Introduction to the FEKO Suite FEKO is a suite of tools that is used for electromagnetic field analysis of 3D structures. It offers several state-of-the-art numerical methods for the solution of Maxwell s equations, enabling its users to solve a wide range of electromagnetic problems encountered in various industries. Solution Methods Applications Special Features Method of Moments (MoM), extended to a wide range of applications e.g. dielectric volumes, planar multi-layered structures, dielectric and magnetic coatings, thin dielectric sheets, ground plane reflections, periodic boundary conditions Multilevel Fast Multipole Method (MLFMM) Finite Element Method (FEM) Physical Optics (PO) Ray-launching Geometrical Optics (RL-GO) Uniform Theory of Diffraction (UTD) Multi-Conductor Transmission Line (MTL) Theory 3D antenna design Antenna placement Microstrip antennas (planar and conformal) Microstrip circuits 3D RF components (waveguide) EMC analysis (including complex cable harnesses) Bio-electromagnetics Scattering analysis (RCS) True hybridisation (MoM with FEM, PO, RL-GO, UTD and MTL) Adaptive Cross-Approximation (ACA) Parallel processing Optimisation Adaptive frequency sampling Circuit co-simulation Domain decomposition Time domain analysis Low frequency analysis GPU acceleration Out-of-core solution Wide range of hardware supported Applications Antenna Analysis FEKO is well-suited to the analysis of wire antennas, horn and aperture antennas, reflector antennas, microstrip antennas, phased array antennas, conformal antennas, broadband antennas and more. Many special formulations enable the analysis of practical antenna problems. One example is a MoM-based solution method that was designed specifically for the analysis of windscreen antennas. Multiple layers of windscreen glass can be taken into account, without meshing the glass. Antenna elements may consist of either wire or metallic elements which are located inside a layer or on the boundary between adjacent layers. Multiple windscreens may be included and coupling with external geometry, e.g. a car body, is accurately modelled. A full 3D MoM formulation is available for the analysis of microstrip antennas with arbitrarily oriented metallic wires and surfaces in multilayered dielectric media. Interpolation tables are used for faster simulation times.
FEKO also offers solutions for mobile and wireless antennas. Inherent parametric modelling and fast and accurate solvers provide quick insight into the initial design performance. CAD import filters can be used to add mechanical data, e.g. device housing and components, to the model. The optimisation platform is ideal for automated modification of the geometry to meet user specified goals. Antenna Placement Measurements of the radiation characteristics of antennas mounted on large platforms are difficult or even impossible to perform, necessitating accurate simulation. The MoM/FEM, MoM/PO, MoM/RL-GO, MoM/UTD hybridisations and the MLFMM enable the analysis of antennas in electrically large environments where the interaction with the nearby structures influences the antenna characteristics, e.g. UHF antennas on aircraft or ships or GSM antennas on motor vehicles. The visualisation of UTD rays can be very informative in identifying high frequency scattering and reflection points. EMC Analysis FEKO is used extensively for EMC analysis, especially in the automotive industry. It has also been used in various lightning protection and RFI mitigation studies. FEKO can efficiently calculate the radiation patterns and antenna factors of EMC antennas. Another application is the investigation of the shielding effectiveness of enclosures, whether metallic or made of non-perfect screening materials. A special technique for metallic enclosures allows for shielding factors of 200 db or more to be computed. It is also a powerful tool for the calculation and visualisation of surface currents and near-fields, and is relied on by engineers to guide them in electromagnetic interference (EMI) characterisation. Cable Coupling Analysis Many problems of electromagnetic compatibility and interference involve cables, which either radiate through imperfect shields and cause coupling into other cables, devices or antennas, or which receive external electromagnetic fields and then cause disturbance voltages and currents which could potentially result in a malfunctioning of the system. FEKO is useful for computing cable-to-cable and cable-to-device coupling and for the investigation of cable radiation effects. It can solve both radiation and irradiation problems, through standard multiconductor transmission line (MTL) theory or its unique combined MoM/ MTL solution method. Supported cable types include single conductor, ribbon, twisted pair, predefined or specified coaxial cable, non-conducting elements and userdefined cable bundles. If shielded, cables can be defined to have solid or braided shields. FEKO provides an internal database listing the transfer impedances for more than 20 popular cable types and additionally allows users to specify their own cable transfer impedance and admittance properties.
Bio-Electromagnetics and Biomedical Applications While MoM offers efficient and accurate solutions for metallic structures, FEM excels at simulation of inhomogeneous dielectric geometries, such as human bodies. Therefore the hybridisation of these two methods is a natural choice for the biomedical industry. MoM can be employed to design or analyse the performance of the radiating structure. Dielectric sheets or coatings can also be analysed efficiently, and a dielectric half space can be used to mimic an anatomical load as an intermediate simulation step. The final simulation of the radiator and detailed anatomical phantom can be analysed with hybridised MoM/FEM, enabling accurate field calculations inside the body for field propagation, dosimetry, SAR and safety analysis. Typical applications include active and passive implants, hearing aids and other body worn antennas, hyperthermia and RF tissue ablation, MRI and other MW imaging technologies. Radiation Exposure Safety Studies The MoM or MLFMM may be used to compute near-field values around complex building and antenna structures where people work. Isosurface plots are then instrumental in determining where the safety boundaries conforming to international radiation safety guidelines are located. Such information is typically used to place signage and barriers at the site, ensuring safety of the public and personnel in proximity to the transmitters. The fields inside lossy dielectric regions may be used for computation of the Specific Absorption Rate (SAR). FEKO reliably calculates the volume averaged SAR in 1g or 10g tissue cubes or as a whole body average. It has been applied extensively in studies regarding the compliance of mobile phone antennas and cellular base stations to international radiation exposure guidelines. Microwave and RF Components and Circuits Components such as filters, circulators, couplers, power dividers, mixers, isolators and others can be simulated in FEKO. Multi-layer planar dielectric MoM for the analysis of substrates can be used for the simulation of microstrip circuits. The FEM is available as an efficient method for solving closed waveguide structures. Circuit co-simulation is often used for feeding and matching networks. Circuit schematics can be created with lumped elements, SPICE network models, S-, Z- and Y-parameter blocks and networks specified by data from Touchstone files. Time Domain Analysis FEKO is based on a frequency domain formulation, but time domain information can be obtained by applying Fourier Transforms on broadband frequencydomain data. An interface is provided in POSTFEKO which facilitates users in the specification of time domain pulse shapes. Time domain analysis has successfully been applied to perform lightning strike analysis and to evaluate time domain characteristics of ultra-wideband antennas, such as fidelity.
The FEKO Suite FEKO offers a graphical user interface (GUI) with easy workflow, running on Windows or Linux. The GUI can be used every step of the way, from model creation in CADFEKO through to visualisation of results in POSTFEKO. Advanced users can resort to EDITFEKO, a scripting interface to the FEKO solver, to obtain full control over functionality. The scripting editor in POSTFEKO may be used for advanced post-processing of results. The GUI provides 3D mouse support, which may be used as input device in addition to a keyboard and standard mouse for convenient manipulation of 3D objects. Modelling in CADFEKO Functionality: Features: Interactive geometry specification. Excitation and port definition. Output requirement specification. Optimisation setup. Automated or custom meshing. Solution control. Create parametric models with variables and mathematical expressions which may be modified to change the geometry, meshing and/or material parameters (e.g. dielectric constant, coating, conductivity). Create canonical structures (cylinders, polygons, spheres, cones, etc.) with the click of a button. Perform boolean operations on geometry objects (e.g. split, union, intersect and subtract). Define various types of curves and surfaces, including analytical curves, splines and NURBS surfaces. Create geometry by spinning, sweeping and lofting lines and curves. Translate, rotate, scale, mirror and align objects. Project points, curves and surfaces onto surfaces or solids. Add cables with user specifiable paths, shields and cross sections. Create surface meshes (triangles) or volume meshes (tetrahedra) with specifiable mesh density for any specific region of the geometry. Import and export filters for complex geometry or mesh models in industry standard CAD formats. Request multiple solution configurations, and set the following globally or per configuration: Solution parameters (e.g. frequency, loads). Excitations (e.g. voltage source, waveguide excitation). Calculation parameters (e.g. far-fields, near-fields, S-parameters, SAR analysis). View and add components to network and cable schematics.
Choice of Solver and Resource Scaling Full-wave techniques (MoM, FEM etc.) generally suffer from poor scalability. This limits the electrical size of the problems that can be solved on typical computers. When using field based solution techniques (FEM, FDTD), the discretisation of the field introduces a very small error as a wave propagates through the mesh. For very large meshes, these errors could add up, resulting in reduced accuracy in results. The error can be reduced by using a finer discretisation, but this increases the resource requirements. The MoM does not require field discretisation, which means that the propagation distance does not degrade the accuracy of the results. With the MoM the memory required relates to the number of basis functions squared (N 2 ). For general structures, a basis function density of about 100 basis functions per λ 2 is recommended. For 1 GByte RAM, and using no symmetry, this translates to a surface area of approximately 82λ 2 that can be solved in-core. Larger problems can be solved using an efficient out-of-core solver in FEKO, but this solution is slower than an in-core solution. The memory requirements for MoM is proportional to N 2, whereas that of the MLFMM is N*log(N) (for metallic surfaces N 100*(A/λ 2 ) with A the surface area). For large N this is a huge difference! Asymptotic predictions of memory usage for the MoM with and without MLFMM N MoM MLFMM Application 100,000 150 GByte 1 GByte Military aircraft at 690 MHz Reflector antenna with aperture size 19λ. 200,000 600 GByte 2 GByte Military aircraft at 960 MHz Reflector antenna with aperture size 27λ. 400,000 2.4 TByte 4.5 GByte Military aircraft at 1.37 GHz. Reflector antenna with aperture size 38λ. 1 000,000 15 TByte 12 GByte Military aircraft at 2.2 GHz Reflector antenna with aperture size 60λ. Although FEKO offers the MLFMM which enables the analysis of electrically large problems, this accurate full-wave method is not sufficient for the solution of electrically huge structures (e.g. aircraft or ship at 10 GHz and above). FEKO offers asymptotic high frequency techniques (PO, RL-GO and the UTD) as solution to the scalability hurdles in such problems. In the PO formulation the currents on the metallic surfaces are simply calculated from the incident field. Large element PO (LE-PO) allows mesh sizes of multiple wavelengths and although it does not support multiple reflections, it can lead to dramatic computational cost savings in cases where it is applicable. The RL-GO works by launching rays from each MoM element and placing Huygens sources on surfaces, while with the UTD only the closed form reflection and diffraction (edge and corner) coefficients are used in the solution. The size of the object, therefore, does not influence the memory requirement. The coefficients (terms) and the number of interactions do however influence the run-time. The UTD formulation requires that the smallest dimension of the UTD objects be at least in the order of a wavelength.
Whereas the triangles (for PO and RL-GO) are well suited to represent complex geometry, the use of flat polygonal plates restrict the application of the UTD to geometries which can be modelled sufficiently with such plates (e.g. a ship). In FEKO, the generally applicable MoM has been hybridised with the Physical Optics (PO), ray-launching Geometrical Optics (RL-GO) and the Uniform Theory of Diffraction (UTD). This hybridisation enables the solution of large problems on small computers. The hybridisation allows for full wave analysis where required, and approximations to be used when applicable. Post-processing with POSTFEKO Functionality: Features: Model validation. Post-processing and visualisation of results. Support for multiple 2D and 3D views with multiple geometry (*.fek) and result (*.bof) files in a single session. Support for multiple results of the same type, e.g. displaying more than one near-field ortho-slice in the same 3D view. 2D results can be displayed in various formats on Cartesian graphs, polar plots and Smith charts. 3D views can be set up to display geometry, meshes, currents, near-fields and/or far-fields. 2D graph measurements and annotations for values such as local and global maxima and minima, beamwidth, bandwidth and side lobe levels. Multiple and arbitrarily oriented cutplanes with selectable cut entities are supported for 3D views. Graph and data import and export (e.g. import of measurements for comparison purposes). Full multiport S-parameter extraction. Advanced Specific Absorption Rate (SAR) display options (IEEE standard compliant whole body average, 10g cube localised, 1g cube localised). UTD ray colours indicate their relative amplitudes. Electrical surface currents and electrical charge density display options. Characteristic mode currents, fields, eigenvalues, modal significance and characteristic angle display options. Scripting based advanced post-processing as well as automation with the Lua POSTFEKO API. Export of images and animations to popular file formats. Automatic report generation via simple or template based mechanisms to MS PowerPoint, MS Word or PDF file formats. Visualisation of optimisation results. Support for time domain results processing.