids➜ Box to create the air box. The first point is (x,y,z)=(-9, -9, -4) and the size is (18, 18, 10). Name the object airbox. The last object we need is a solid called slab. Slab will be an object positioned at the beginning of the trace. The one face that touches the trace will later be assigned a so-called “port” through which the fields enter the system. How large should this port be? Keep in mind that HFSS thinks in terms of fields. The port should be large enough to accommodate the field pattern of the TEM microstrip mode. Ansoft recommends that the port be 5 to 10 times as wide as the width of the trace and 5 times as high as the thickness of the dielectric. Here, the trace is almost 0.5 cm wide, so let’s make the port 3 cm wide. The dielectric is 0.16 cm thick, so let’s make the port 0.8 cm high. Further, one edge of the port should coincide with the ground plane. Just like the fields in the microstrip, it should touch the ground plane and not go through it. A port is two-dimensional. Since HFSS has no way of knowing in which direction the initial excitation should go, the port should be backed by a metal slab if it doesn’t happen to be lying on the outside of your model. This slab is not shorting the port! It’s just the way the software has been set up. That is the reason why we will create this 3D object called slab. Later, we define one face of it as port. Time to create the slab! For a change, we’ll create the box by sweeping a rectangle. Use Lines➜ Rectangle to create a covered rectangle of which the first point is (-5, -1.5, -0.8), which is parallel to the y,z plane, and which has a size of 3 in the y direction and 0.8 in the z direction. Call the rectangle slab. Next, create the solid by sweeping this rectangle over a distance of –0.2 (this is arbitrary, as long as it’s not extremely thin) in the x direction. Choose Solids➜ Sweep➜ Along Vector. Select the slab and make the vector (-0.2, 0, 0). Note that our model is symmetrical with respect to the x,z plane. We can take advantage of this symmetry by cutting the model in half along this plane. This will save memory, disk space and computation time. Select Solids➜ Split , then select the x,z plane to be the split plane and keep the fragments above the plane. Click Enter. In the next box that comes up, select all the objects and click OK. You now have a model of half the geometry.

Fig. 3 The final model after the split operation This completes the drawing. Save and Exit. This brings you back to the Main Menu.

2. Setup Materials Choose Setup Materials from the Main Menu. The Material Setup window comes up. Note that in the objects list, only the three-dimensional objects are listed. The two-dimensional ones will be taken care of by a boundary condition. E.g. two-dimensional metal will not receive metal as a material property but will get a high conductivity as boundary condition. Assign material parameters to the air box and to the metal slab. For the air box, select the object in the objects list, select the material air in the materials list, and click Assign. For the slab, follow a similar procedure, but now the material is perf_conductor. For dielbot and dieltop, add a new material to the list. Choose Material➜ Add. Under Material Attributes, give it a name, e.g. eps254, and to the right of that, a permittivity of

2.54. Click on Enter. The new material is now part of the materials database. Now select both objects dielbot and dieltop and Assign them the material parameters of eps254. Once all objects have been assigned material parameters, Exit and Save. This brings you back to the Main Menu.

3. Setup Boundaries and Sources In the Main Menu, choose Setup Boundaries/Sources. The 3D Boundary/Source Manager window comes up. Let’s first assign perfect conductivity to a few two-dimensional metal objects that didn’t get any material parameters yet. Choose Edit➜ Select➜ By Name. In the little window that comes up, make sure Object is checked; we want to select 2D objects, not just faces. Select the ground, the patch and the trace simultaneously. Note that they change color in the picture. Below the picture, give the new boundary condition the name metals and make sure that boundary rather than source is checked. The type of boundary is Perfect E. This means the metals are perfectly conducting. Assign. Of course, you could have given these three objects their boundary condition one by one. Let’s make the appropriate face of the slab a port. This is the face that touches the microstrip. Zoom in on the slab. Choose Edit➜ Select➜ By Name. In the little window that comes up, make sure that Face is checked. Select the object slab and try the faces one by one until you have selected the face that is going to be the port. Click Done. Below the picture, make sure that Source rather than Boundary is checked. The source type is port. Don’t worry about the rest and click Assign.

Fig. 4 Selection of proper face of slab to be the port. The face to be selected is the one that touches the

signal trace. At this point, there are two more boundaries that need to be defined. HFSS doesn’t know yet that the slot is an opening in the ground plane and it doesn’t know that the antenna is supposed to radiate into free space. If you would exit now, the slot in the ground plane would be filled up with the Perfect E boundary that you just assigned to the entire ground object, and further HFSS would assume a metal box around the air. Let’s take care of the slot. Choose Edit➜ Select➜ By Name, make sure Object is checked and select the slot. Click Done. Below the picture, give the boundary condition the name aperture, make sure Boundary is checked, and make the type Perfect H / Natural. Natural indicates a natural transition between two media. It is this boundary condition that makes the opening in the ground plane. Then, Assign. Read the warning that comes up. In this case, everything is fine, since we assigned Perfect E to the ground first and Natural to the slot afterwards. Had we done it in the opposite order, the Perfect E condition for the ground would have overwritten the Natural condition for the slot. Select the object airbox and assign it the radiation boundary condition.

At this point, all six faces of the air box have radiation boundary conditions. However, one of them needs to have a symmetry boundary condition: the face in the x,z plane. We can simply overwrite the radiation boundary condition on this face with a symmetry boundary condition. Alternatively, we could have been more precise in the previous step and have assigned the radiation boundary to five faces only. To assign the symmetry boundary condition to the airbox face in the x,z plane, do the following: 1. Deselect all object and faces if necessary to start “clean”. 2. Make sure that under Graphical Pick on the left, Face is checked. 3. Select the appropriate face graphically. Maybe you need to rotate the model before

selecting the face, or maybe you select another face that is in front of the desired one and make use of the “Next Behind” option under the right mouse button.

4. Give the new boundary condition a name, e.g. symmH. 5. Make sure Boundary is checked and select “Symmetry / PerfectH” from the list. It is

important to select “Symmetry / Perfect H” rather than “Perfect H/Natural”, since the Post Processor will later look for Symmetry boundary conditions explicitly. If you would select “Perfect H/Natural” you would get correct S parameters and fields inside your model but wrong near and far fields outside your model.

6. Click Assign. It’s always important to check the ports and boundaries before proceeding. Choose Model➜ Boundary Display. Check the boundaries one by one. Note that only the slab shows up for “s_metal”, not the ground, patch or trace. That is correct, since “s_metal” only indicates the surfaces of 3D metal objects. When you have checked all the boundaries, return to Setup Boundaries/Sources, save your work, and return to the Main Menu. Along the way, enter 0.5 for the impedance multiplier when prompted, and ignore the warnings about overlapping boundaries.

Note: The reason why we need an impedance multiplier of 0.5 is the following: the impedance of a port can be expressed as V/I. In this half-port, we have the same voltage, but only half the current. Hence, HFSS (although it doesn’t explicitly work with voltage in this case) will come up with an impedance that is a factor 2 too high unless you supply this impedance multiplier to correct for it. With a Symmetry / Perfect E boundary the situation is just the opposite and the impedance multiplier is 2. If you make a mistake here, it has NO consequences for the S parameters, the fields, and the antenna radiation patterns: they will still be correct. You would notice it, however, when you renormalize the impedance of a port.

4. Setup Solution Parameters and Solve Skip the menu Setup Executive Parameters and choose Setup Solution. If you find this exercise difficult or have little time, set things up as follows. The frequency will be 2.1 GHz, the number of adaptive passes 6 and the Delta S 0.02. Request a Fast Frequency Sweep between 1.9 GHz and 2.4 GHz with 200 steps. Click OK and then Solve to run the simulation. Move on to the next chapter.

If you are curious to explore more possibilities in HFSS, set things up as follows. The frequency will be 2.1 GHz, the number of adaptive passes 2 and the Delta S 0.02. Do not select any frequency sweep. As the starting mesh, select the initial mesh and select Mesh Options➜ Initial Mesh➜ Define Seed Operations. A new window, called mesh3d, comes up. We can now force the mesh generator to put extra points in the mesh. What we want is to seed the radiation boundary with points that are a sixth of a wavelength apart. The reason is that we want the mesh points on this boundary to be dense enough to get an accurate far field later. The far field follows from an integration over the radiation boundary. Choose on Edit➜ Select Faces and select the five faces that are radiation boundaries. Then choose Seed➜ Object Face➜ By Length. In the small window that pops up, set the maximum number of elements to be added to 2000 and set the Maximum Element Length to 2.4 cm. Click “OK”. Exit from this mesh3d window and save your work when prompted. In the Initial Mesh Refinement Window, make sure both options are checked and click OK. Make sure again that frequency sweep is not checked and accept the other defaults. Return to the Main Menu by clicking OK and click Solve. HFSS refines the initial mesh such that no single tetrahedron is larger than 40% of a wavelength (lambda refinement) and that no tetrahedron edge is larger than 2.4 cm on the radiation boundary (our seeding). It refines the mesh strongly in the port to generate the correct excitation. It then computes the first 3D solution, finds out where the solution is most inaccurate, refines the mesh there, and computes the second 3D solution. When it’s done, check the S parameter. Note that it indicates a large reflection. That is to be expected, since we have a resonant structure here, and it’s likely that we’re just missing the resonance by a little bit. Such a situation is not to our advantage, since HFSS will, in the next one or two adaptive passes, pay more attention to mesh refinement in the microstrip (where fields are strong) than in the air (which has almost zero field right now). We will manually force the mesh to get closer to what we, as good engineers, think it should be. Go back to Setup Solution. Request 2 more adaptive passes, and a Fast Frequency Sweep between 1.9 GHz and 2.4 GHz in 200 steps. Further, choose Mesh Options➜ Manual Mesh➜ Define Manual Mesh (starting from current mesh). The Mesh3d window comes up. Earlier, when we were seeding, we were adding points on surfaces before the first adaptive pass. Now, we will really refine the current, most recent mesh in 3D. Let’s refine the mesh in the air box a little bit. Choose Edit➜ Select Bodies or use the SEL icon to select the air box. Choose Refine➜ Object➜ By Length. A new window comes up that tells you how many tetrahedra you have now in the air box, and what their maximum, minimum and RMS lengths are. You are asked for a maximum number of tetrahedra to be added and a maximum element length. Let’s be modest here and add no more than just 300 tetrahedra while asking for a maximum element length of 3 cm. Click OK. After the refinement is done, deselect the air box. In many other applications, you may want to use this feature while allowing several thousand tetrahedra to be added.

Fig. 5 Manual mesh refinement. Refine-Object-By Length has been selected. Let’s also make sure that the region closest to the patch has adequate refinement. Deselect the air box and choose Refine➜ Box➜ By Length. On the left, define the starting point of the box at (-2.5, 0, -0.5) and the size (5, 2, 1.3). Choose the maximum number of elements to be added 2000 and the maximum element length 1.5 cm. Click OK. When it’s done, you can, if you like, choose Mesh➜ Mesh Info and Mesh➜ Show Mesh to get an idea of what it looks like. Choose File➜ Save and File➜ Exit to return to the Solution Setup menu. There, make sure that the starting mesh is Manual. Start the solution process again. It is important to emphasize that the automatic adaptive mesh refinement is often good enough to provide you with reasonable results without you going through all this. The manual mesher is an advantage for experienced engineers who know where the mesh refinement is needed and want to give HFSS a headstart to converge quicker. There is, however, the danger of “overkill”: you may create too many tetrahedra and slow yourself down. Compare your results and solution time with those of a co-worker who did not use manual meshing. If results are different, you may assume that yours are more accurate.

Make a judgement if the improved accuracy was worth the extra time. FYI: A simulation with an even denser manual mesh and more adaptive passes would put the resonance at 2.13 GHz.

5. Post Process ➜ Matrix Data If you find this exercise difficult or you are running out of time, you can skip this chapter and the next one, and continue with the chapter on Fields Post Processing. Select Post Process ➜ Matrix Data from the Main Menu. The Matrix Data menu comes up. This menu gives you the possibility to do the following processes: 1. deembed, i.e. add or subtract a section of transmission line 2. renormalize the port impedance to a certain value 3. compute the impedance matrix Deembedding is to be done first. Right now, the plane of reference is the plane where the port is located. Suppose you want the point of reference to be right at the slot. This means you want to subtract a section of uniform transmission line. The process of adding or subtracting transmission line is called deembedding. In the Matrix Data menu, choose Compute ➜ De-embed while S_1 (sweep 1) is selected. The Matrix Data Deembedding menu comes up. In the left part of the menu, set a distance of 5 cm and make sure that the arrow in the picture points in the correct direction. The options “Into Object” and “Out from Object” refer to the object that the port is defined on. As soon as you click OK, you get back to the Matrix Data menu, where you can see a new quantity in the list: D_1, which is S_1 deembedded. When you compare S_1 and D_1, you see that the difference between the two is a phase difference in the S parameter, corresponding to the two-way difference in transmission line length. Remember our transmission line is lossless, so only the phase changes. After this correction for the location of the reference plane, you can renormalize the impedance of the transmission line. In the Matrix Data menu, make sure D_1 is selected in the list of solutions. To the right of that, click on Port Zo. Note that the port impedance is close to 50 Ohm, but still a few Ohms off. Suppose you want to have your results referenced to 50 Ohms exactly. The renormalize menu can provide this. Choose Compute ➜ Renormalize, accept the defaults in the next window that comes up, and click OK. In the Matrix Data window, you now have an extra solution quantity: R_1, which is D_1 renormalized. Compare the S parameters of R_1 and D_1. They differ a little bit in both magnitude and phase. At the resonance frequency, S11 in R_1 is a little lower than S11 in D_1, since 50 Ohm is a little closer to the input impedance of the antenna (see below). Had we deembedded over a different length, we might have found slightly different results, since there would have been a section of “old” microstrip line left between the slot and the perfect 50 Ohm line. Now it’s time to compute the input impedance of the antenna. We could have gone here without deembedding and without renormalizing.

Make sure R_1 is selected. In the Matrix Data window, choose Compute ➜ Z Matrix. Accept the default in the next little window and click OK. Note that, with R_1 selected, we can now view the Z matrix, which was “grayed out” before. The Z matrix is just one entry ( 1 x 1 matrix), since this is a one-port device. We will have a closer look at it in the next chapter. Choose File➜ Exit and save changes.

6. Post Process ➜ Matrix Plot The first result we’d like to inspect is the S parameter as a function of frequency. This has a direct relationship with quantities like return loss, mismatch loss and VSWR. In the Main Menu, click on Post Process ➜ Matrix Plot. The Matrix Plot window comes up. In that window, in the menu on top, select Plot ➜ New Plot. Inspect all the defaults to see whether you can accept them, and if you agree click OK. A plot of S11 as a function of frequency appears. Change the scales and the divisions if you like by double-clicking anywhere in the graph and making changes in the little menu that pops up. Note that S11 is low but not very low at the resonant frequency: about 15-20% of the power is reflected (remember S parameters are proportional to fields and power is proportional to the square of the field). Also note that this antenna is not a broadband antenna. The bandwidth can easily be determined from a plot in dB. If you like, select Plot ➜ New Plot again and request the plot in dB now. The menu View ➜ Show Coordinates or its corresponding icon can help you to determine the bandwidth.

Fig. 6 S11 as a function of frequency between 2.0 and 2.2 GHz Plots like this can be adjusted. Double-click anywhere in the plot and a window will pop up that allows you to make changes. Another interesting way to display data is in a Smith Chart. Select Plot ➜ New Plot again and request the S11 results of the sweep in a Smith Chart. A Smith Chart may look complicated, but is in fact not much more than a polar plot of the complex reflection coefficient. Points near the edge of the circle indicate poor matching to the transmission line (magnitude of reflection almost one) while points near the center indicate good matching (magnitude of reflection almost zero). Remember that the direction of a plot in a Smith Chart is always clockwise with increasing frequency. The Smith Chart is a valuable tool for the design of a matching network. We won’t go deeper into that subject here.

Fig. 7 Smith Chart 2.0-2.3 GHz. Point of reference is at the slot. Choose Window ➜ Close All to get rid of the plots. Finally, select Plot ➜ New Plot once more and plot the input impedance. For this, you need to have R_1 and Z matrix selected. Also, have “magnitude” selected. Once you have the plot on the screen, choose Plot ➜ Add to Plot, and add the phase of the antenna impedance to the plot. Note that the reactive part of the input impedance is zero at the frequency where the antenna resonates.

Fig. 8 Input impedance 2.0-2.3 GHz Leave this menu (File➜ Exit). There is no need to save anything.

7. Post Process ➜ Fields In this final part of post processing you will take a look at fields rather than S and Z parameters: you will produce antenna patterns and have a look at fields inside the model. Before entering the post processor, click on Matrix in the Main Menu (or look at your plots once more) to determine which frequency is the resonant frequency for this structure. You will do the post processing for that frequency. Choose Post Process ➜ Fields from the Main Menu. The Post Processor 3D window comes up. This takes a few seconds, as it is a large executable and it needs to load the entire field solution for all the tetrahedra.

Once the post processor is there, choose Data ➜ Edit Sources. This is an important menu, though it is easily overlooked. In a multiport and/or multimode device, it allows you to turn ports and modes on and off, and excite them with any magnitude and phase. In a scattering problem, it allows you to toggle between Total Fields and Scattered Fields. Also, after a fast frequency sweep, it allows you to choose the frequency. That is what you will use it for in this case. Check the box Specify Frequency, specify the resonant frequency and click OK. Let’s produce an antenna pattern. To do this, choose Radiation ➜ Compute ➜ Far Field. The next window that comes up asks you to specify angles. Take a moment to understand the angles. The two antenna patterns you will construct will be in the x,z plane and in the y,z plane. Take a moment to visualize that. HFSS works with angles theta and phi in sperical coordinates. Theta is the angle from the z axis and phi is the angle from the x axis. Hence, an antenna pattern in the x,z plane will have phi=0 and an antenna pattern in the y,z plane will have phi=90 degrees. In the boxes for phi, enter start=0, stop=90, steps=1. Both antenna patterns will have theta going “full circle”. In the boxes for theta, enter start=0, stop=360, steps=72. Click OK. Use the next window that comes up to plot the antenna directivity pattern for phi=0 and phi=90. The patterns are proportional to power (square of fields), and are relative to the power that would be radiated from an isotropic radiator, i.e. a source that radiates power equally in all directions. To produce an antenna gain pattern, choose Plot ➜ Far Field, and make the appropriate selections. In this case, it looks just like the directivity pattern. It would be different if the antenna had internal losses. The gain accounts for those. Explore some menu selections like Window ➜ Tile, Window ➜ Cascade, Plot ➜ Modify, Plot ➜ Delete and Window ➜ Close. Some antenna parameters can be produced through Radiation ➜ Display Data ➜ Far Field. Among other things, it will tell you how much power (of the 1 W you started with) makes it into the antenna (follows directly from S11), and, since the antenna can have internal losses, how much power is actually radiated (follows from an integration over the radiation boundary). The latter value may show an inaccuracy of about a percent. After all, for perfect accuracy you’d need infinite computer resources and a lot of patience. To finish this exercise, let’s make a plot of the fields in the model on the x,z plane. First, make a “cutplane” that coincides with the x,z plane. (Note: You can plot on the x,z plane without making a cutplane, since it already appears in relevant lists by default. Nevertheless, just for the sake of exercise, let’s make a cutplane here). Choose Geometry➜ Create➜ Cutplane. Next, in the left-hand side of the window, make (x,y,z)=(0,0,0). Name the cutplane cutxz. Click the Set button under Origin. Next, make (x,y,z)=(0,1,0) and click the Set button under Normal. Click OK.

Fig. 9 Antenna directivity patterns, phi=0 (x,z plane) and phi=90 (y,z plane) Now that the cutplane exists, choose Plot➜ Field. In the window that comes up, select Mag E and Surface cutxz. Note that our newly defined cutplane appears in this list, together with a list of default planes and object surfaces on which you can plot. Click OK. In the next window, accept the defaults and click OK. Note that the plot that appears needs some modification, since all the colors are related to the maximum field strength and in the transmission line the field strength is orders of magnitude larger than in the air. Double-click on the scale and, in the little window that comes up, change the maximum value to one-twentieth or less of what it is. Change the minimum value to zero if necessary. Click OK. Rotate the plot and zoom in if necessary. How about a movie? Remember the maximum field value that you used once you had corrected the plot. Choose Plot➜ Field again and select Mag E and Surface cutxz. This time, check the box Phase Animation as well. Follow the steps and produce your movie. Increase the speed of the animation on the left-hand side of the window. To stop this, click on Stop or Done. Exit from the software. This concludes this exercise.

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