Ansoft HFSS Advanced Training Exercise Antenna Post ProcessingThis exercise assumes that you already have some experience with Ansoft HFSS. Therefore, not every button click will be described in detail. 1. Introduction In this exercise, we will concentrate on antenna post processing. Specifically, we will have a look at axial ratio and polarization ratio, and get familiar with the calculator. The very simple model we are going to build has two important advantages. First, due to its simplicity we will spend little time drawing and setting up the model. Further, once it’s solved, we will be able to create any linearly, circularly and elliptically polarized wave by playing with the amplitudes and phases of the two modes in the port, and we will have a good feeling for the kind of results we can expect. Fig. 1 Square waveguide radiating into air The model we are going to build is presented in figure 1. It is a square open-ended waveguide radiating into air in the z direction. The port is at the bottom of the waveguide. We will solve for two modes, one with the electric field polarized in the x direction and one with the electric field polarized in the y direction. Then. First. Create a box with its base point in (-10. One doesn’t want those non-propagating higher-order modes to reach the port and decrease the accuracy. select the waveguide (Edit/Select or SEL icon). Exit from the Draw menu. 20. The outer faces of the airbox. This will be the waveguide. Draw the model Choose millimeters as the unit of length. and return to the Executive Commands window. which is usually a distance at which non-propagating higher-order modes that may be generated in the aperture will have died out. About the choices we made here: we intend to run this model at 10 GHz. 0) and a size of (20. Save. This completes the drawing process. -10. Exit from the Setup Materials menu. At that frequency. Save. This will be the air into which the open-ended waveguide radiates. Third. When prompted. Name it airbox. Edit/Duplicate the waveguide in order to have a copy that can be used (and be lost) in the subtraction process. The resulting model looks like what you had before. where we will apply a radiation boundary. Setup Materials Assign air to both the waveguide and the airbox. To get rid of the overlap. Name it waveguide.2. but now the airbox has a hole in it that is exactly large enough for the waveguide to stick into. choose Solid/Subtract. are all at least a quarter-wavelength away from the aperture of the waveguide. A good estimate of the safe-distance of the port involves the propagation constant of the higher-order modes. then select the copy of the waveguide and click OK. We’re not getting into that here. . The port is a third of a wavelength away from the aperture. 19). click OK. select the airbox first. and return to the Executive Commands window. The top face of the airbox is even 40% of a wavelength away. the free-space wavelength is 30 mm. 3) and a size of (36. 10). Create another box with its base point in (-18. -18. At this point. the waveguide needs to be subtracted from the airbox. 36. we have two objects that are partially overlapping. 3. from voltage and power. You have now defined an impedance line. 4. Click Assign. Back at the impedance line.4. Click Assign to complete the definition of Port 1. let’s define a calibration line. It makes sure that mode 1 is polarized the way we want it: along the lines we just defined.1 Setup Boundaries and Sources Port Definition We start with the port. . check the box under Polarize E Field. When you see the correct vector. An illustration is provided in figure 2. Try to snap to the center of one appropriate edge. Impedance can be calculated from voltage and current.g. An impedance line is used by HFSS to compute a voltage in the port. Rotate the picture of the model (CTRL key in combination with the left mouse button) to view the model from the bottom. e. Change “Graphical Pick” to “Object” (left part of window) and select the airbox by clicking it with the mouse.2 Boundary Conditions We want to assign a radiation boundary to the outer surfaces of the airbox. Choose Edit Line / Copy Impedance. Then try to snap to the point on the opposite edge. When you get the correct ones. Let’s define an impedance line. Don’t click the Assign button yet. Enter 2 for the number of modes. Check the box in front of Use Calibration Line. 4. Make sure “Boundary” and “Radiation” are selected and give the new boundary a name. this time along the y axis. If you have to try it more than once. click Enter under Vector Length. Without an impedance line. In the upper-left part of the window. A calibration lines removes a potential 180-degree phase ambiguity by telling the software how the E field is directed at phase zero. Next. OK to confirm. below the coordinates. check the box Use Impedance Line. click Edit Line / Set. only power and current are available. and from power and current. We want a line along the x axis from one edge center to the opposite edge center. don’t click too fast. Make sure Source and Port are selected. which is needed in two of the three impedance definitions. Finally. Set polarization and impedance lines for mode 2 as well. change the snap-to mode to other only (not vertex and not grid) and pick edge center from the options that pop up. Select the bottom face of the waveguide. abc for absorbing boundary condition. With mode 1 highlighted. Keep an eye on the coordinates that are selected (upper left). This is an important step in this model. click the Enter button below Set Impedance Start. Give the new boundary a name. e. aperture. we want to make the walls of the waveguide perfectly conducting. . We will overwrite that with Perfect_H / Natural. Choose Model / Boundary Display to check the port and the boundaries. since we are assigning boundaries in the correct order. e. A warning pops up because part of the waveguide is “port” already. “walls”. with “Graphical Pick / Object” still selected. Close the Boundary Display and File / Exit the 3D Boundary / Source Manager.g. At this moment. Click Assign. select the appropriate face through the menu. A port won’t be overwritten. That’s fine.Fig. with impedance and calibration lines. The quickest way to do that. Make sure “Boundary” and “Perfect_E” are selected. the aperture of the waveguide has a Perfect_E boundary condition as well. For a change. Click Edit / Select / By Name. 2 Setting up port 1 with two modes. select it and click Done. Find out what the correct face is. Click Assign. make sure “Face” is checked and select the object “waveguide”. is to select the entire waveguide object with the mouse. Make sure “Boundary” and “Perfect_H / Natural” are selected and give the new boundary a name. When you’re satisfied. and with the polarization fixed along those lines. Save your work. In the next window.g. A warning pops up. We’re okay here. Next. The Mesh3D window comes up. 20% tet refinement. one is likely to end up with linear combinations of these degenerate modes. In the Setup Solution Menu. on the left-hand side.000 (just some large number to make sure that our refinement value will be reached). select Port1 by clicking on it in the list. Back in the Initial Mesh Refinement window. select a frequency of 10 GHz. select the airbox and choose Seed / Object Face / By Length. It represents the E fields of mode 1. Make sure the Sweep box is unchecked. Since the far field is computed from an integration over the radiation boundary. and a Delta S of 0. In the next window that comes up. Click OK and choose File / Exit and Save changes. Click on Matrix (top of HFSS Executive Commands window). Now it’s time to setup the solution parameters for the full 3D field simulation. Once the solution process is complete. It allows you to check the modes in the port before doing the time-consuming 3D field solution. “Ports Only” should not be checked. In order to seed mesh points on the radiation surface. Do this by using the Ctrl key. Request 3 adaptive passes. check “Ports Only”. However. Under “Solve”. The default ports field accuracy of 2% is adequate. check “All” under “Solve”.002. The “3D Boundary / Source Manager” window comes up. Notice the arrow plot that shows up right away. except for a difference caused by discretization. The “Ports Only” solution is very useful. probably in less than a minute. see the top of figure 3. make sure “All Modes” has been selected. File / Exit from the Boundary / Source Manager. That allows you to inspect port impedances and propagation constants as well for the two modes. In the Setup Solution menu. The starting mesh will be the initial mesh. enter a maximum element length of 5 mm and make the maximum number of elements to be added 10. you get the arrow plot for mode 2. The starting mesh will be the initial mesh. Check the Single Frequency box and uncheck the Adaptive box. Setup Solution We will first perform a quick “Ports Only” solution to check the modes in the port. see the bottom of figure 3. Note that the propagation constants are equal. It is important to be aware of that. that will give us more far-field accuracy. click on Define Seed Operations. under Mesh Options select Initial Mesh once more. zoom in on the port. the Shift key and the left mouse button simultaneously. Accept the defaults in the rest of the window and click OK. make sure that both “Lambda Refinement” and “Seed Based Refinement” are checked and click OK. . There are limited plot options under the button “Port Fields”. In that window. If one doesn’t set a polarization line. Then. click on Setup Executive Parameters / Port Impedances. In the next window. we want to have extra mesh points on the faces of the airbox (the radiation boundary) with a spacing of one-sixth of a wavelength.5. By selecting mode 2 from the port setup info below the plot. This means that modes 1 and 2 are degenerate modes. There. Check “Single Frequency” and check “Adaptive”. Under “Port Solution”. Select a frequency of 10 GHz. use Shift+mouse to shift and Ctrl+mouse to rotate as well. Click OK and hit the Solve button. If necessary. Delta S needs to be small here since S11 itself will be small. Make sure “Sweep” is NOT checked. After that. 3 Two of the windows related to the seeding process 6.Fig. Solve Click Solve. one can easily be too aggressive with that! The third meshing process is wave length seeding. then applies the seeding.25√3 times the free- . click on Profile (upper left) to keep track of the processes. Notice that HFSS first makes the initial mesh. Obviously. which is a volumetric refinement based on the free-space wavelength. The seeding adds a large number of tetrahedra. It makes sure no tetrahedron is larger than 0. The menu allows you to modify powers and phases. don’t change anything. select a deembedding distance of 7 mm Into Object. Note the red arrow in the picture when you Set Distance. The total solution time is about 12 minutes on a 266 MHz PC with two processors. 4). Make sure D_1 is highlighted and select Compute / Z matrix. This brings the reference plane from the port to the aperture. Make a note of the input impedance Z of this antenna (close to 700 Ohm). By default. Make sure the last adaptive pass in the list A_1. 8. 7. click on Matrix to check results and on Convergence to check convergence.1 Post Process / Fields Linear polarization In the Main Menu. There. If you would have performed a fast frequency sweep. Port1:Mode2 is not excited. Then. in this menu you could modify the frequency as well. select Post Process / Fields to enter the Fields Post Processor. A_3. A_2. let’s deembed first. Click OK if you’re satisfied. The Edit Source Values window comes up (fig. This brings you back to the Matrix Data menu. Make a note of the port impedance Zpi (close to 625 Ohm). In the Matrix Data menu. under “View”. make sure Z-matrix is selected under “View” in the right-hand part of the window. In this particular exercise. In the new menu that comes up. a very important menu option is Data / Edit Sources. Click Cancel. Select Post Process / Matrix Data. This leaves you with the default excitation. Select Compute / Deembed. They should be very close. Post Process / Matrix Data Before we start with fields post processing. . we want to obtain the input impedance of this antenna. Then compute (Zpi-Z)/(Zpi+Z) and compare it with S11 of D_1. Next.… is highlighted.space wavelength. For now. 8. Select File / Exit to leave the Matrix Data Post Processor. select Port Zo. Port1:Mode1 is excited with 1 Watt average power and the field in the port has phase zero. The wave length seeding doesn’t add many tetrahedra in this particular case. Note that there is an extra item in the list: D_1 which is the deembedded S matrix of the last adaptive pass. Accept the default that pops up by clicking OK. Select it now. HFSS does some mesh refinement in and near the port before it really starts on the adaptive passes. During the adaptive passes. The accepted power is 1-|S11|2 . never mind that the cross pol you get is not symmetrical – you’re looking at numerical noise. directivity for the phi component at phi=0 (cross-pol). Therefore. It should be equal to the accepted power minus the internal losses (dielectric.g.Fig. 4 Data / Edit Sources allows you to modify the excitations Compute a far-field pattern by selecting Radiation / Compute / Far Field. a symmetrical antenna. there should be no cross polarization. in absolute values and in dB. Once the far field has been calculated. choose phi from 0 to 90 degrees in one step and theta from -180 to 180 degrees in 90 steps. Plot some directivity and gain patterns. and get rid of plots by selecting Window / Close (multiple times if needed). This gives you a full circle in the xz plane (phi=0) and a full circle in the yz plane (phi=90). directivity for the theta component at phi=0 (co-pol). In the Compute Far Field window that pops up. the Plot Far Field window comes up. possibly magnetic . make a normalized directivity plot in dB of the theta and phi components together – this will show you the level of cross pol relative to the main beam. You can bring the plot menu back every time you want it by selecting Plot / Far Field. 2D cartesian and 3D polar plots. you can choose between 2D polar. e. The radiated power is computed by integrating the Poynting vector over the radiation boundary. conductive. Interesting data here are Accepted Power and Radiated Power. Also. Try different polarization options. Wait with 3D polar until the next section. Notice that on the right-hand side of the Plot Far Field window. In this particular case. Select Radiation / Display Data / Far Fields. which should be 100% for a lossless antenna. The Beam Area that is reported in the same list is NOT a 3-dB beamwidth. Therefore.losses). since it approaches zero.φ) contains an integration of fields over the radiation boundary. but is nothing more than Radiated Power divided by maxU. the radiated power should equal the accepted power. Fig. where F(k.θ. the electric field E approaches E = exp(ik•r) F(k. The radiation efficiency. In calculating far-field quantities like directivity. is 99. is the maximum power density per unit solid angle. Click OK to leave this data display. 5 Far-field parameters . etc.φ) / r . This is because the radiation boundary condition is an approximation.θ. The quantity on the bottom. using the electric field itself is not practical.7% in this case. Since this antenna has no internal losses. As the distance r from the antenna to the point of observation approaches infinity. and because the tetrahedra are not infinitesimally small. maxU(theta. phi). gain. Notice that there is an inaccuracy of less than a percent. HFSS uses rE as the basis for the calculation of the other far-field quantities.. 8. but some edge effects will not be included. Highlight it and click OK (fig. It reminds us. Fig. Next. 6 Select Faces List window in the custom surface selection for far-field computation Read the warning that shows up.2 Integration over a user-defined surface In the previous section. Click OK. Now that “aperture” has been selected as integration surface. That is the default and is usually the right thing to do. we will calculate the far field by integrating over the aperture of the antenna. Give it the name “aperture”. while the radiation boundary itself still has to be at a sufficient distance from the antenna. in order to obtain more accuracy for waves striking the boundary under a very oblique angle. You can define any surface to this aim. request phi from 0 to 180 degrees in 12 steps. click OK in the Compute Far Field window. HFSS also offers the possibility to compute the far field by integrating over a user-defined surface. This can be useful in cases where. Theta should go full circle as before. select the object “waveguide” and select the proper face (trial and error) that represents the aperture. First. Check the box for “Custom Surface” and click Set. Hence. In this case. the far field was computed from an integration over the radiation boundary. among other things. The faces list “aperture” that you just defined should be in the list. we can go ahead with it. 6). The “Select Faces List” window pops up. This will give you a far field which is not too different from what you had before. . you have replaced (part of) the radiation boundary by a Perfectly Matched Layer. in this case you lose accuracy. and you want to include those surfaces in the far-field calculation. In this exercise. that this integration surface is not quite right. Still. select Radiation / Compute / Far Field. It is part of this exercise just to show you the technique. since it doesn’t really surround the source. It can also be useful when you expect more accuracy when your integration surface is closer to the antenna. Select Geometry / Create / Faces List. define a faces list that contains the aperture. Zoom in a bit on the aperture if you like. Name the cutplane cutz10.0. Enter (0. You stop here at 345 since 360 would be equal to 0 again. Click OK.1 Create elliptical polarization To create an elliptically polarized wave.3 Directivity and Gain Now that we have changed the excitation of the antenna. Highlight Port1:Mode2.1 Watt and it’s phase 90 degrees. choose Start 0. and click OK. select Plot Quantity Vector_E. display directivity and gain patterns. the Plot Variable window. and click on Normal:Set. let’s have a look at the fields. Increase the speed of it if you like (left-hand side of window). On Geometry cutz10.Once the computation has been done. Now click OK. Try a 3D polar plot of gain or directivity! You can rotate the 3D plot by pressing the CTRL button and dragging the left mouse button. Click OK. Make the size 5 and the spacing 4. Request phi start=0. Click Set followed by OK. stop=180. make sure that the box for “Map Size” is checked. Create a cutplane in the aperture. Select Plot / Field. In the next little window.11) in the coordinate boxes upper left. e. 8.3. Make sure “custom surface” is UNchecked. (If you would have forgotten essential coordinates.10) and click on Origin:Set.g. stop=90. You will see a nice representation of the elliptical polarization with rotating vectors. Click OK. we need to recompute the far field. Vectors closer to the edges have different ratios since every edge attenuates the electric field tangential to it. 8. In the picture of the model. 8. Leave Port1:Mode1 at 1 Watt zero phase. 1 step. Don’t hit OK yet. theta start=-180. enter coordinates (0.3 Elliptical polarization 8. In the Vector Surface Plot window that comes up next. In the left-hand part of the window.3.2 Create a vector plot on a cut plane First.3. Select Geometry / Create / Cutplane. double-click near the center of top edge of the window (but still inside the picture) while holding down the CTRL key. 90 steps.0. This should produce a top view of the model. Select Radiation / Clear and Radiation / Compute / Far Field. select Data / Edit Sources. . Make it’s magnitude (power) 0. check the box for Phase Animation. In the Create Plot window. you can do the same things as in the previous section. We’ll make a vector plot of the fields in the aperture. Stop 345. Notice that the vector in the middle of the aperture has the polarization ratio you would expect of about 3:1 (√10:1). Delta 15 (degrees). you could get them easily by clicking with the cursor on vertices and looking at the coordinates in the upper-left part of the window). Click Done when you’ve seen enough. Notice the 10 dB difference in the main beam. there is a 10 dB difference between the levels in the main beam.A plot of Directivity or Gain for the Total field shows you that they haven’t changed in the direction of boresight (straight up). The antenna transmits elliptical polarization. respectively. . Phi and theta components of the field in the phi=0 and phi=90 degrees planes show the expected 10 dB difference between the two components in the main beam. as expected. Use the right mouse button to get rid of the marker. 7 Cartesian Gain plot in dB. Otherwise you couldn’t get a gain that stays below zero dB for all angles for a lossless antenna. Use Plot / Show Coordinates or the marker icon to measure coordinates. These directivities and gains represent what you would measure if you performed the experiment with a receiving antenna that receives only phi or only theta polarization. These are the results you would obtain in measurements if your receiving antenna only receives x or y polarization. You can also modify the scale etc. Fig. You can also plot Directivity or Gain for the x and y components of the field. Use Plot / Far Field to produce plots of Directivity or Gain for the phi and theta components of the field in the phi=0 and phi=90 degrees planes. Again. Note that the total radiated power is still factored in. under Plot in the menu. the field vectors have a ratio of √10 :1 . In the main beam. These are the results you would obtain in measurements if your receiving antenna only receives lefthand circular or right-hand circular polarization. which equals 10 dB.4 Axial ratio Select Plot / Far Field and plot the Axial Ratio in dB. 8 Axial ratio in dB. like the one we saw before when we did the animated vector plot. of the ellipse that is traced by the electric field vector.7 dB. we have very little power and we can get almost any axial ratio. Use Window / Close if needed to get rid of some far-field plots. 8. This value will be explained in a later section. plot Directivity or Gain for the LHCP and RHCP polarizations.3. respectively.Finally. Use the marker to measure the difference between the two patterns in the main beam. In directions “far out”. Note that this difference is about 5. You will get a plot similar to the one in figure 8. The antenna transmits elliptical polarization. The axial ratio is the ratio between the long axis and the short axis Fig. . 9 Polarization ratio. respectively. They are based on Ludwig’s third definition of polarization ratio.5 Polarization ratio Next. Fig. What do these quantities Ludwig3/X and Ludwig3/Y tell us? Ludwig3/X provides the ratio of co-polarized to cross-polarized fields for an antenna that radiates predominantly in the x direction.8.ϕ) will define copolarized and cross-polarized field strengths by . these values would have been √10 and 1/√10 .3. an observer in the far field at spherical coordinates (θ. and Ludwig3/Y is close to –10 dB for both phi=0 and phi=90. Select Plot / Far Field. select “Polarization Ratio” and Ludwig3/X and Ludwig3/Y (magnitude) for phi=0 and phi=90. If you had chosen not to plot in dB. Ludwig3/Y provides the ratio of co-polarized to cross-polarized fields for an antenna that radiates predominantly in the y direction. This results in four graphs in one plot (figure 9). Make sure dB is checked. let’s look at some polarization ratios. For an antenna that transmits x-polarized fields in the z direction. In the Plot Far Field window. since these are field quantities. Ludwig 3/X and Ludwig 3/Y for elliptical polarization Ludwig3/X is close to 10 dB in the main beam for both phi=0 and phi=90. e. In the Plot Far Field window.x) = Eθsinϕ + Eϕcosϕ . In the case that we’re looking at now.y). HFSS decomposes the elliptical polarization you have in a fraction left-hand circular polarization (LHCP) and a fraction right-hand circular polarization (RHCP). You can verify these equations yourself very easily for ϕ=0 and ϕ=90 degrees. +10 dB and –10 dB. This results in LHCP=2. Spherical/Phi is close to 10 dB in the main beam for phi=90. The other two are close to –10 dB in the main beam. For Sperical/Phi it is |Eϕ/Eθ|. it becomes harder to do. Ludwig3/X is defined as the absolute value of E(co-pol. and we are observing the far field in one of the principal pattern cuts φ=0 or φ=90 degrees.Eϕsinϕ .g. corresponding to polarization ratios of slightly less than 2 and slightly more than 0. Note that Ludwig3/X and Ludwig3/Y are always each other’s opposite when you plot in dB. That explains the values for Ludwig3/X and Ludwig3/Y that we observe in the main beam.5. select “Polarization Ratio” and “Circular/LHCP” and “Circular/RHCP” (magnitude) for phi=0 and phi=90. plot in dB. They are each other’s inverse when you don’t plot in dB. We have to take sines and cosines of θ and φ into account. Now where is our familiar 10 dB level in the main beam? We see levels of ±5. You would use the first one for a predominantly phi-polarized antenna and the second one for a predominantly theta-polarized antenna. For an antenna that transmits y-polarized fields in the z direction. for Spherical/Theta it is |Eθ/Eϕ|.08 and RHCP=1. These values would be √10 and 1/√10 if we wouldn’t plot in dB.g.Eϕsinϕ E(cross-pol. In the Plot Far Field Window. Select Plot / Far Field. By following his equations. not actual field strengths. √10 and 1/√10. .E(co-pol. plot in dB.x). What you see in the plots are the ratios |LHCP/RHCP| and |RHCP/LHCP|.x) = Eθcosϕ .7 dB. since √10 : 1 is the ratio of long axis to short axis in the ellipse.x)/E(cross-pol. Again. You can find the relative fractions by solving LHCP+RHCP = √10 LHCP-RHCP = 1. e. What is happening here is the following. Ludwig3/Y is defined as the absolute value of E(co-pol.y) = Eθcosϕ . we can figure out easily what is co-pol and what is cross-pol.y) = Eθsinϕ + Eϕcosϕ E(cross-pol. These are just relative numbers. For arbitrary directions however. Ludwig has done this for us.ϕ) will define co-polarized and cross-polarized field strengths by E(co-pol. In plain English: if we have an antenna that radiates predominantly in the x or y direction.08 (at boresight). This results in four graphs in one plot. in the main beam |Ex|=√10|Ey|. select “Polarization Ratio” and Spherical/Phi and Spherical/Theta (magnitude) for phi=0 and phi=90.y)/E(cross-pol. an observer in the far field at spherical coordinates (θ. This results in four graphs in one plot. we are looking at ratios of co-polarized to cross-polarized fields. Spherical/Theta for phi=0 is also close to 10 dB in the main beam. we can find co-pol and cross-pol and their ratios in any direction. Select Plot / Far Field. these are co-pol to cross-pol ratios. Fig. If you like. in this case for predominantly left-hand circularly and predominantly right-hand circularly polarized antennas.4 Calculator Finally. As an example. At this point. 8. use Plot / Visibility or even Plot / Delete. most far-field post-processing options. 10 Polarization Ratios. left-hand / right-hand and right-hand / left-hand circular for the case of an elliptically polarized antenna. use Data / Edit Sources to try more polarizations. Select Data / Calculator. like Plot / Mesh and View / Boundary Display. and instead of the software-supplied Poynting vector we’ll use the cross product of E and H explicitly. let’s have a look at the calculator. Explore other menu options as well. we’ll calculate the power flow through the top face of the airbox alone. Click Clear to get rid of any data that may be present in the stack. we have explored. respectively. . The field calculator comes up (figure 11).Again. To make a mesh plot invisible. and hopefully understood. . independent of the phase.Fig. Load the magnetic field vector by selecting Qty / H under “Input”. Select Num / Scalar under “Input” and select 0. 11 The Field Calculator Load the electric field vector by selecting Qty / E under “Input”. Select Cmplx / Conj under “General”.5 E×Hconjugate . This operation immediately takes the complex conjugate of the quantity that is on top in the stack. The complex vector <Hx. The complex vector <Ex.Ez> pops up in the stack. but HFSS still treats it as complex. Select Cmplx / At Phase under “General” to get the real vector E×Hconj at phase zero. We can make it real by evaluating it at an arbitrary phase. Click on Cross under “Vector” to obtain E×Hconj .Hy. Click OK. the next step is to take the complex conjugate of H.Hz> pops up in the stack. We know that E×Hconj is a real vector.Ey. Since the time-averaged Poynting vector is defined as 0. What we need is the integration surface. Click OK. so we need to define it. In the field calculator. This concludes this exercise on antenna post processing. In the Field Post Processor. Click “Cancel”. Click on Geom / Surface under “Input”. Enter “topface” as the new name. and select the top face of the airbox by trial and error. and File / Exit to exit the field post processor. Select “topface” and click OK. Click on the integration symbol ∫ under “Scalar” to integrate over the surface.Select Num / Scalar under “Input” and enter 0. The top of the airbox isn’t there yet. The quantity in the stack is now a scalar. the cutplanes and surfaces lists you defined earlier. the radiation surface (=abc surface). Select Normal under “Vector” to obtain the dot product of the vector and the normal to the surface. We now have the quantity we want to integrate. and the principal coordinate planes. click on Eval under “Output”. select Geom / Surface under “Input”. select the object “airbox”. Select * under “General” to multiply E×Hconj by 0.5. select Geometry / Create / Faces List. Click OK. Finally. . Click Done to exit the field calculator. The resulting number tells you how much power flows through the top face of the airbox. We now have a surface and a real vector in the stack. Note that the list already contains the surfaces of the objects.5.