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# Tag: EM

## All Things Ansys 082: High Frequency Updates on Ansys 2021 R1

## High Frequency Updates in Ansys 2021 R1 – Webinar

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

# Phase Variation for Selected Frequencies

# Amplitude Variation for Selected Cases

# Drawback

## Frequency Dependent Material Definition in ANSYS HFSS

# Background

# Frequency Dependent Material Definition in HFSS and Q3D

## Cole Cole Material
Model

## Visualization

## Automatically use
causal materials

# References

# Useful Links

## “Equation Based Surface” for Conformal and Non-Planar Antenna Design

## Equation Based Surface

## Application of Equation Based Surface in Conformal and Non-Planar Antennas

## Wave Port Placement using Equation Based Curve

## Effect of Curvature on Antenna Matching

@ANSYS #ANSYS

Whether leveraging improved workflows or leading-edge capabilities with Ansys 2021 R1, teams are tackling design challenges head on, eliminating the need to make costly workflow tradeoffs, developing next-generation innovations with increased speed and significantly enhancing productivity, all in order to deliver high-quality products to market faster than ever.

When it comes to high frequency electromagnetics, Ansys 2021 R1 delivers a plethora of groundbreaking enhancements. Ansys HFSS Mesh Fusion enables simulation of large, never before possible electromagnetic systems with efficiency and scalability. This release also allows for encrypted 3D components supported in HFSS 3D Layout for PCBs, IC packages and IC designs to enable suppliers to share detailed 3D component designs for creating highly accurate simulations.

Join PADT’s Lead Electromagnetics Engineer and high frequency expert Michael Griesi for a presentation on updates made to the Ansys HF suite in the 2021 R1 release, including advancements for:

- Electronics Desktop

- HFSS

- Circuits

- EMIT

- And Much More

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!**

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).*

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.*

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.*

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.

If you would like more information or have any questions please reach out to us at info@padtinc.com.

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.

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 (*p _{GDR}*) 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, ε_{s }is the permittivity at ωτ>>1, and *j ^{2}*=-1. The magnitude of the dispersion is ∆ε = ε

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 α_{n}, 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].

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, *j ^{2}*=-1, ω

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 ε_{∞ }tan δ_{1}.

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).

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.

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.

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.

If you would like more information or have any questions about ANSYS products please email info@padtinc.com

- 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/.
- ANSYS HFSS Online Help, Nov. 2013, Assigning Materials.
- 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. - ANSYS HFSS Online Help, 2019, Materials Technical Notes.

ANYSY HFSS provides many options for creating non-planar and conformal shapes. In MCAD you may use shapes such as cylinders or spheres, and with some steps, you can design you antennas on various surfaces. In some applications, it is necessary to study the effect of curvatures and shapes on the antenna performance. For example for wearable antennas it is important to study the effect of bending, crumpling and air-gap between antenna and human body.

One of the tools that HFSS offers and can be used to do parametric sweep or optimization, is “Draw equation based surface”. This can be accessed under “Draw” “Equation Based Surface” or by using “Draw” tab and choosing it from the banner (Fig. 1)

Once this is selected the Equation Based Surface window that opens gives you options to enter the equation with the two variables (_u, _v_) to define a surface. Each point of the surface can be a function of (_u,_v). The range of (_u, _v) will also be determined in this window. The types of functions that are available can be seen in “Edit Equation” window, by clicking on “…” next to X, Y or Z (Fig. 2). Alternatively, the equation can be typed inside this window. Project or Design Variables can also be used or introduced here.

For example an elliptical cylinder along *y* axis can be represented by:

This equation can be entered as shown in Fig. 3.

Variation of this equation can be obtained by changing variables *R1*, *R2*, *L* and *beta*. Two examples are shown in Fig. 4.

To make use of this function to transfer a planar design to a non-planar design of interest, the following steps can be taken:

- Start with a planar design. Keep in mind that changing the surface shape can change the characteristics of the antenna. It is a good idea to use a parameterized model, to be able to change and optimize the dimensions after transferring the design on a non-planar surface. As an example we started with a planar meandered line antenna that works around 700MHz, as shown in Fig. 5. The model is excited by a wave port. Since the cylindrical surface will be built around y-axis, the model is transferred to a height to allow the substrate surface to be made (Fig 5. b)

- Next, using
equation based surface, create the desired shape and with the same length as
the planar substrate. Make sure that the original deisgn is at a higher
location. Select the non-planar surface. Use
**Modeler->Surface->Thicken Sheet …**and thicken the surface with the substrate thickenss. Alternatively, by choosing “**Draw**” tab, one can expand the**Sheet**dropdown menu and choose**Thicken Sheet**. Now select the sheet, change the material to the substrate material.

- At this point you
are ready to transfer the antenna design to the curved surface. Select both
traces of the antenna and the curved substrate (as shown in Fig. 7). Then use
**Modeler->Surface->Project Sheet…**, this will transfer the traces to the curved surface. Please note that the original substrate is still remaining. You need not delete it.

- Next step is to generate the ground plane and
move the wave port. In our example design we have a partial ground plane. For
ground plane surface we use the same method to generate an equation based
surface. Please keep in mind that the Z coordinate of this surface should be
the same as substrate minus the thickness of the substrate. (If you thickened
the substrate surface to both sides, this should be the height of substrate
minus half of the substrate thickness). Once this sheet is generate assign a
Perfect E or Finite Conductivity Boundary (by selecting the surface, right
click and
**Assign Boundary**). Delete the old planar ground plane.

A new wave port can be defined by the following steps:

- Delete the old port.
- Use
**Draw->Equation Based Curve.**Mimicking the equation used for ground plane (Fig. 9).

- Select the line from the Model tree, select
**Draw->Sweep->Along Vector**. Draw a vector in the direction of port height. Then by selecting the*SweepAlongVector*from Model tree and double clicking, the window allows you to set the correct size of port height and vector start point (Fig. 10). - Assign wave port to this new surface.

Similar method can be used to generate (sin)^n or (cos)^n surfaces. Some examples are shown in Fig. 11. Fig. 11 (a) shows how the surface was defined.

Bending a substrate can change the transmission line and antenna impedance. By using equation based port the change in transmission line impedance effect is removed. However, the overall radiation surface is also changed that will have effects on S11. The results of S11 for the planar design, cylindrical design (Fig. 8), cos (Fig. 11 b), and cos^3 (Fig. 11 c) designs are shown in Fig. 12. If it is of interest to include the change in the transmission line impedance, the port should be kept in a rectangular shape.

Equation based curves and surfaces can take a bit of time to get used to but with a little practice these methods can really open the door to some sophisticated geometry. It is also interesting to see how much the geometry can impact a simple antenna design, especially with today’s growing popularity in flex circuitry. Be sure to check out this related webinar that touches on the impact of packaging antennas as well. If you would like more information on how these tools may be able to help you and your design, please let us know at info@padtinc.com.

You can also click here to download a copy of this example.

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