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## Efficient and Accurate Simulation of Antenna Arrays in HFSS

### Unit-cell in HFSS

HFSS offers different method of creating and simulating a large array. The explicit method, shown in Figure 1(a) might be the first method that comes to our mind. This is where you create the exact CAD of the array and solve it. While this is the most accurate method of simulating an array, it is computationally extensive. This method may be non-feasible for the initial design of a large array. The use of unit cell (Figure 1(b)) and array theory helps us to start with an estimate of the array performance by a few assumptions. Finite Array Domain Decomposition (or FADDM) takes advantage of unit cell simplicity and creates a full model using the meshing information generated in a unit cell. In this blog we will review the creation of unit cell. In the next blog we will explain how a unit cell can be used to simulate a large array and FADDM.

In a unit cell, the following assumptions are made:

• The pattern of each element is identical.
• The array is uniformly excited in amplitude, but not necessarily in phase.
• Edge affects and mutual coupling are ignored

A unit cell works based on Master/Slave (or Primary/Secondary) boundary around the cell. Master/Slave boundaries are always paired. In a rectangular cell you may use the new Lattice Pair boundary that is introduced in Ansys HFSS 2020R1. These boundaries are means of simulating an infinite array and estimating the performance of a relatively large arrays. The use of unit cell reduces the required RAM and solve time.

Primary/Secondary (Master/Slave) (or P/S) boundaries can be combined with Floquet port, radiation or PML boundary to be used in an infinite array or large array setting, as shown in Figure 3.

To create a unit cell with P/S boundary, first start with a single element with the exact dimensions of the cell. The next step is creating a vacuum or airbox around the cell. For this step, set the padding in the location of P/S boundary to zero. For example, Figure 4 shows a microstrip patch antenna that we intend to create a 2D array based on this model. The array is placed on the XY plane. An air box is created around the unit cell with zero padding in X and Y directions.

You notice that in this example the vacuum box is larger than usual size of quarter wavelength that is usually used in creating a vacuum region around the antenna. We will get to calculation of this size in a bit, for now let’s just assign a value or parameter to it, as it will be determined later. The next step is to define P/S to generate the lattice. In AEDT 2020R1 this boundary is under “Coupled” boundary. There are two methods to create P/S: (1) Lattice Pair, (2) Primary/Secondary boundary.

Lattice Pair

The Lattice Pair works best for square lattices. It automatically assigns the primary and secondary boundaries. To assign a lattice pair boundary select the two sides that are supposed to create infinite periodic cells, right-click->Assign Boundary->Coupled->Lattice Pair, choose a name and enter the scan angles. Note that scan angles can be assigned as parameters. This feature that is introduced in 2020R1 does not require the user to define the UV directions, they are automatically assigned.

### Primary/Secondary

Primary/Secondary boundary is the same as what used to be called Master/Slave boundary. In this case, each Secondary (Slave) boundary should be assigned following a Primary (Master) boundary UV directions. First choose the side of the cell that Primary boundary. Right-click->Assign Boundary->Coupled->Primary. In Primary Boundary window define U vector. Next select the secondary wall, right-click->Assign Boundary->Couple->Secondary, choose the Primary Boundary and define U vector exactly in the same direction as the Primary, add the scan angles (the same as Primary scan angles)

### Floquet Port and Modes Calculator

Floquet port excites and terminates waves propagating down the unit cell. They are similar to waveguide modes. Floquet port is always linked to P/S boundaries. Set of TE and TM modes travel inside the cell. However, keep in mind that the number of modes that are absorbed by the Floquet port are determined by the user. All the other modes are short-circuited back into the model. To assign a Floquet port two major steps should be taken:

Defining Floquet Port

Select the face of the cell that you like to assign the Floquet port. This is determined by the location of P/S boundary. The lattice vectors A and B directions are defined by the direction of lattice (Figure 7).

The number of modes to be included are defined with the help of Modes Calculator. In the Mode Setup tab of the Floquet Port window, choose a high number of modes (e.g. 20) and click on Modes Calculator. The Mode Table Calculator will request your input of Frequency and Scan Angles. After selecting those, a table of modes and their attenuation using dB/length units are created. This is your guide in selecting the height of the unit cell and vaccume box. The attenation multiplied by the height of the unit cell (in the project units, defined in Modeler->Units) should be large enough to make sure the modes are attenuated enough so removing them from the calcuatlion does not cause errors. If the unit cell is too short, then you will see many modes are not attenuated enough. The product of the attenuatin and height of the airbox should be at least 50 dB. After the correct size for the airbox is calcualted and entered, the model with high attenuation can be removed from the Floquet port definition.

The 3D Refinement tab is used to control the inclusion of the modes in the 3D refinement of the mesh. It is recommended not to select them for the antenna arrays.

In our example, Figure 8 shows that the 5th mode has an attenuation of 2.59dB/length. The height of the airbox is around 19.5mm, providing 19.5mm*2.59dB/mm=50.505dB attenuation for the 5th mode. Therefore, only the first 4 modes are kept for the calculations. If the height of the airbox was less than 19.5mm, we would need to increase the height so accordingly for an attenuation of at least 50dB.

A simpler alternative for Floquet port is radiation boundary. It is important to note that the size of the airbox should still be kept around the same size that was calculated for the Floquet port, therefore, higher order modes sufficiently attenuated. In this case the traditional quarter wavelength padding might not be adequate.

Perfectly Matched Layer

Although using radiation boundary is much simpler than Floquet port, it is not accurate for large scan angles. It can be a good alternative to Floquet port only if the beam scanning is limited to small angles. Another alternative to Floquet port is to cover the cell by a layer of PML. This is a good compromise and provides very similar results to Floquet port models. However, the P/S boundary need to surround the PML layer as well, which means a few additional steps are required. Here is how you can do it:

1. Reduce the size of the airbox* slightly, so after adding the PML layer, the unit cell height is the same as the one that was generated using the Modes Calculation. (For example, in our model airbox height was 19mm+substrte thickness, the PML height was 3mm, so we reduced the airbox height to 16mm).
2. Choose the top face and add PML boundary.
3. Select each side of the airbox and create an object from that face (Figure 10).
4. Select each side of the PML and create objects from those faces (Figure 10).
5. Select the two faces that are on the same plane from the faces created from airbox and PML and unite them to create a side wall (Figure 10).
6. Then assign P/S boundary to each pair of walls (Figure 10).

*Please note for this method, an auto-size “region” cannot be used, instead draw a box for air/vacuum box. The region does not let you create the faces you need to combine with PML faces.

The advantage of PML termination over Floquet port is that it is simpler and sometimes faster calculation. The advantage over Radiation Boundary termination is that it provides accurate results for large scan angles. For better accuracy the mesh for the PML region can be defined as length based.

Seed the Mesh

To improve the accuracy of the PML model further, an option is to use length-based mesh. To do this select the PML box, from the project tree in Project Manager window right-click on Mesh->Assign Mesh Operation->On Selection->Length Based. Select a length smaller than lambda/10.

Scanning the Angle

In phased array simulation, we are mostly interested in the performance of the unit cell and array at different scan angles. To add the scanning option, the phase of P/S boundary should be defined by project or design parameters. The parameters can be used to run a parametric sweep, like the one shown in Figure 12. In this example the theta angle is scanned from 0 to 60 degrees.

Comparing PML and Floquet Port with Radiation Boundary

To see the accuracy of the radiation boundary vs. PML and Floquet Port, I ran the simulations for scan angles up to 60 degrees for a single element patch antenna. Figure 13 shows that the accuracy of the Radiation boundary drops after around 15 degrees scanning. However, PML and Floquet port show similar performance.

S Parameters

To compare the accuracy, we can also check the S parameters. Figure 14 shows the comparison of active S at port 1 for PML and Floquet port models. Active S parameters were used since the unit cell antenna has two ports. Figure 15 shows how S parameters compare for the model with the radiation boundary and the one with the Floquet port.

### Conclusion

The unit cell definition and options on terminating the cell were discussed here. Stay tuned. In the next blog we discuss how the unit cell is utilized in modeling antenna arrays.

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## MAPDL – Elements, Contact & Solver Updates in Ansys 2020 R1 – Webinar

The ANSYS finite element solvers enable a breadth and depth of capabilities unmatched by anyone in the world of computer-aided simulation. Thermal, Structural, Acoustic, Piezoelectric, Electrostatic and Circuit Coupled Electromagnetics are just an example of what can be simulated. Regardless of the type of simulation, each model is represented by a powerful scripting language, the ANSYS Parametric Design Language (APDL).

APDL is the foundation for all sophisticated features, many of which are not exposed in the Workbench Mechanical user interface. It also offers many conveniences such as parameterization, macros, branching and looping, and complex math operations. All these benefits are accessible within the ANSYS Mechanical APDL user interface.

Join PADT’s Principle & Co-Owner Eric Miller for a look at what’s new for MAPDL in ANSYS 2020 R1, regarding:

• Linear Dynamics
• Elements
• Contacts
• Post Processing
• Solver Components
• And Much More

Register Here

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## All Things ANSYS 057: Simulation for Additive Manufacturing in ANSYS 2020 R1

 Published on: February 24th, 2020 With: Eric Miller & Doug Oatis Description: In this episode your host and Co-Founder of PADT, Eric Miller is joined by Lead Mechanical Engineer Doug Oatis for a discussion on the latest advancements in simulation for additive manufacturing and topology optimization in ANSYS 2020 R1. If you would like to learn more about what this release is capable of, check out our webinar on the topic here: https://www.brighttalk.com/webcast/15747/384528 If you have any questions, comments, or would like to suggest a topic for the next episode, shoot us an email at podcast@padtinc.com we would love to hear from you! Listen: Subscribe:

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## Introducing the Stratasys J826 – Full-color, multi-material printing for the enterprise design world

Taking risks attempting to capture design intent at the end of the process requires a lot of post-processing (coloring, assemblies, a mix of technologies, etc.) – when its too time consuming, expensive and late to make changes or correct errors. Stratasys PolyJet 3D printing technology is developed to elevate designs by realizing ideas more quickly and more accurately and taking color copies to the next level.

By putting realistic models in a designer’s hands earlier in the process, companies can promote better decisions and a superior final product. Now, with the Stratasys J8 Series, the same is true for prototypes. This tried and tested technology simplifies the entire design process, streamlining workflows so you can spend more time on what matters –creating, refining, and designing the best product possible.

PADT is excited to introduce the new Stratasys J826 3D printer

Based on J850 technology, the J826 supplies the same end-to-end solution for the design process and ultra-realistic simulation at a lower price point.
Better communicate design intent and drive more confident results with prototypes that realistically portray an array of design alternatives.

The Stratasys J826 3D Printer is able to deliver realism, shorter time to market, and streamlined application thanks to a variety of unique attributes that set it apart from most other Polyjet printers:

• High Quality – The J826 can accurately print smaller features at a layer thickness of 14µm to 27µm. As part of the J8 series of printers it is also capable of printing in ultra-realistic Pantone validated colors.
• Speed & Productivity – Three printing speed modes (high speed, high quality & high mix) allows the J826 to always operate at the most efficient speed for each print. It can also avoid unnecessary down-time associate with material changeovers thanks to it’s built-in material cabinet and workstation.
• Easy to Use – A smooth workflow with the J826 comes from simple integration with the CAD format of your choice, as well as a removable tray for easy clean up, and automated support creation and removal.

Are you ready to learn how the new Stratasys J826 provides the same quality and accuracy as other J8 series printers at a lower cost?

Provide the requested information via the form linked below and one of PADT’s additive experts will reach out to share more on what makes this new offering so exciting for the enterprise design world.

Start a Conversation

## Reduce EMI with Good Signal Integrity Habits

Recently the ‘Signal Integrity Journal’ posted their ‘Top 10 Articles’ of 2019. All of the articles included were incredible, however, one stood out to me from the rest – ‘Seven Habits of Successful 2-Layer Board Designers’ by Dr. Eric Bogatin (https://www.signalintegrityjournal.com/blogs/12-fundamentals/post/1207-seven-habits-of-successful-2-layer-board-designers). In this work, Dr. Bogatin and his students were developing a 2-Layer printed circuit board (PCB), while trying to minimize signal and power Integrity issues as much as possible. As a result, they developed a board and described seven ‘golden habits’ for this board development. These are fantastic habits that I’m confident we can all agree with. In particular, there was one habit at which I wanted to take a deeper look:

“…Habit 4: When you need to route a cross-under on the bottom layer, make it short. When you can’t make it short, add a return strap over it..”

Generally speaking, this habit suggests to be very careful with the routing of signal traces over the gap on the ground plane. From the signal integrity point of view, Dr. Bogatin explained it perfectly – “..The signal traces routed above this gap will see a gap in the return path and generate cross talk to other signals also crossing the gap..”. On one hand, crosstalk won’t be a problem if there are no other nets around, so the layout might work just fine in that case. However, crosstalk is not the only risk. Fundamentally, crosstalk is an EMI problem. So, I wanted to explore what happens when this habit is ignored and there are no nearby nets to worry about.

To investigate, I created a simple 2-Layer board with the signal trace, connected to 5V voltage source, going over an air gap. Then I observed the near field and far field results using ANSYS SIwave solution. Here is what I found.

## Near and Far Field Analysis

Typically, near and far fields are characterized by solved E and H fields around the model. This feature in ANSYS SIwave gives the engineer the ability to simulate both E and H fields for near field analysis, and E field for Far Field analysis.

First and foremost, we can see, as expected, that both near and far Field have resonances at the same frequencies. Additionally, we can observe from Figure 1 that both E and H fields for near field have the largest radiation spikes at 786.3 MHz and 2.349GHz resonant frequencies.

Figure 1. Plotted E and H fields for both Near and Far Field solutions

If we plot E and H fields for Near Field, we can see at which physical locations we have the maximum radiation.

Figure 2. Plotted E and H fields for Near field simulations

As expected, we see the maximum radiation occurring over the air gap, where there is no return path for the current. Since we know that current is directly related to electromagnetic fields, we can also compute AC current to better understand the flow of the current over the air gap.

## Compute AC Currents (PSI)

This feature has a very simple setup interface. The user only needs to make sure that the excitation sources are read correctly and that the frequency range is properly indicated. A few minutes after setting up the simulation, we get frequency dependent results for current. We can review the current flow at any simulated frequency point or view the current flow dynamically by animating the plot.

Figure 3. Computed AC currents

As seen in Figure 3, we observe the current being transferred from the energy source, along the transmission line to the open end of the trace. On the ground layer, we see the return current directed back to the source. However at the location of the air gap there is no metal for the return current to flow, therefore, we can see the unwanted concentration of energy along the plane edges. This energy may cause electromagnetic radiation and potential problems with emission.

If we have a very complicated multi-layer board design, it won’t be easy to simulate current flow on near and far fields for the whole board. It is possible, but the engineer will have to have either extra computing time or extra computing power. To address this issue, SIwave has a feature called EMI Scanner, which helps identify problematic areas on the board without running full simulations.

## EMI Scanner

ANSYS EMI Scanner, which is based on geometric rule checks, identifies design issues that might result in electromagnetic interference problems during operation. So, I ran the EMI Scanner to quickly identify areas on the board which may create unwanted EMI effects. It is recommended for engineers, after finding all potentially problematic areas on the board using EMI Scanner, to run more detailed analyses on those areas using other SIwave features or HFSS.

Currently the EMI Scanner contains 17 rules, which are categorized as ‘Signal Reference’, ‘Wiring/Crosstalk’, ‘Decoupling’ and ‘Placement’. For this project, I focused on the ‘Signal Reference’ rules group, to find violations for ‘Net Crossing Split’ and ‘Net Near Edge of Reference’. I will discuss other EMI Scanner rules in more detail in a future blog (so be sure to check back for updates).

Figure 4. Selected rules in EMI Scanner (left) and predicted violations in the project (right)

As expected, the EMI Scanner properly identified 3 violations as highlighted in Figure 4. You can either review or export the report, or we can analyze violations with iQ-Harmony. With this feature, besides generating a user-friendly report with graphical explanations, we are also able to run ‘What-if’ scenarios to see possible results of the geometrical optimization.

Figure 5. Generated report in iQ-Harmony with ‘What-If’ scenario

Based on these results of quick EMI Scanner, the engineer would need to either redesign the board right away or to run more analysis using a more accurate approach.

## Conclusion

In this blog, we were able to successfully run simulations using ANSYS SIwave solution to understand the effect of not following Dr.Bogatin’s advice on routing the signal trace over the gap on a 2-Layer board. We also were able to use 4 different features in SIwave, each of which delivered the correct, expected results.

Overall, it is not easy to think about all possible SI/PI/EMI issues while developing a complex board. In these modern times, engineers don’t need to manufacture a physical board to evaluate EMI problems. A lot of developmental steps can now be performed during simulations, and ANSYS SIwave tool in conjunction with HFSS Solver can help to deliver the right design on the first try.

## Defining Antenna Array Excitations with Nested-If Statements in HFSS

HFSS offers various methods to define array excitations. For a large array, you may take advantage of an option “Load from File” to load the magnitude and phase of each port. However, in many situations you may have specific cases of array excitation. For example, changing amplitude tapering or the phase variations that happens due to frequency change. In this blog we will look at using the “Edit Sources” method to change the magnitude and phase of each excitation. There are cases that might not be easily automated using a parametric sweep. If the array is relatively small and there are not many individual cases to examine you may set up the cases using “array parameters” and “nested-if”.

In the following example, I used nested-if statements to parameterize the excitations of the pre-built example “planar_flare_dipole_array”, which can be found by choosing File->Open Examples->HFSS->Antennas (Fig. 1) so you can follow along. The file was then saved as “planar_flare_dipole_array_if”. Then one project was copied to create two examples (Phase Variations, Amplitude Variations).

Fig. 1. Planar_flare_dipole_array with 5 antenna elements (HFSS pre-built example).

# Phase Variation for Selected Frequencies

In this example, I assumed there were three different frequencies that each had a set of coefficients for the phase shift. Therefore, three array parameters were created. Each array parameter has 5 elements, because the array has 5 excitations:

A1: [0, 0, 0, 0, 0]

A2: [0, 1, 2, 3, 4]

A3: [0, 2, 4, 6, 8]

Then 5 coefficients were created using a nested_if statement. “Freq” is one of built-in HFSS variables that refers to frequency. The simulation was setup for a discrete sweep of 3 frequencies (1.8, 1.9 and 2.0 GHz) (Fig. 2). The coefficients were defined as (Fig. 3):

E1: if(Freq==1.8GHz,A1[0],if(Freq==1.9GHz,A2[0],if(Freq==2.0GHz,A3[0],0)))

E2: if(Freq==1.8GHz,A1[1],if(Freq==1.9GHz,A2[1],if(Freq==2.0GHz,A3[1],0)))

E3: if(Freq==1.8GHz,A1[2],if(Freq==1.9GHz,A2[2],if(Freq==2.0GHz,A3[2],0)))

E4: if(Freq==1.8GHz,A1[3],if(Freq==1.9GHz,A2[3],if(Freq==2.0GHz,A3[3],0)))

E5: if(Freq==1.8GHz,A1[4],if(Freq==1.9GHz,A2[4],if(Freq==2.0GHz,A3[4],0)))

Please note that the last case is the default, so if frequency is none of the three frequencies that were given in the nested-if, the default phase coefficient is chosen (“0” in this case).

Fig. 2. Analysis Setup.

Fig. 3. Parameters definition for phase varaitioin case.

By selecting the menu item HFSS ->Fields->Edit Sources, I defined E1-E5 as coefficients for the phase shift. Note that phase_shift is a variable defined to control the phase, and E1-E5 are meant to be coefficients (Fig. 4):

Fig. 4. Edit sources using the defined variables.

The radiation pattern can now be plotted at each frequency for the phase shifts that were defined (A1 for 1.8 GHz, A2 for 1.9 GHz and A3 for 2.0 GHz) (Figs 5-6):

Fig. 5. Settings for radiation pattern plots.

Fig. 6. Radiation patten for phi=90 degrees and different frequencies, the variation of phase shifts shows how the main beam has shifted for each frequency.

# Amplitude Variation for Selected Cases

In the second example I created three cases that were controlled using the variable “CN”. CN is simply the case number with no units.

The variable definition was similar to the first case. I defined 3 array parameters and 5 coefficients. This time the coefficients were used for the Magnitude. The variable in the nested-if was CN. That means 3 cases and a default case were created. The default coefficient here was chosen as “1” (Figs. 7-8).

A1: [1, 1.5, 2, 1.5, 1]

A2: [1, 1, 1, 1, 1]

A3: [2, 1, 0, 1, 2]

E1: if(CN==1,A1[0],if(CN==2,A2[0],if(CN==3,A3[0],1)))*1W

E2: if(CN==1,A1[1],if(CN==2,A2[1],if(CN==3,A3[1],1)))*1W

E3: if(CN==1,A1[2],if(CN==2,A2[2],if(CN==3,A3[2],1)))*1W

E4: if(CN==1,A1[3],if(CN==2,A2[3],if(CN==3,A3[3],1)))*1W

E5: if(CN==1,A1[4],if(CN==2,A2[4],if(CN==3,A3[4],1)))*1W

Fig. 7. Parameters definition for amplitude varaitioin case.

Fig. 8. Exciation setting for amplitude variation case.

Notice that CN in the parametric definition has the value of “1”. To create the solution for all three cases I used a parametric sweep definition by selecting the menu item Optimetrics->Add->Parametric. In the Add/Edit Sweep I chose the variable “CN”, Start: 1, Stop:3, Step:1. Also, in the Options tab I chose to “Save Fields and Mesh” and “Copy geometrically equivalent meshes”, and “Solve with copied meshes only”. This selection helps not to redo the adaptive meshing as the geometry is not changed (Fig. 9). In plotting the patterns I could now choose the parameter CN and the results of plotting for CN=1, 2, and 3 is shown in Fig. 10. You can see how the tapering of amplitude has affected the side lobe level.

Fig. 9. Parameters definition for amplitude varaitioin case.

Fig. 10. Radiation patten for phi=90 degrees and different cases of amplitude tapering, the variation of amplitude tapering has caused chagne in the beamwidth and side lobe levels.

# Drawback

The drawback of this method is that array parameters are not post-processing variables. This means changing them will create the need to re-run the simulations. Therefore, it is needed that all the possible cases to be defined before running the simulation.

## All Thing ANSYS 050: Updates and Enhancements in ANSYS Mechanical 2019 R3

 Published on: November 4th, 2019 With: Eric Miller, Joe Woodward, & Ted Harris Description: In this episode, your host and Co-Founder of PADT, Eric Miller is joined by PADT’s Specialist Mechanical Engineer/Lead Trainer Joe Woodward, and Simulation Support Manager Ted Harris, for a discussion on what’s new in the mechanical release for ANSYS 2019 R3, as well as a look at their favorite features. This includes a focus on updates and enhancements to improve ease of use, reduce set-up time, and provide more valuable solutions. If you would like to learn more about what this release is capable of, check out our webinar on the topic here: https://www.brighttalk.com/webcast/15747/376304 If you have any questions, comments, or would like to suggest a topic for the next episode, shoot us an email at podcast@padtinc.com we would love to hear from you! Listen: Subscribe:

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## Predicting & Controlling Environmental Pollution with ANSYS Simulation – Webinar

Environmental pollution has been a fact of life for many centuries, though it became a real issue after the start of the industrial revolution. An estimated 6.5 million premature deaths have been linked to air pollution every year.

In order to properly combat this growing issue, the world’s leading minds have turned to a more effective tool for environmental analysis; numerical simulation. Computational fluid dynamics has proven to be a powerful tool when it comes to predicting and controlling air, water, and noise pollution.

Join PADT’s CFD Team Lead Engineer Clinton Smith to learn how ANSYS fluid mechanics solutions provide insight and detailed understanding of the formation and dispersion of pollutants such as NOx, SOx, CO & Soot as well as effective ways for modelling pollution control equipment such as ESP’s, bag filters, and wastewater treatment plants.

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## Frequency Dependent Material Definition in ANSYS HFSS

Electromagnetic models, especially those covering a frequency bandwidth, require a frequency dependent definition of dielectric materials. Material definitions in ANSYS Electronics Desktop can include frequency dependent curves for use in tools such as HFSS and Q3D. However, there are 5 different models to choose from, so you may be asking: What’s the difference?

In this blog, I will cover each of the options in detail. At the end, I will also show how to activate the automatic setting for applying a frequency dependent model that satisfies the Kramers-Kronig conditions for causality and requires a single frequency definition.

# Background

Recalling that the dielectric properties of material are coming from the material’s polarization

where D is the electric flux density, E is the electric field intensity, and P is the polarization vector. The material polarization can be written as the convolution of a general dielectric response (pGDR) and the electric field intensity.

The dielectric polarization spectrum is characterized by three dispersion relaxation regions α, β, and γ for low (Hz), medium (KHz to MHz) and high frequencies (GHz and above). For example, in the case of human tissue, tissue permittivity increases and effective conductivity decreases with the increase in frequency [1].

Each of these regions can be modeled with a relaxation time constant

where τ is the relaxation time.

The well-known Debye expression can be found by use of spectral representation of complex permittivity (ε(ω)) and it is given as:

where ε is the permittivity at frequencies where ωτ>>1, εs is the permittivity at ωτ>>1, and j2=-1. The magnitude of the dispersion is ∆ε = εs.

The multiple pole Debye dispersion equation has also been used to characterize dispersive dielectric properties [2]

In particular, the complexity of the structure and composition of biological materials may cause that each dispersion region be broadened by multiple combinations. In that case a distribution parameter is introduced and the Debye model is modified to what is known as Cole-Cole model

where αn, the distribution parameter, is a measure of broadening of the dispersion.

Gabriel et. al [3] measured a number of human tissues in the range of 10 Hz – 100 GHz at the body temperature (37℃). This data is freely available to the public by IFAC [4].

# Frequency Dependent Material Definition in HFSS and Q3D

In HFSS you can assign conductivity either directly as bulk conductivity, or as a loss tangent. This provides flexibility, but you should only provide the loss once. The solver uses the loss values just as they are entered.

To define a user-defined material choose Tools->Edit Libraries->Materials (Fig. 2). In Edit Libraries window either find your material from the library or choose “Add Material”.

To add frequency dependence information, choose “Set Frequency Dependency” from the “View/Edit Material” window, this will open “Frequency Dependent Material Setup Option” that provides five different ways of defining materials properties (Fig. 3).

Before choosing a method of defining the material please note [5]:

• The Piecewise Linear and Frequency Dependent Data Points models apply to both the electric and magnetic properties of the material. However, they do not guarantee that the material satisfies causality conditions, and so they should only be used for frequency-domain applications.
• The Debye, Multipole Debye and Djordjevic-Sarkar models apply only to the electrical properties of dielectric materials. These models satisfy the Kramers-Kronig conditions for causality, and so are preferred for applications (such as TDR or Full-Wave SPICE) where time-domain results are needed. They also include an automatic Djordjevic-Sarkar model to ensure causal solutions when solving frequency sweeps for simple constant material properties.
• HFSS and Q3D can interpolate the property’s values at the desired frequencies during solution generation.

Piecewise Linear

This option is the simplest way to define frequency dependence. It divides the frequency band into three regions. Therefore, two frequencies are needed as input. Lower Frequency and Upper Frequency, and for each frequency Relative Permittivity, Relative Permeability, Dielectric Loss Tangent, and Magnetic Loss Tangent are entered as the input. Between these corner frequencies, both HFSS and Q3D linearly interpolate the material properties; above and below the corner frequencies, HFSS and Q3D extrapolate the property values as constants (Fig. 4).

Once these values are entered, 4 different data sets are created (\$ds_epsr1, \$ds_mur1, \$ds_tande1, \$ds_tandm1). These data sets now can be edited. To do so choose Project ->Data sets, and choose the data set you like to edit and click Edit (Fig. 5). This data set can be modified with additional points if desired (Fig. 6).

Frequency Dependent

Frequency Dependent material definition is similar to Piecewise Linear method, with one difference. After selecting this option, Enter Frequency Dependent Data Point opens that gives the user the option to use which material property is defined as a dataset, and for each one of them a dataset should be defined. The datasets can be defined ahead of time or on-the-fly. Any number of data points may be entered. There is also the option of importing or editing frequency dependent data sets for each material property (Fig. 7).

Djordjevic-Sarkar

This model was developed initially for FR-4, commonly used in printed circuit boards and packages [6]. In fact, it uses an infinite distribution of poles to model the frequency response, and in particular the nearly constant loss tangent, of these materials.

where ε is the permittivity at very high frequency,  is the conductivity at low (DC) frequency,  j2=-1, ωA is the lower angular frequency (below this frequency permittivity approaches its DC value), ωB is the upper angular frequency (above this frequency permittivity quickly approaches its high-frequency permittivity). The magnitude of the dispersion is ∆ε = εs-ε∞.

Both HFSS and Q3D allow the user to enter the relative permittivity and loss tangent at a single measurement frequency. The relative permittivity and conductivity at DC may optionally be entered. Writing permittivity in the form of complex permittivity [7]

Therefore, at the measurement frequency one can separate real and imaginary parts

where

Therefore, the parameters of Djordjevic-Sarkar can be extracted, if the DC conductivity is known

If DC conductivity is not known, then a heuristic approximation is De = 10 εtan δ1.

The window shown in Fig. 8 is to enter the measurement values.

Debye Model

As explained in the background section single pole Debye model is a good approximation of lossy dispersive dielectric materials within a limited range of frequency. In some materials, up to about a 10 GHz limit, ion and dipole polarization dominate and a single pole Debye model is adequate.

The Debye parameters can be calculated from the two measurements [7]

Both HFSS and Q3D allow you to specify upper and lower measurement frequencies, and the loss tangent and relative permittivity values at these frequencies. You may optionally enter the permittivity at high frequency, the DC conductivity, and a constant relative permeability (Fig. 9).

Multipole Debye Model

For Multipole Debye Model multiple frequency measurements are required. The input window provides entry points for the data of relative permittivity and loss tangent versus frequency. Based on this data the software dynamically generates frequency dependent expressions for relative permittivity and loss tangent through the Multipole Debye Model. The input dialog plots these expressions together with your input data through the linear interpolations (Fig. 10).

## Cole Cole Material Model

The Cole Cole Model is not an option in the material definition, however, it is possible to generate the frequency dependent datasets and use Frequency Dependent option to upload these values. In fact ANSYS Human Body Models are built based on the data from IFAC database and Frequency Dependent option.

## Visualization

Frequency-dependent properties can be plotted in a few different ways. In View/Edit Material dialog right-click and choose View Property vs. Frequency. In addition, the dialogs for each of the frequency dependent material setup options contain plots displaying frequency dependence of the properties.

You can also double-click the material property name to view the plot.

## Automatically use causal materials

As mentioned at the beginning, there is a simple automatic method for applying a frequency dependent model in HFSS. Select the menu item HFSS->Design Setting, and check the box next to Automatically use casual materials under Lossy Dielectrics tab.

This option will automatically apply the Djordjevic-Sarkar model described above to objects with constant material permittivity greater than 1 and dielectric loss tangent greater than 0. Keep in mind, not only is this feature simple to use, but the Djordjevic-Sarkar model satisfies the Kramers-Kronig conditions for causality which is particularly preferred for wideband applications and where time-domain results will also be needed. Please note that if the assigned material is already frequency dependent, automatic creation of frequency dependent lossy materials is ignored.

# References

• D.T. Price, MEMS and electrical impedance spectroscopy (EIS) for non-invasive measurement of cells, in MEMS for Biomedical Applications, 2012, https://www.sciencedirect.com/topics/materials-science/electrical-impedance
• W. D. Hurt, “Multiterm Debye dispersion relations for permittivity of muscle,” IEEE Trans. Biomed. Eng, vol. 32, pp. 60-64, 1985.
• S. Gabriel, R. W. Lau, and C. Gabriel. “The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues.” Physics in Medicine & Biology, vol. 41, no. 11, pp. 2271, 1996.
• Dielectric Properties of Body Tissues in the Frequency Range 10 Hz – 100 GHz, http://niremf.ifac.cnr.it/tissprop/.
• A. R. Djordjevic, R. D. Biljic, V. D. Likar-Smiljani, and T. K. Sarkar, “Wideband frequency-domain characterization of FR-4 and time-domain causality,” IEEE Trans. on Electromagnetic Compatibility, vol. 43, no. 4, p. 662-667, Nov. 2001.

Piecewise Linear Input

Debye Model Input

Multipole Debye Model Input

Djordjevic-Sarkar

Enter Frequency Dependent Data Points

## Topology Optimization & Simulation for Additive Manufacturing in ANSYS 2019 R3 – Webinar

ANSYS offers a complete simulation workflow for additive manufacturing (AM) that allows you to transition your R&D efforts for metal additive manufacturing into a successful manufacturing operation. This best-in-class solution for additive manufacturing enables simulation at every step in your AM process. It will help you optimize material configurations and machine and parts setup before you begin to print. As a result, you’ll greatly reduce — and potentially eliminate — the physical process of trial-and- error testing.

Through the use of ANSYS tools such as Additive Prep, Print, and Science, paired with topology optimization capabilities in ANSYS Mechanical Workbench, the need for physical process of trial-and-error testing has been greatly reduced.

Join PADT’s Simulation Support and Application Engineer Doug Oatis for an exploration of the ANSYS tools that help to optimize additive manufacturing, and what new capabilities are available for them when upgrading to ANSYS 2019 R3. This presentation includes updates regarding:

• Level-set based topology optimization
• The export of build files directly to AM machines
• Switching between viewing STL supports, mesh, or element densities
• Multiple support being made in a single simulation (volume-less & solid supports)
• And much more

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## All Things ANSYS 047: Mechanical Solver, Element, & Contact Enhancements in ANSYS 2019 R3

 Published on: September 24th, 2019 With: Eric Miller, Joe Woodward, Doug Oatis, & Ted Harris Description: In this episode, your host and Co-Founder of PADT, Eric Miller is joined by PADT’s simulation support manager Ted Harris, specialist mechanical engineer Joe Woodward, and simulation support & application engineer Doug Oatis for a discussion on what is new in ANSYS 2019 R3 with regards to the mechanical solver, element, and contact enhancements. If you would like to learn more about what’s new in this latest mechanical release, check out our webinar on the topic here: https://www.brighttalk.com/webcast/15747/371263 If you have any questions, comments, or would like to suggest a topic for the next episode, shoot us an email at podcast@padtinc.com we would love to hear from you! Listen: Subscribe:

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## Mechanical Solver, Element, & Contact Enhancements in ANSYS 2019 R3 – Webinar

ANSYS 2019 R3 brings a whole host of improvements to various mechanical features, designed to enhance overall optimization and ease of use. Key updates such as those made in regards to the mechanical solver, MAPDL elements, and contact modeling capabilities help make this release essential for performing effective analyses, and deriving valuable results from said analyses.

For example, being able to simulate contact correctly means that engineers can simulate the change in load paths when parts deform and confidently predict how assemblies will behave in the real world.

Join PADT’s Simulation Support Manager Ted Harris, for a look at the latest mechanical solver, element, and contact updates available in ANSYS 2019 R3. This presentation includes enhancements made for:

Improved scaling for various solvers

Surface stress evaluation for axisymmetric solid elements

Piezoelectric analyses