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Modelling & Analysis of Anechoic Chambers

A white paper demonstrating how FEKO models were used during the design stages of an anechoic chamber that operates in UHF ranges.

Introduction

Anechoic_chamber_layout.jpgAnechoic chamber design is often a trade-off between optimum quite zone performance and minimum system cost.  These trade-offs 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 FEM-based, 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 FEM-MoM 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.

CADFEKO_rectangular_chamber_dimensions.png

 

CADFEKO_rectangular_chamber_internal_dimensions.png

W x H x L = 7.32 m x 5.18 m x 9.91 m

At 500MHz, this equates to dimensions in wavelength:

W x H x L = 12.22 λ x 8.64 λ x 16.54 λ

Total volume = 1746 λ2

Outside dimensionsInternal dimensions
Anechoic chamber dimensions

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”) absorber_pyramids_geometry.png
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.

absorber_permittivity_real.png absorber_permittivity_imaginary.png
RealImaginary
Permittivity
Frequencyε'rε"rtan 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.

GainE-Plane 3dB BWH-Plane 3dB BW
Low 68° 111°
Medium 65° 67°

FEM_current_sources_antenna_model.png

FEM line sources antenna model

antenna_model_E_plane_performance.png

antenna_model_H_plane_performance.png

E-Plane PerformanceH-Plane Performance
antenna_model_low_gain_performance.png antenna_model_medium_gain_performance.png
Low Gain Antenna PerformanceMedium 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_math_formulation.png chamber_axial_ratio_math_formulation.png
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

POSTFEKO_chambererror_150MHz_H-pol.png POSTFEKO_chambererror_150MHz_V-pol.png
H-Pol - Low gain antenna
Maximum error = 2.1 dB
V-Pol - Medium gain antenna
Maximum error = 2.4 dB

 

250 MHz Chamber Error

POSTFEKO_chambererror_250MHz_H-pol.png POSTFEKO_chambererror_250MHz_V-pol.png
H-Pol - Low gain antenna
Maximum error = 0.9 dB
V-Pol - Medium gain antenna
Maximum error = 1.1 dB

500 MHz Chamber Error

POSTFEKO_chambererror_FEM_500MHz_H-pol.png

H-Pol - 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.

POSTFEKO_chambererror_FEM_500MHz_H-pol_altscale.png POSTFEKO_chambererror_PO_500MHz_H-pol_altscale.png
FEM (Full wave solution)
H-Pol - Low gain antenna
PO (High frequency asymptotic solution)
H-Pol - Low gain antenna

POSTFEKO_chambererror_FEM-PO-delta_500MHz_H-pol.png

Difference between FEM and PO (maximum difference = 1.0 dB)

Axial Ratio

axial_ratio_performance_150MHz_250MHz.png POSTFEKO_chamber_axial_ratio.png
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