Statistical model of an undermoded reverberation chamber

Weibull distribution is adopted to model the electric field component of a Reverberation Chamber (RC). Its first property is to include the asymptotic laws, such as Rayleigh and exponential, and its main advantage lies in the fact that the Weibull shape parameter enables a model of the departure from overmoded to undermoded RC regime. Applications are given, such as an RC modal finite element modeling and a Monte Carlo simulation: they prove that the Weibull two-parameter distribution correctly models the quality factor influence. Moreover, the relevance of the use of this extreme value distribution is illustrated.     

Experimental determination of the higher electric field level inside an overmoded reverberation chamber using the generalized extreme value distribution

Reverberation chamber (RC), in which a complex electromagnetic environment is created, is of great interest as a versatile test and measurement tool, and its performance is conveniently evaluated through the field statistics. Following a previous paper in which the generalized extreme value (GEV) distribution was proposed to model the maximum field inside an RC, this work presents an experimental validation of the GEV use for the overmoded RC. The electric field is measured with a small sensor for a large number of points inside the RC, and the GEV parameters are accurately estimated. Since the maximum field distribution for this overmoded RC is found to be of reverse Weibull type, the field distribution is right bounded by a higher level that can be determined.     

Cavity losses modeling using lossless FDTD method

The impulse response of a lossless resonant system, usually obtained using the finite-difference time-domain method, permits us to determine the resonant frequencies through the Fourier transform. However, the obtained spectrum has no physical meaning since the losses have not been implemented. Rather than modeling physically the losses, we propose to apply a specific time-domain window to the already simulated signal of the lossless system. This Losses window depends on a user-defined quality factor. The advantage of this postsimulation losses implementation is a capability of parametric study of composite losses. Losses of various physical origins are found for example in the case of reverberation chambers.     

Maximum Field Inside a Reverberation Chamber Modeled by the Generalized Extreme Value Distribution

Classically, the statistical model of the maximum field inside a reverberation chamber (RC) is derived from the field magnitude model that is only known for the overmoded RC. We propose in this paper to model the maximum field by the generalized extreme value (GEV) distribution, as an application of the Fisher-Tippett theorem that formulates the asymptotic distributions of sample maximum. As the knowledge of the parent distribution (field magnitude) is not required, the GEV distribution is suitable for both overmoded and undermoded regimes (few modes excited). A Monte Carlo simulation illustrates the use of the GEV distribution for the overmoded RC. Modal FEM analysis of the RC extends the application to the undermoded regime. Special attention is brought to the issue of GEV parameter estimation: The so-called L-moments technique is advantageously employed to estimate the parameters from the small data sample. Dispersion of the estimated parameters is approximated and reduced by averaging uncorrelated values obtained from a narrow frequency band     

On the FEM Modal Approach for a Reverberation Chamber Analysis

We review the difficulties linked to the modal approach when modeling a reverberation chamber by the finite element method (FEM). The numerical challenge is due to the large-scale problem involved by the overdimensioned cavity. Moreover, the field singularity on the stirrer has to be captured by the FEM. First, the following issues are discussed: existence of null-frequency solutions, convergence rate for h and p adaption, and formulation type in E or H field. The modal analysis is then compared to the classical harmonic one. Focus is put on the field singularity at the source point     

Chaoticity of a Reverberation Chamber Assessed From the Analysis of Modal Distributions Obtained by FEM

Wave chaos theory is used to study a modeled reverberation chamber (RC). The first 200 modes at a given stirrer position are determined by the finite element method, and the Weyl formula is checked for various RC geometries, from integrable to chaotic. The eigenfrequency spacing distribution varies according to the degree of ray chaos in the RC related to its geometry. The eigenmode distributions are also analyzed and compared to the theoretical Gaussian distribution: close to the lower useable frequency, the modes of the studied chaotic RC fairly respect this asymptotic property. A general result of chaotic systems is illustrated: when perturbed by the stirrer rotation, the resonant frequencies of a chaotic RC avoid crossing. This implies that the frequency sweeps tend to vanish at high frequency.