# How to design Frequency Selective Surfaces (FSS) in Altair Feko

**Altair Employee**

**Frequency selected surfaces (FSS)** are periodic surfaces 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.

A typical example is the sub-reflector design of a **Cassegrain dual-reflector system**.

The Figure above shows the gain pattern 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 is designed for **transmission in the X-band **and **reflection in the Ka-band**.

The design is built from a **four-legged shape** that is embedded in a dielectric. The cartesian graph of the transmission (blue curve) and reflection coefficients (red curve) show the desired behavior.

There are many shapes and multilayer options to design a FSS. The key to FSS-design and optimization is using parameterized models for simulation with **periodic boundary conditions (PBC)**. With the compact PBC models in Feko [1] the computation times are low and therefore the frequency-dependent behavior can be computed efficiently. This is also a door-opener for the application of **optimization techniques**, that are available in OPTFEKO or in HyperStudy [2] .

If you want to learn more about FSS design strategies you may look into Munk’s well-known textbook [3], which gives a nice overview on the topic.

**Workflow for FSS design **

The workflow to evaluate and optimize frequency selective surfaces has improved in recent CADFEKO versions:

A new **Periodic Structures extension** has been added to CADFEKO2022.2. This extension supports the preparation of **frequency selective surfaces (FSS), radome’s and radar absorbing material (RAM)**. The new shapes, geometry and unit-cell tool can be used to quickly define simple or complex parametric unit-cell representations of multi-layer FSS structures for material characterization and transmission analysis using a periodic boundary condition approach.

The TR-coefficients of the PBC-simulation can be exported and applied directly as **characterized surfaces** to faces of complex 3D models. To solve such large problems efficiently (like the Cassegrain dual reflector) the characterised surface approach has been **extended** in Feko2022.2 from RL-GO **to MoM/MLFMM**. This provides an extremely powerful, flexible, and efficient approach for FSS-, radome- or RAM-analysis.

A detailed step-by-step workflow for the setup of characterized surfaces for MoM/MLFMM in CADFEKO 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.

The near-field results of the Feko simulations show the principal behavior of wave propagation in the two frequency bands. In the X-band, the FSS-subreflector is transparent, while in the Ka-band it is fully reflective.

**References:**

- [1] Altair Feko: https://altair.com/feko-applications
- [2] Altair HyperStudy: https://altair.com/hyperstudy
- [3] A. Munk:
*Frequency Selective Surfaces, Theory and Design*, Wiley 2000. - [4] 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