|Published on:||August 25th, 2021|
|With:||Eric Miller & Aleksandr Gafarov|
In this episode your host and Co-Founder of PADT, Eric Miller is joined by PADT’s application engineer and high frequency electronics expert, Aleksandr Gafarov for a look at what’s new for this product offering in Ansys 2021 R2.
If you have any questions, comments, or would like to suggest a topic for the next episode, shoot us an email at firstname.lastname@example.org we would love to hear from you!
Simulation itself is no longer a new concept in engineering, but individual fields, applications, and physics are continually improved upon and integrated into the toolbox that is an engineer’s arsenal. Many times, these are incremental additions to a particular solver’s capabilities or a more specialized method of post processing, however this can also occasionally be present through new cross-connections between separate tools or even an entirely new piece of software. As a result of all this, Ansys has now reached critical mass for its solution space surrounding Electronics Reliability. That is, we can essentially approach an electronics reliability problem from any major physics perspective that we like.
So, what is Electronics Reliability and what physics am I referring to? Great question, and I’m glad you asked – I’d like to run through some examples of each physics and their typical use-case / importance, as well as where Ansys fits in. Of course, real life is a convoluted Multiphysics problem in most cases, so having the capability to accommodate and link many different physics together is also an important piece of this puzzle.
Running down the list, we should perhaps start with the most obvious category given the name – Electrical Reliability. In a broad sense, this encompasses all things related to electromagnetic fields as they pertain to transmission of both power and signals. While the electrical side of this topic is not typically in my wheelhouse, it is relatively straightforward to understand the basics around a couple key concepts, Power Integrity and Signal Integrity.
Power integrity, as its name suggests, is the idea that we need to maintain certain standards of quality for the electrical power in a device/board/system. While some kinds of electronics are robust enough that they will continue to function even under large variations in supplied voltage or current, there are also many that rely on extremely regular power supplies that only vary above certain limits or within narrow bounds. Even if we’re looking at a single PCB (as in the image below), in today’s technological environment it will no doubt have electrical traces mapped all throughout it as well as multiple devices present that operate under their own specified electrical conditions.
If we were determined to do so, we could certainly measure trace lengths, widths, thicknesses, etc., and make some educated guesses for the resulting voltage drops to individual components. However, considerably more effort would need to be made to account for bends, corners, or variable widths, and that would still completely neglect any environmental effects or potential interactions between traces. It is much better to be able to represent and solve for the entire geometry at once using a dedicated field solver – this is where Ansys SIwave or Ansys HFSS typically come in, giving us the flexibility to accurately determine the electrical reliability, whether we’re talking about AC or DC power sources.
Signal integrity is very much related, except that “signals” in this context often involve different pathways, less energy, and a different set of regulations and tolerances. Common applications involve Chip-signal modeling and DDRx virtual compliance – these have to do with not only the previous general concerns regarding stability and reliability, but also adherence to specific standards (JEDEC) through virtual compliance tests. After all, inductive electromagnetic effects can still occur over nonconductive gaps, and this can be a significant source of noise and instability in cases where conductive paths (like board traces or external connections) cross or run very near each other.
Whether we are looking at timings between components, transition times, jitter, or even just noise, HFSS and SIWave can both play roles here. In either case, being able to use a simulation environment to confirm that a certain design will or will not meet certain standards can provide invaluable feedback to the design process.
Other relevant topics to Electrical Reliability may include Electromagnetic Interference (EMI) analysis, antenna performance, and Electrostatic Discharge (ESD) analysis. While I will not expand on these in great detail here, I think it is enough to realize that an excellent electrical design (such as for an antenna) requires some awareness of the operational environment. For instance, we might want to ensure that our chosen or designed component will adequately function while in the presence of some radiation environment, or maybe we would like to test the effectiveness of the environmental shielding on a region of our board. Maybe, there is some concern about the propagation of an ESD through a PCB, and we would like to see how vulnerable certain components are. Ansys tools provide us the capabilities needed to do all of this.
The second area of primary interest is Thermal Reliability, as just about anyone who has worked with or even used electronics knows, they generate some amount of heat while in use. Of course, the quantity, density, and distribution of that heat can vary tremendously depending on the exact device or system under question, but this heat will ultimately result in a rise in temperature somewhere. The point of thermal reliability basically boils down to realizing that the performance and function of many electrical components depends on their temperature. Whether it is simply a matter of accounting for a change in electrical conductivity as temperature rises or a hard limit of functionality for a particular transistor at 150 °C, acknowledging and accounting for these thermal effects is critical when considering electronics reliability. This is a problem with several potential solutions depending on the scale of interest, but generally we cover the package/chip, board, and full system levels. For the component/chip level, a designer will often want to provide some package level specs for OEMs so that a component can be properly scoped in a larger design. Ansys Icepak has toolkits available to help with this process; whether it is simplifying a 3D package down to a detailed network thermal model or identifying the most critical hot spot within a package based on a particular heat distribution. Typically, network models are generated through temperature measurements taken from a sample in a standardized JEDEC test chamber, but Icepak can assist through automatically generating these test environments, as below, and then using simulation results to extract well defined JB and JC values for the package under test.
On the PCB level of detail, we are likely interested in how heat moves across the entire board from component to component or out to the environment. Ansys Icepak lets us read in a detailed ECAD description for said PCB and process its trace and via definitions into an accurate thermal conductivity map that will improve our simulation accuracy. After all, two boards with identical sizing and different copper trace layouts may conduct heat very differently from each other.
On the system level of thermal reliability, we are likely looking at the effectiveness of a particular cooling solution on our electronic design. Icepak makes it easy to include the effects of a heat exchanger (like a coldplate) without having to explicitly model its computationally expensive geometry by using a flow network model. Also, many of today’s electronics are expected to constantly run right up against their limit and are kept within thermal spec by using software to throttle their input power in conjunction with an existing cooling strategy. We can use Icepak to implement and test these dynamic thermal management algorithms so that we can track and evaluate their performance across a range of environmental conditions.
The next topic that we should consider is that of Mechanical Reliability. Mechanical concepts tend to be a little more intuitive and relatable due to their more hands-on nature than the other two, though the exact details behind the cause and significance of stresses in materials is of course more involved. In the most general sense, stress is a result of applying force to an object. If this stress is high compared to what is allowed by a material, then bad things tend to happen – like permanent deformation or fracture. For electronic devices consisting of many materials, small structures, and particularly delicate components, we have once again surpassed what can be reasonably accomplished with hand calculations. Whether we are looking at an individual package, the integrity of an entire PCB, or the stability that a rigid housing will provide to a set of PCBs, Ansys has a solution. We might use Ansys Mechanical to look at manufacturing allowances for the permissible force used while mounting a complicated leaded component onto a board, as seen below. Or maybe, we will use mechanical simulation to find the optimal positioning of leads on a new package such that its natural vibrational frequencies are outside normal ambient conditions.
At the PCB level, we face many of the same detail-oriented challenges around representing traces and vias that have been mentioned for the electrical applications. They may not be quite as critical and more easily approximated in some ways, but that does not change the fact that copper traces are mechanically quite different from the resin composites often used as the substrate (like FR-4). Ansys tools like Sherlock provide best in class PCB modeling on this front, allowing us to directly bring in ECAD models with full trace and component detail, and then model them mechanically at several different levels depending on the exact need. Automating a materials property averaging scheme based on the local density of traces may be sufficient if we are looking at the general bending behavior of a board, but we can take it to the next level by explicitly modeling traces as “reinforcement” elements. This brings us to the level of detail where we can much more reliably look at the stresses present in individual traces, such that we can make good design decisions to reduce the risk of traces peeling or delaminating from the surface.
Beyond just looking at possible improvements in the design process, we can also make use of Ansys tools like LS-DYNA or Mechanical to replicate testing or accident conditions that an existing design could be subjected to. As a real-world example, many of us are all too familiar with the occasional consequences of accidentally dropping our smart phones – Ansys is used to test designs against these kind of shock events, where impact against a hard surface can result in high stresses in key locations. This helps us understand where to reinforce a design to protect against the worst damage or even what angle of impact is most likely to cause an operational failure.
As the finale for all of this, I come back to the first comment of reality being a complex Multiphysics problem. Many of the previous topics are not truly isolated to their respective physics (as much as we often simplify them as such), and this is one of the big ways in which the Ansys ecosystem shines: Comprehensive Multiphysics. For the topic of thermal reliability, I simply stated that electronics give off heat. This may be obvious, but that heat is not just a magical result of the device being turned on but is instead a physical and calculable result of the actual electrical behavior. Indeed, this the exact kind of result that we can extract from one of the relevant electronics tools. An HFSS solution will provide us with not only the electrical performance of an antenna but also the three-dimensional distribution of heat that is consequently produced. Ansys lets us very easily feed this information into an Icepak simulation, which then has the ability to give us far more accurate results than a typical uniform heat load assumption provides.
If we find that our temperatures are particularly high, we might then decide to bring these results back into HFSS to locally change material properties as a function of temperature to get an even more accurate set of electrical results. It could be that this results in an appreciable shift in our antenna’s frequency, or perhaps the efficiency has decreased, and aspects of the design need to be revisited. These are some of the things that we would likely miss without a comprehensive Multiphysics environment.
On a more mechanical side, the effects on stress and strain from thermal conditions are very well known and understood at this point, but there is no reason we could not use Ansys to bring the electrical alongside this established thermal-mechanical behavior. After all, what is a better representation of the real physics involved than using SIwave or HFSS to model the electrical behavior of a PCB, bringing those result into an Icepak simulation as a heat load to test the performance of a cooling loop or heat sink, and then using at least some of those thermal results to look at stresses through not only a PCB as a whole but also individual traces? Not a whole lot at this moment in time, I would say.
The extension that we can make on these examples, is that they have by and large been representative cases of how an electronics device responds to a particular event or condition and judging its reliability metrics based on that set of results, however many physics might be involved. There is one more piece of the puzzle we have access to that also interweaves itself throughout the Multiphysics domain and that is Reliability Physics. This is mostly relevant to us in electronics reliability for considering how different events, or even just a repetition of the same event, can stack together and accumulate to contribute towards some failure in the future. An easy example of this is a plastic hinge or clip that you might find on any number of inexpensive products – flexing a thin piece of plastic like in these hinges can provide a very convenient method of motion for quite some time, but that hinge will gradually accumulate damage until it inevitably cracks and fails. Every connection within a PCB is susceptible to this same kind of behavior, whether it is the laminations of the PCB itself, the components soldered to the surface, or even the individual leads on a component. If our PCB is mounted on the control board of a bus, satellite, or boat, there will be some vibrations and thermal cycles associated with its life. A single one of these events may be of much smaller magnitude and seemingly negligible compared to something dramatic like a drop test, and yet they can still add up to the point of being significant over a period of months or years.
This is exactly the kind of thing that Ansys Sherlock proves invaluable for: letting us define and track the effect of events that may occur over a PCB’s entire lifecycle. Many of these will revolve around mechanical concepts of fatigue accumulating as a result of material stresses, but it is still important to consider the potential Multiphysics origins of stress. Different simulations will be required for each of mechanical bending during assembly, vibration during transport, and thermal cycling during operation, yet each of these contributes towards the final objective of electronics reliability. Sherlock will bring each of these and more together in a clear description of which components on a board are most likely to fail, how likely they are to fail as a function of time, and which life events are the most impactful.
Really, what all of this comes down to is that when we design and create products, we generally want to make sure that they function in the way that we intend them to. This might be due to a personal pride in our profession or even just the desire to maximize profit through minimizing the costs associated with a component failure, however at the end it just makes sense to anticipate and try to prevent the failures that might occur under normal operating conditions.
For complex problems like electronics devices, there are many physics all intimately tied together in the consideration of overall reliability, but the Ansys ecosystem of tools allows us to approach these problems in a realistic way. Whether we’re looking at the electrical reliability of a circuit or antenna, the thermal performance of a cooling solution or algorithm, or the mechanical resilience of a PCB mounted on a bracket, Ansys provides a path forward.
If you have any questions or would like to learn more, please contact us at email@example.com or visit www.padtinc.com.
|Published on:||February 26th, 2021|
|With:||Eric Miller & Aleksandr Gafarov|
In this episode your host and Co-Founder of PADT, Eric Miller is joined by PADT’s Electronics Application Engineer Aleksandr Gafarov for a look at what’s new in this electromagnetics release.
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.
If you have any questions, comments, or would like to suggest a topic for the next episode, shoot us an email at firstname.lastname@example.org we would love to hear from you!
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:
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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):
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]
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.
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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 (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 .
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-ε∞.
The multiple pole Debye dispersion equation has also been used to characterize dispersive dielectric properties 
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  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 .
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 :
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 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).
This model was developed initially for FR-4, commonly used in printed circuit boards and packages . 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 
Therefore, at the measurement frequency one can separate real and imaginary parts
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 δ1.
The window shown in Fig. 8 is to enter the measurement values.
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 
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.
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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:
A new wave port can be defined by the following steps:
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 email@example.com.
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