Frequency selective surfaces (FSS) have useful properties for intelligent HF design of radomes, reflectors or radar absorbing materials. This article describes how such designs can be modelled and analysed with new specialised tools in Feko.
Altair EmployeeFrequency Selective Surfaces (FSS) Modeling Improvements in Feko
Antenna, Radome and RCS Problems
Frequency selective surfaces (FSS) are periodic Metasurfaces with identical two-dimensional arrays of elements arranged in a multilayer dielectric substrate. They form a 3D-filter for incident electromagnetic plane waves and transmit or reflect them for different frequency ranges. FSS were frequently used in reflector antennas (dichroic sub-reflectors), hybrid radomes and radar absorbing materials (so-called circuit analog absorbers).
Altair Feko offers several tools to model, analyze and optimize FSS. The following examples show the approach and provide a brief introduction to the topic. To dig deeper into the FSS topic, I recommend the textbook “Frequency Selective Surfaces” from Ben A. Munk [1], which enriches the theory with many practical examples.
Introduction to FSS
A passive periodic FSS array will interact with an incident plane EM wave. The plane wave will be partly transmitted in the forward direction and partly reflected in the specular direction. In the past decades many different FSS types have been investigated. Munk [1] gives a classification with 4 different groups:
- Group 1: “Center connected” or “N-Poles”
- Group 2: “Loop Types”
- Group 3: "Solid Interior” or “Plate Type”
- Group 4: "Combinations”
Complementary structures are often used in the construction of an FSS: It can be created with a subtraction operation from a planar metallic surface. From “Babinet’s principle” it can be concluded that reflection and transmission coefficients will be exchanged. For example, an inductive grid FSS will act as a high pass filter for EM waves and the corresponding complementary patch structure (capacitive grid) forms a low pass filter. Note, that this nice property is valid only for infinitely thin PEC surfaces. If dielectric layers are added and if two or more arrays are cascaded, the situation becomes more complex and then numerical simulation is the best approach to understand the transmission and reflection behavior.
Additional dielectric layers are usually required to fix the structure and increase stability. Due to the modified wavelength in the dielectric, the FSS resonance frequencies will shift to lower frequencies. Therefore, the dielectric parameter must be considered in the design process from the very beginning.
Simulation driven FSS-Design with periodic Boundary Conditions
Periodic Boundary Conditions (PBC) are very useful to analyze FSS reflection and transmission behavior in a very efficient way. Feko supports PBC in one or two dimensions. For the previous grid example they can be defined as a regular rectangular boundary. For other FSS shapes more complex periodic patterns with trapezoidal PBC definitions can be applied, as shown for this trifilar pattern.
The PBC approach allows simulation with low memory requirements (118 MB for the trifilar model embedded into a dielectric) in a large frequency range. The trifilar structure with branch length L = 6mm and strip width Ws = 0.49 mm is embedded in a dielectric with permittivity er = 2.2 and thickness t = 508 µm. The band pass FSS model and its complementary band stop FSS model are simulated in the frequency range 500 MHz – 20 GHz.
Dotted lines in the plot for transmission and reflection coefficient represent the band pass model results and solid lines the complementary band stop model. The differences between transmission coefficient of one model and reflection coefficient of the complementary model are caused by the dielectric material.
Let’s design an FSS with high transmission properties in the X-band and high reflection in the Ka-band. Goal is to use this structure as a dichroic sub-reflector in a Cassegrain antenna system. The design is built from a four-legged shape that is embedded in a dielectric. This FSS belongs to the “Loop-type” of Munk’s classification. In the “Periodic Structures” tab in CADFEKO several templates for typical FSS structures like crosses, rings, hexagons, planes, ellipses and trifilars are available. In the “Unit Cell” tool it can be selected if the cross shaped strip shall be handled as metallic strip or if the complementary aperture case is required.
This allows a complete parametric design to optimize the design variables to customized specifications. The optimization can be done directly in Feko [2] with the internal optimizer OPTFEKO or (if more functionality like Design of Experiments (DoE) or stochastic evaluation is required) Feko can be coupled with HyperStudy [3]. The cartesian graph of the transmission (blue curve) and reflection coefficients (red curve) show the desired behavior of the FSS in the frequency range 5 GHz – 40 GHz. . The simulation has been done using adaptive frequency interpolation and the corresponding Feko files are attached to this article.
These results can be exported into a tr-file, that can be used to characterize transmission and reflection properties of surfaces in larger scenarios. This approach is called “characterised surfaces” in Feko and can be applied to surfaces in a model for full-wave MLFMM simulation or for asymptotic RL-GO (Ray Launching Geometrical Optics) simulation.
Cassegrain Antenna with dichroic Sub-Reflector
As first application example we integrate this four-legged FSS into a Sub-reflector of a Cassegrain dual-reflector system.
The figure shows the configuration with both associated patterns of such a dual antenna system: The horn at the top is the feeding antenna at 9.5 GHz (X-band) and the smaller horn near the main reflector works at 35.75 GHz (Ka-band). Therefore, the sub-reflector of the antenna system needs to be designed for transmission in the X-band and reflection in the Ka-band. A detailed step-by-step workflow in CADFEKO for the setup of characterised surfaces (with tr-files from PBC simulation) for MoM/MLFMM is described in [4].
The Cassegrain dual reflector antenna model of this example has 159.385 triangle elements in the X-band and is solved with MLFMM in 103 seconds using 10.8 GB memory. In the Ka-band the model is electrically much larger with 2.189.807 triangle elements solved in 2387 seconds using 130 GB memory. Both simulations use 24 parallel processes on 2 CPUs.
Antenna Simulation with FSS Radome
Frequency selective surfaces are often used at radome structures as bandstop filters. In the next example an equivalent patch array (described by 20 x 20 Hertzian dipols) is placed above a gimbal with pitch angle 10° and is radiating in the X-band (9.55 GHz). The radome shape is described as superspheroid and modeled with the characterised surface approach using the transmission coefficients from the previous example of the four-legged cross. Both cases with and without radome are simulated. The FSS is almost transparent in this frequency range and only a small attenuation can be observed at the antenna main lobe.
RCS Simulation with FSS Radome
The FSS band-stop filter design is intended to shield the antenna from unknown external out-of-band sources. To demonstrate this property RCS simulations are performed for that radome model. For a plane wave excitation arriving from above (q = 0°) the bistatic radar cross section (RCS) is computed. In the antenna frequency band the reflection behaviour is very similar for the cases with and without radome. Both pattern show a maximum at q = 20° that is caused by the reflection on the gimbal with pitch angle 10°.
The behavior is different for an out-of-band frequency: At 5.5 GHz the gimbal orientation is not visible any more in the bistatic RSC pattern. When the radome is removed then the 20° maximum appears again.
This method can be easily extended to develop radar-absorbing materials (RAM) with band-stop properties for radomes. For this purpose, usually multilayer configuration with dielectrics, resistive sheets and FSS are assembled. In a periodic-boundary-condition model they can be easily parametrized and optimized regarding the desired specification. We refrain from showing an example of this and refer to Munk's textbook [1], where such structures are described.
References:
- B. A. Munk: Frequency Selective Surfaces, Theory and Design, Wiley 2000 .
- Altair Feko: https://altair.com/feko-applications
- Altair HyperStudy: https://altair.com/hyperstudy
- D. Le Roux: Altair Feko: Radome Modelling with MoM Characterised Surfaces: Workflow & Limitations, Article at Altair Community 2023. https://community.altair.com/community?id=kb_article&sysparm_article=KB0122369