Modelling & Analysis of Anechoic Chambers
Introduction
Anechoic chamber design is often a tradeoff between optimum quite zone performance and minimum system cost. These tradeoffs are in turn influenced by the operational frequency range that the chamber is being designed for and the available space and shape of the chamber.
Typical design methods that are used include empirical formulae and ray tracing methods. Unfortunately mathematical methods in the ray tracing family suffer from numerical inaccuracy, especially in scenarios where the room's characteristic dimensions are only a couple of wavelengths in size (i.e. typical VHF/UHF frequency bands).
The following information is based on the work of Campbell et. al. [1] and demonstrates how full wave EM simulation of a chamber at VHF/UHF frequencies is a useful tool that may be used to predict performance of a new chamber design.
Factors that may be investigation using the methods described by Campbell et. al. include:
 Absorber design, incl. various material parameters, shape of the absorbing cones and layout of the absorbers in the chamber.
 Separation and beam width of antennas in the chamber.
 Geometry and materials used in construction of positioning equipment.
Numerical Models
Constructing appropriate numerical models for the modelling of an anechoic chamber leverages FEKO's hybrid FEM/MoM formulation. The chamber itself is electrically large, while the absorbers are great in numbers and geometrically complex dieletric structures. For this combination of simulation requirements the FEM is well suited to modelling field propagation inside the chamber for the VHF/UHF frequencies of interest.
The FEKO models that are described further in this section model the entire internal chamber (space, absorbers and antennas) inside a FEM region which is decoupled from the MoM region. This invokes a particularly useful feature of FEKO's FEM implementation in that a PEC metallic boundary condition is applied to the FEM region and no MoM external problem is solved. The full solution is thus FEMbased, which forms sparse matrices during the solution phase and is therefore a memory efficient solution method for this problem.
The following paragraphs describe the detail of the different model elements.
Chamber
The chamber itself is essentially a PEC bounding box for the FEM problem to be solved here. In the decoupled FEMMoM problem, the surface area of the box is of no concern from a computational requirements perspective as the MoM problem will not be solved. The internal volume is of concern as this has to be meshed using FEM tetrahedra and although this forms a sparse matrix during the solution phase, storage is still required for the mesh geometry and related preconditioners. The total internal volume of the chamber thus plays a significant role in determining the total memory requirements of the solution.
Absorbers
Typical rectangular base cones are used to form the absorbing boundaries inside the chamber. Two sizes of cone are used in different areas, which have the following dimensions. Once a single cone has been created using CADFEKO primitives, this cone can be copied to the required extents very simply using the "Copy Special... and Translate" geometry duplication feature.
Transmit Wall: Base (8” x 8” x 4”); Height (24”)  
Center Patch: Base (12” x 12” x 6”); Height (36”)  
Absorber dimensions 

The absorbers are made from material with dieletric properties that vary with frequency. The following graphs demonstrate the permittivity of the absorber material and specific frequencies of interest to VHF/UHF simulations. The relevant frequency parameters can easily be setup as a custom material in CADFEKO.
Real  Imaginary 

Permittivity 
Frequency  ε'_{r}  ε"_{r}  tan δ 

150 MHz  4.76  4.47  0.9388 
250 MHz  3.50  3.00  0.8571 
500 MHz  2.40  1.95  0.8125 
1000 MHz  1.95  1.40  0.7179 
Antenna
The antennas inside the FEM region of this problem space is modeled as a combination of current sources. These current sources combine appropriately to form both a low and medium gain antenna with performance detailed in the following table and images.
Gain  EPlane 3dB BW  HPlane 3dB BW 

Low  68°  111° 
Medium  65°  67° 
FEM line sources antenna model 


EPlane Performance  HPlane Performance 
Low Gain Antenna Performance  Medium Gain Antenna Performance 
Performance Analysis
Metrics
The fundamental purpose of an anechoic chamber is to approximate an infinite measurement space in a confined environment. As such, the performance metrics of an anechoic chamber measure how closely the chamber reproduces an infinite measurement space. This is done with two metrics:
 Chamber error that represents the ratio between any particular field component in the chamber and the corresponding component in free space.
 Axial ratio that demonstrates the differences in magnitude between horisontal and vertical polarisation of any particular field component.
These metrics are formulated mathematically as follows:
Chamber error  Axial ratio 
Chamber error was computed for the chamber in question at the following frequencies:
 150 MHz
 250 MHz
 500 MHz
150 MHz Chamber Error
HPol  Low gain antenna Maximum error = 2.1 dB  VPol  Medium gain antenna Maximum error = 2.4 dB 

250 MHz Chamber Error
HPol  Low gain antenna Maximum error = 0.9 dB  VPol  Medium gain antenna Maximum error = 1.1 dB 

500 MHz Chamber Error
HPol  Low gain antenna Maximum error = 0.8 dB 

At 500 MHz the computational requirements for the simulation was already significant in terms of available resources and Physical Optics (PO) was investigated as a high frequency asymptotic method for modelling of the same problem. The following comparisons demonstrate that in the current scenario PO produced accurate results for the chamber error metric, differing by less than 1dB from the FEM result across the entire area of interest.
FEM (Full wave solution) HPol  Low gain antenna  PO (High frequency asymptotic solution) HPol  Low gain antenna 

Difference between FEM and PO (maximum difference = 1.0 dB) 
Axial Ratio
Axial ratios for low and medium gain antennas at 150 MHz and 250 MHz 

Conclusions
This white paper has demonstrated that FEKO's hybrid FEM/MoM formulation is well suited to the modelling of anechoic chambers at VHF/UHF frequency ranges, where traditional design and qualification processes are difficult and time consuming. The chamber in question has been characterized and chamber performance has been evaluated for medium and lower gain antennas. In this case the medium gain antenna has superior quite zone and axial ratio performance.
References:
[1]  D. Campbell (1), G. Gampala (1), C.J. Reddy (1), M. Winebrand (2), J. Aubin(2), "Modeling and Analysis of Anechoic Chamber using CEM Tools," Proceedings of AMTA 2012 Conference, October 2012, (1) EM Software & Systems (USA) Inc., USA, (2) ORBIT/FR Inc., USA 