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

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.

Equation Based Surface

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)

Fig. 1. (a) Select Draw -> Equation Based Surface
Fig. 1. (b) click on the icon that is highlighted

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.

Fig. 2. (a) Equation Based Surface window
Fig. 2. (b) Clikc on the “…” next to X and see the “Edit Equation: window to build the equation for X

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

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

Fig. 3. Elliptical surface equation

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

Fig. 4. Elliptical surface equation

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

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)
Fig. 5. Planar meandered antenna (a) on xy plane, (b) moved to a height of 5cm
  • 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.
Fig. 6. Thicken the equation based surface to generate the substrate
  • 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.
Fig. 7. Steps for transferring the design to the curved surface (a)

Fig. 7. Steps for transferring the design to the curved surface (b)

Fig. 7. Steps for transferring the design to the curved surface (c)
  • 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.
Fig. 8. Non-planar meandered antenna with non-planar ground

Wave Port Placement using Equation Based Curve

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).
Fig. 9. Use Equation Based Curve to start a new wave port (a) Equation Based Curve definition window (b) wave pot terminal created using equation based curve and sweep along vector
  • 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.
Fig. 10. Sweep along vector to create the new wave port location

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.

Fig. 11. (a) Equation based surface definition using “cos” function, (b), (c), & (d) three different surfaces generated by this equation based surface.

Effect of Curvature on Antenna Matching

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.

Fig. 12. Effect of curvature on the resonance frequency.

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.

DesignCon 2017 Trends in Chip, Board, and System Design


Considered the “largest gathering of chip, board, and systems designers in the country,” with over 5,000 attendees this year and over 150 technical presentations and workshops, DesignCon exhibits state of the art trends in high-speed communications and semiconductor communities.

Here are the top 5 trends I noticed while attending DesignCon 2017:

1. Higher data rates and power efficiency.

This is of course a continuing trend and the most obvious. Still, I like to see this trend alive and well because I think this gets a bit trickier every year. Aiming towards 400 Gbps solutions, many vendors and papers were demonstrating 56 Gbps and 112 Gbps channels, with no less than 19 sessions with 56 Gbps or more in the title. While IC manufacturers continue to develop low-power chips, connector manufacturers are offering more vented housings as well as integrated sinks to address thermal challenges.

2. More conductor-based signaling.

PAM4 was everywhere on the exhibition floor and there were 11 sessions with PAM4 in the title. Shielded twinaxial cables was the predominant conductor-based technology such as Samtec’s Twinax Flyover and Molex’s BiPass.

A touted feature of twinax is the ability to route over components and free up PCB real estate (but there is still concern for enclosing the cabling). My DesignCon 2017 session, titled Replacing High-Speed Bottlenecks with PCB Superhighways, would also fall into this category. Instead of using twinax, I explored the idea of using rectangular waveguides (along with coax feeds), which you can read more about here. I also offered a modular concept that reflects similar routing and real estate advantages.

3. Less optical-based signaling.

Don’t get me wrong, optical-based signaling is still a strong solution for high-speed channels. Many of the twinax solutions are being designed to be compatible with fiber connections and, as Teledyne put it in their QPHY-56G-PAM4 option release at DesignCon, Optical Internetworking Forum (OIF) and IEEE are both rapidly standardizing PAM4-based interfaces. Still, the focus from the vendors was on lower cost conductor-based solutions. So, I think the question of when a full optical transition will be necessary still stands.
With that in mind, this trend is relative to what I saw only a couple years back. At DesignCon 2015, it looked as if the path forward was going to be fully embracing optical-based signaling. This year, I saw only one session on fiber and, as far as I could tell, none on photonic devices. That’s compared to DesignCon 2015 with at least 5 sessions on fiber and photonics, as well as a keynote session on silicon photonics from Intel Fellow Dr. Mario Paniccia.

4. More Physics-based Simulations.

As margins continue to shrink, the demand for accurate simulation grows. Dr. Zoltan Cendes, founder of Ansoft, shared the difficulties of electromagnetic simulation over the past 40+ years and how Ansoft (now ANSYS) has improved accuracy, simplified the simulation process, and significantly reduced simulation time. To my personal delight, he also had a rectangular waveguide in his presentation (and I think we were the only two). Dr. Cendes sees high-speed electrical design at a transition point, where engineers have been or will ultimately need to place physics-based simulations at the forefront of the design process, or as he put it, “turning signal integrity simulation inside out.” A closer look at Dr. Cendes’ keynote presentation can be found in DesignNews.

5. More Detailed IC Models.

This may or may not be a trend yet, but improving IC models (including improved data sheet details) was a popular topic among presenters and attendees alike; so if nothing else it was a trend of comradery. There were 12 sessions with IBIS-AMI in the title. In truth, I don’t typically attend these sessions, but since behavioral models (such as IBIS-AMI) impact everyone at DesignCon, this topic came up in several sessions that I did attend even though they weren’t focused on this topic. Perhaps with continued development of simulation solutions like ANSYS’ Chip-Package-System, Dr. Cende’s prediction will one day make a comprehensive physics-based design (to include IC models) a practical reality. Until then, I would like to share an interesting quote from George E. P. Box that was restated in one of the sessions: “Essentially all models are wrong, but some are useful.” I think this is good advice that I use for clarity in the moment and excitement for the future.

By the way, the visual notes shown above were created by Kelly Kingman from kingmanink.com on the spot during presentations. As an engineer, I was blown away by this. I have a tendency to obsess over details but she somehow captured all of the critical points on the fly with great graphics that clearly relay the message. Amazing!