As winter snowfall blanketed the United States over the past holiday season, many people gathered on the couch to stay cozy in their houses and stream some holiday favorites. However, for one cat owner who also happened to be a satellite internet customer, their day of watching movies at home may have been cut short:
Fig 1: A group of cats enjoying the selfheating feature of the Starlink dish designed to melt snow. Aaron Taylor via Twitter.
Twitter user Aaron Taylor posted the picture above on New Year’s Eve 2021, which shows 5 cats nestled together on top of the Starlink antenna, which happens to have a heating feature originally designed to melt snow which would otherwise build up on top of the dish. Starlink is a satellite internet service operated by SpaceX, with the professed goal of providing highbandwidth internet service anywhere on the globe using a constellation of many hundreds of small satellites in lowearth orbit. While this picture seems to show that this feature works to prevent the accumulation of snow, to everyone’s surprise, it seems to have encouraged an accumulation of cats, which seemed to degrade the signal!
Fig 2: User reporting having internet bandwidth impacted by the presence of feline loading
Having a background in RF/Microwave engineering and the use of ANSYS HFSS, I had to know how the presence of this furry pileup would impact the performance of the antenna and thought it would be the perfect opportunity to demonstrate the use of HFSS’ Hybrid solver.
To simulate this situation, we’ll first need a dish antenna that operates over the entire range specified for the Starlink dish  10.7 GHz to 30 GHz. To standin for the actual Starlink antenna – which is a phased array of a couple of hundred small aperturecoupled patch antennas worthy of a blog post itself –, I’ll be using a more traditional hornfed parabolic dish reflector antenna, generated with the Antenna Toolkit ACT extension included in HFSS. The Antenna Toolkit is a very useful extension that allows the user to synthesize any basic antenna for an arbitrary design frequency in seconds, which you can check out in the patch antenna synthesis example video seen here. The default settings were used, apart from setting the center frequency to 17.3 GHz, and the “A” and “B” dimensions to 29 cm to match the frequency range and diameter of the Starlink dish.
Fig 3: Parabolic reflector antenna matching approximate dimensions of Starlink dish, with center frequency 17.3 GHz
The antenna toolkit has set up this dish with Hybrid Regions, a very powerful capability within HFSS that allows users to use different solver types in parallel to solve one geometry, resulting in solution times orders of magnitude faster and more memory efficient than using the FEM solver alone. FEM stands for Finite Element Method and is the default solver within HFSS. This solver subdivides the solution volume containing given geometry into many tetrahedral mesh elements, at each of which discretized forms of Maxwell’s equations are enforced. The remaining nonFEM solvers are integral equation (IE solver) or raytracing based (PO, SBR+ solvers), and can solve electrically large open scattering, and reflector problems very quickly compared to FEM. An arbitrary number of FEM and nonFEM regions can be combined in one hybrid solution.
Below, the two types of solutions which comprise the hybrid solve, and the geometry being used with each solver is shown – the horn feed antenna inside of a small FEM volume, and the reflector unbounded and designated as a nonFEM hybrid region:
4: FEM and NonFEM solution regions in Antenna Toolkit generated hybrid solutions
By default, Antenna Toolkit has set up the reflector design to use the IE solver on the reflector. Examining the properties of this design, another solver might be more appropriate which brings us to the question of when to use each of the unbounded, nonFEM solvers available to us: IE, PO, or SBR+.
Over the course of our experiences using hybrid simulations at Rand, we have developed a few guidelines for when to use a particular solver. The first question is when to use a hybrid solution. Hybrid solutions are appropriate when there are electrically large volumes of free space in which you aren’t interested in seeing the specific E and H field values. Examples include multiantenna studies, antenna placement studies, scattering, and radar crosssection simulations.
When it is appropriate to use the hybrid solver, ask the following questions for each object in the hybrid solution: If an object to be simulated is less than 10 wavelengths long at the highest frequency in the solution (λ_{min} ) the FEM solver can be used. If the largest dimension of the nonFEM geometry is less than 30, use the IE solver. If greater than 30, use one of the raytracing solvers (PO or SBR+). If the object will only require one ray bounce to accurately simulate (single reflector designs, RCS, and antenna placement on convex objects) use PO, if it will require many bounces (all other applications) use SBR+. SBR+ has the added benefit of allowing the user to plot the rays fired as part of the simulation, as well as more fine control over the number of rays fired, so err on the side of using SBR+ if there is ambiguity between whether to use it or the PO solver. Details for the other two hybrid region types (FEBI and Dielectric Cavity) can be seen tabulated in Appendix 1.
Fig 5: Flowchart detailing decision tree for deciding what solver to use in a hybrid solution
Fig 6: PO v.s. IE calculated radar crosssections of a sphere with varying diameters. It can be seen how the responses converge past 30 lambdas, under which PO should not be trusted to have the most physical response.
In our case, we have a single reflector antenna, which is around 58 cm in diameter. Our highest frequency in our simulation range is 30 GHz, so our minimum freespace wavelength is (c/3e10) = 0.01 m = 1cm. This puts us in the > 30*λ_{min }range, and since only one reflection is needed, the PO solver is most appropriate for our case. To reassign, I deleted the hybrid region corresponding to the dish and assigned a PO hybrid region to the sheet representing the dish.
Fig 7: Deleting IE region assigned by the Antenna Toolkit and reassigning a PO region
With this, the catfree dish antenna is ready to simulate. With default solver settings, the solution took 4 minutes and 50 seconds to simulate, with 178k matrix elements. As a point of comparison, I set the solution type back to HFSS without hybrid regions and set up the volume with FEM only. In one hour, the adaptive meshing process did not complete, and at the time of the last iteration, the mesh had 21 million elements. It is safe to say that this simulation would have taken more than a day to solve on the same hardware, showing that using the hybrid solve represents at least a 300% speedup in solve time for our case.
Figure 8: Comparison of FEM only and Hybrid matrix sizes
Let’s take a look at how our base case performs. As expected for an electrically large dish antenna, the 3D pattern is very directive, as plotted below for the 20 GHz case. The maximum gain is 37.5 dB at the anticipated theta = 90 degrees, phi = 90 degrees.
Fig 9: 3D radiation pattern for Antenna Toolkit dish
For the case of spontaneous feline loading, a CAD model of a sleeping cat was downloaded from a 3D file hosting site and assigned the appropriate material properties: a relative permittivity of 50, and a bulk conductivity of 0.2, as found corresponding to aggregate human electrical properties.
Fig 10: Material properties and 3D model of sleeping cat
Now, since our simulation geometry has changed, we can reevaluate whether PO is the proper solver for our case. Since it may be the case that a ray could bounce off our catnapping pet and onto the reflector, the most appropriate solver would now be SBR+ as per our flowchart in Figure 5. The reflector was reassigned to be an SBR+ region as described in Figure 7, and likewise, the cat was assigned as an SBR+ region.
The inclusion of our cat resulted in an increased solution time of 21 minutes and would compare similarly to an equivalent FEM simulation as the base case seen in Figure 8.
Now that we have both sets of results, we can see just how badly our antenna’s performance is affected. Plotted below is the total gain along the plane of symmetry (YZ) of our dish, for 3 points in the frequency range of interest, 10, 20, and 30 GHz. We see again a very directive radiation pattern for the unloaded dish, with the main lobe having a maximum gain of about 37 dB for the 20 and 30 GHz case, and 34 dB for the 10 GHz case. Our kitten degrades the directivity of our antenna, with the maximum gain being reduced to around 28 dB for the 10 and 20 GHz cases, and 31 for the 30 GHz, making for an average 7 dB decrease in gain across the band.
Fig 11: Comparisons of gain patterns between felineloaded and unloaded conditions. In bottom plots, dotted lines represent variation with cat.
The impact of an average 7dB drop in antenna gain over a band on the bandwidth of a satellite internet connection would be dependent on the coding scheme and the amount of margin used in the antenna. It would correspond to a reduction in signal strength to onequarter of the catfree baseline. It can be confidently concluded, however, that spontaneous feline loading is detrimental to antenna performance.
Solver Name 
FEBI 
IE 
PO 
SBR+ 
Dielectric Cavity 
Description 
Region assigned to the boundary between an FEM region and an unbounded solver in a hybrid solver 
Solves Integral formulations of Maxwell’s Equations on boundaries 
Ray Tracing simulation, capable of simulating one bounce 
Ray Tracing simulation, capable of simulating many bounces 
Uses FEBI behind the scenes to avoid meshing a large dielectric cavity 
When to use? 
(Implicitly applied to the boundary of any FEM region in a hybrid solve. ) 
Any design < 30*λ_{min} 
Simple designs > 30*λ_{min} 
Complex designs > 30*λ_{min} 
Large dielectric regions WITHIN FEM region 
Material constraints 
Only on boundaries 
Dielectric or conducting objects or sheets 
Dielectric or conducting objects or sheets 
Dielectric or conducting objects or sheets 
Uniform dielectric cavities 
Example Applications 
Multiple antennas to be solved by FEM separated by a large distance 
Antenna placement, cosite 
Large Single Reflector Antennas Antenna placement on platform 
Large Multireflector antennas Antenna placement of many antennas RCS of large objects of arbitrary geometry 
 Large lens for loading

Appendix 1: Relative comparison of hybrid solvers