## 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

## High Frequency Electromagnetic Updates in ANSYS 2019 R2 – Webinar

HFSS (High Frequency Structure Simulator) employs versatile solvers and an intuitive GUI to provide unparalleled performance, as well as deep insight, into a wide variety of 3D electromagnetic (EM) problems. ANSYS HFSS is the premier EM tool for R&D and virtual design prototyping. It reduces design cycle time and boosts your product’s reliability and performance.

The ANSYS HFSS simulation suite consists of a comprehensive set of solvers to address diverse electromagnetic problems, ranging in detail and scale from passive IC components to extremely large-scale EM analyses. Its reliable automatic adaptive mesh refinement allows users to focus on the design instead of spending time determining and creating the best mesh.

Join PADT’s Lead Electromagnetics Engineer Michael Griesi for a look at what new capabilities are available for HFSS users in ANSYS 2019 R2.

This presentation will include updates for the following topics:

• Solve speed
• Electronics Desktop
• ANSYS Cloud
• Post processing
• And much more

Register Here

If this is your first time registering for one of our Bright Talk webinars, simply click the link and fill out the attached form. We promise that the information you provide will only be shared with those promoting the event (PADT).

You will only have to do this once! For all future webinars, you can simply click the link, add the reminder to your calendar and you’re good to go!

## Introducing ANSYS 2019 R1

PADT is excited to announce the release of ANSYS 2019 R1, the first group of updates for the suite of ANSYS simulation software this year. The release features updates for a wide variety of applications, including simulation for fluids, structures, electronics, 3D design, and much more.

We will be hosting a series of live webinars over the course of 2019 that will allow you to learn about what’s new in this release, from PADT’s team of expert support engineers.

Take a look at the following upcoming product update webinars for 2019 R1 and register by clicking the links below.

There is more to come, so stay tuned

Fluent Updates in ANSYS 2019 R1
Wednesday, February 13th – 11:00 am – 12:00 pm MST AZ

Computational Fluid Dynamics (CFD) is a tool with amazing flexibility, accuracy and breadth of application. Serious CFD, the kind that provides insights to help you optimize your designs, could be out of reach unless you choose your software carefully. Experienced engineers need to go further and faster with well-validated CFD results across a wide range of applications, and with ANSYS Fluent users are able to do just that; delivering reliable and accurate results.

Join Padt’s CFD Team Lead Engineer, Clinton Smith for a look at what new capabilities are available for the latest version of Fluent, in ANSYS 2019 R1.

Register Here

Mechanical Updates in ANSYS 2019 R1
Wednesday, March 13th – 11:00 am – 12:00 pm MST AZ

From designers and occasional users looking for quick, easy, and accurate results, to experts looking to model complex materials, large assemblies, and nonlinear behavior, ANSYS Mechanical enables engineers of all levels to get answers fast and with confidence. With applications for everything form strength analysis to topology optimization, it’s no wonder this comprehensive suite of tools continues to serve as the flagship mechanical engineering software solution.

Join PADT’s Simulation Support Manager, Ted Harris for a look at what new capabilities are available for ANSYS Mechanical, in the latest version; 2019 R1.

Register Here

High Frequency Electromagnetics Updates in ANSYS 2019 R1
Wednesday, April 10th – 11:00 am – 12:00 pm MST AZ

In today’s world of high performance electronics and advanced electrification systems, the effects of electromagnetic fields on circuits and systems cannot be ignored. ANSYS software can uniquely simulate electromagnetic performance across component, circuit and system design, evaluating temperature, vibration and other critical mechanical effects.

Join PADT’s Electrical Engineer, Michael Griesi for a look at what new capabilities are available with regards to High Frequency Electromagnetics, in the latest version of ANSYS; 2019 R1

Register Here

Discovery Updates in ANSYS 2019 R1
Wednesday, May 8th – 11:00 am – 12:00 pm MST AZ

The ANSYS 3D Design family of products enables CAD modeling and simulation for all design engineers. Since the demands on today’s design engineer to build optimized, lighter and smarter products are greater than ever, using the appropriate design tools is more important than ever.

Join PADT’s Simulation Support Manager, Ted Harris for a look at what exciting new features are available for design engineers in both Discovery Live and AIM, in ANSYS 2019 R1.

Register Here

If this is your first time registering for one of our Bright Talk webinars, simply click the link and fill out the attached form. We promise that the information you provide will only be shared with those promoting the event (PADT).

You will only have to do this once! For all future webinars, you can simply click the link, add the reminder to your calendar and you’re good to go!

## Parameterizing Solid Models for ANSYS HFSS

ANSYS HFSS features an integrated “history-based modeler”. This means that an object’s final shape is dependent on each and every operation performed on that object. History-based modelers are a perfect choice for analysis since they naturally support parameterization for design exploration and optimization. However, editing imported solid 3D Mechanical CAD (or MCAD) models can sometimes be challenging with a history-based modeler since there are no imported parameters, the order of operation is important, and operational dependencies can sometimes lead to logic errors. Conversely, direct modelers are not bound by previous operations which can offer more freedom to edit geometry in any order without historic logic errors. This makes direct modelers a popular choice for CAD software but, since dependencies are not maintained, they are not typically the natural choice for parametric analysis. If only there was a way to leverage the best of both worlds… Well, with ANSYS, there is a way.

As discussed in a previous blog post, since the release of ANSYS 18.1, ANSYS SpaceClaim Direct Modeler (SCDM) and the MCAD translator used to import geometry from third-party CAD tools are now packaged together. The post also covered a few simple procedures to import and prepare a solid model for electromagnetic analysis. However, this blog post will demonstrate how to define parameters in SCDM, directly link the model in SCDM to HFSS, and drive a parametric sweep from HFSS. This link unites the geometric flexibility of a direct modeler to the parametric flexibility of a history-based modeler.

[1] To begin, open ANSYS SpaceClaim and select File > Open to import the step file.

[2] Split the patch antenna and reference plane from the dielectric. Click here for steps to splitting geometry. Notice the objects can be renamed and colors can be changed under the Display tab.

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[1] Click and hold the center mouse button to rotate the model, zoom into the microstrip feed using the mouse scroll, then select the side of the trace.

[2] Rotate to the other side of the microstrip feed, hold the Ctrl key, and select the other side of the trace. Note the distance between the faces is shown as 3mm in the Status Bar at the bottom of the screen, which is the initial trace width.

[3] Select Design > Edit > Pull and select No merge under Options – Pull.

[4] Click the yellow arrow in the model, and drag the side of the trace. Notice how both faces move in or out to change the trace width. After releasing the mouse, a P will appear next to the measurement box. Click this P to create a parameter.

[5] Select the Groups panel under the Structure tree. Change “Group1” to “traceWidth” and reset the Ruler dimension to 0mm. Then, save the project as UWB_Patch_Antenna_PCB.scdoc and leave SCDM open.

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[1] Open ANSYS Electronics Desktop (AEDT), insert a new HFSS Design, and select the menu item Modeler > SpaceClaim Link > Connect to Active Session… Notice that there is an option to browse and open any SCDM project if the session is not currently active (or open).

[2] Select the active UWB_Patch_Antenna_PCB session and click Connect.

[3] The geometry from SCDM is automatically imported into HFSS.

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[1] Double-click the SpaceClaim1 model in the HFSS modeler tree and select the Parameters tab in the pop-up dialogue box. Notice the SCDM parameter can now be controlled within HFSS. Change the Value of traceWidth to SCDM_traceWidth to create a local variable and set SCDM_traceWidth equal to -1mm. Then click OK. Notice a lightning bolt over the SpaceClaim1 model to indicate changes have been made.

[2] Right-click SpaceClaim1 in the modeler tree and select Send Parameters and Generate.

[3] Notice how the HFSS geometry reflects the changes.

[4] Notice how the SCDM also reflects the changes. In practice, it is generally recommended to browse to unopen SCDM projects (rather than connecting to an active session) to avoid accidentally editing the same geometry in two places.

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At this point, not only can the geometry in SCDM be controlled by variables in HFSS, but a parametric analysis can now be performed on geometry within a direct modeler. The best of both worlds!

Use the typical steps within HFSS to setup a parametric sweep or optimization. When performing a parametric analysis, the geometry will automatically update the link between HFSS and SCDM, so step [2] above does not need to be performed manually. Be sure to follow the typical HFSS setup procedures such as assigning materials, defining ports and boundaries, and creating a solution setup before solving.

1. Create local variables in HFSS that can be used for both local and linked geometry. For example, create a variable in HFSS for traceWidth = 3mm (which was the previously noted width). Define SCDM_traceWidth = (traceWidth-3mm)/2. Now the port width can scale with the trace width.

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1. Link to multiple SCDM projects. Either move and rotate parts as needed or create a separate coordinate system for each component. For example, link an SMA end connector to the same HFSS project to analyze both components. Notice that each component has variables and the substrate thickness changes both SCDM projects.

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1. Design other objects in the native HFSS history-based modeler that are dependent on the SCDM design variables. For example, the void in an enclosure could be a function of SCDM_dielectricHeight. Notice that the enclosure void is dependent on the SCDM dielectric height.

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## Exploring High-Frequency Electromagnetic Theory with ANSYS HFSS

I recently had the opportunity to present an interesting experimental research paper at DesignCon 2017, titled Replacing High-Speed Bottlenecks with PCB Superhighways. The motivation behind the research was to develop a new high-speed signaling system using rectangular waveguides, but the most exciting aspect for me personally was salvaging a (perhaps contentious) 70 year old first-principles electromagnetic model. While it took some time to really understand how to apply the mathematics to design, their application led to an exciting convergence of theory, simulation, and measurement.

One of the most critical aspects of the design was exciting the waveguide with a monopole probe antenna. Many different techniques have been developed to match the antenna impedance to the waveguide impedance at the desired frequency, as well as increase the bandwidth. Yet, all of them rely on assumptions and empirical measurement studies. Optimizing a design to nanometer precision empirically would be difficult at best and even if the answer was found it wouldn’t inherently reveal the physics. To solve this problem, we needed a first-principles model, a simulation tool that could quickly iterate designs accurately, and some measurements to validate the simulation methodology.

A rigorous first-principles model was developed by Robert Collin in 1960, but this solution has since been forgotten and replaced by simplified rules. Unfortunately, these simplified rules are unable to deliver an optimal design or offer any useful insight to the critical parameters. In fairness, Collin’s equations are difficult to implement in design and validating them with measurement would be tedious and expensive. Because of this, empirical measurements have been considered a faster and cheaper alternative. However, we wanted the best of both worlds… we wanted the best design, for the lowest cost, and we wanted the results quickly.

For this study, we used ANSYS HFSS to simulate our designs. Before exploring new designs, we first wanted to validate our simulation methodology by correlating results with available measurements. We were able to demonstrate a strong agreement between Collin’s theory, ANSYS HFSS simulation, and VNA measurement.

To perform a series of parametric studies, we swept thousands of antenna design iterations across a wide frequency range of 50 GHz for structures ranging from 50-100 guide wavelengths long. High-performance computing gave us the ability to solve return loss and insertion loss S-parameters within just a few minutes for each design iteration by distributing across 48 cores.

Finally, we used the lessons we learned from Collin’s equations and the parametric study to develop a new signaling system with probe antenna performance never before demonstrated. You can read the full DesignCon paper here. The outcome also pertains to RF applications in addition to potentially addressing Signal Integrity concerns for future high-speed communication channels.

Rules-of-thumb are important to fast and practical design, but their application can many times be limited. Competitive innovation demands we explore beyond these limitations but the only way to match the speed and accuracy of design rules is to use simulations capable of offering fast design exploration with the same reliability as measurement. ANSYS HFSS gave us the ability to, not only optimize our design, but also teach us about the physics that explain our design and allow us to accurately predict the behavior of new innovative designs.