Florian Monsef

Average Number of Significant Modes Excited in a Mode-Stirred Reverberation Chamber

Although the number of significant modes is intuitive, this concept has never been clearly defined, mainly because of the unbound number of modes involved in modal overlap. In the present paper, we show that, for a perfect stirring process, the effect of modal overlap can be modeled as an equivalent filtering formulation. By introducing the statistical-bandwidth concept, we show that the electromagnetic field statistics due to an infinite number of modes can be summarized by a finite number of significant modes. The case of the electric-energy density in an mode-stirred reverberation chamber has been considered and a new expression of its variability has been established. The good agreement found between the new expression and the experimental and simulation results support the several concepts introduced in this paper.

Why a Reverberation Chamber Works at Low Modal Overlap

The physical parameter well adapted to assess the degree of overmodedness of a reverberation chamber (RC) is the number MM of modes overlapping in a mode bandwidth. The lowest usable frequency of an RC often corresponds to a low modal overlap of one or two modes. Notwithstanding, in spite of this poor number of modes the RC still works. We show, using Monte Carlo simulation, that the number of modes must, in fact, not be restrained to MM and that the number of modes contributing to the field statistics can be, even at low modal overlap, somewhat larger than expected.

Goodness-of-Fit Tests in Reverberation Chambers: Is Sample Independence Necessary?

Goodness-of-fit (GoF) tests are interesting tools to test the overmodedness of the field inside a reverberation chamber (RC). In the definition of GoF tests independent and identically distributed samples are required. In this study, we focus on the effect of partial data correlation on GoF tests. We analyze the sensitivity of the most common GoF tests used in electromagnetic compatibility. The results presented herein are based on numerical and experimental data. We show that most of GoF tests are insensitive to correlations up to rather high values depending on the type of GoF test chosen. Implications for practical applications are discussed.

Influence of Medium Statistics on Robustness of Time-Reversal Transmissions

The problem of predicting the performance of time-reversal transmissions (TRT) in a time-varying complex medium is addressed in this letter. The loss of coherence in the propagation medium and its nominal energy contrast are proven sufficient to predict the average loss of quality in received signals. In particular, it is shown how a perturbation in the medium affects in a different way coherent focusing and background fluctuations. In the extreme case of a diffusive medium (e.g., Rayleigh channels), the fluctuations intensity is unaltered. The predictions of the proposed theoretical models are validated against experimental results measured in a reverberation chamber, where a mechanical paddle (stirrer) acts as the source of perturbation in the medium. It is confirmed that, depending on the medium statistics, perturbations can have a varying impact on TRT performance.

Relative variance of the mean-squared pressure in multimode media: Rehabilitating former approaches

The commonly accepted model for the relative variance of transmission functions in room acoustics, derived by Weaver, aims at including the effects of correlation between eigenfrequencies. This model is based on an analytical expression of the relative variance derived by means of an approximated correlation function. The relevance of the approximation used for modeling such correlation is questioned here. Weavers model was motivated by the fact that earlier models derived by Davy and Lyon assumed independent eigenfrequencies and led to an overestimation with respect to relative variances found in practice. It is shown here that this overestimation is due to an inadequate truncation of the modal expansion, and to an improper choice of the frequency range over which ensemble averages of the eigenfrequencies is defined. An alternative definition is proposed, settling the inconsistency; predicted relative variances are found to be in good agreement with experimental data. These results rehabilitate former approaches that were based on independence assumptions between eigenfrequencies. Some former studies showed that simpler correlation models could be used to predict the statistics of some field-related physical quantity at low modal overlap. The present work confirms that this is also the case when dealing with transmission functions.

A Possible Minimum Relevance Requirement for a Statistical Approach in a Reverberation Chamber

Modal overlap in a reverberation chamber (RC) involves, strictly speaking, an infinite number of modes in the field statistics. The degree of overmodedness of an RC is often assessed by introducing an arbitrary reference bandwidth in which a number of overlapping modes is computed. We introduce a statistical model of the field in which the number of modes is rigorously finite. The model is chosen such that the number of degrees of freedom (DOF) of the field can be assessed. The number of DOF is assessed by considering the degree of homogeneity of the average power received by a linearly polarized antenna. It is considered that a statistical approach requires at least a single degree of freedom. Based on this criterion, the minimum frequency at which a statistical approach would make sense is evaluated and compared to the lowest useable frequency (LUF) commonly considered in EMC.

A Dielectric Low-Perturbation Field Scanner for Multi-Path Environments

Well-established solutions capable of scanning electromagnetic fields in anechoic environments essentially rely on the massive use of absorbers, in order to keep under check energy scattered by the metallic parts of an automatic positioning system. Solutions of this kind are convenient whenever the field to scan is the result of line-of-sight (LOS) propagation. In complex media, where multipath propagation imply non-LOS contributions, the introduction of absorbing materials can irremediably alter the behavior of the medium under test and therefore the field to be scanned. In this case, a field scanner rather needs to be as transparent as possible. This paper introduces the main ideas behind an alternative automatic positioning system designed in order to ensure a low perturbation of the response of a medium. The impact of the scanner is assessed when used in a reverberation chamber with a varying degree of reverberation, in order to emulate the conditions found in realistic complex media. Expected applications are mainly found in sounding propagation in complex media.

Limitations of the equivalence between spatial and ensemble estimators in the case of a single-tone excitation

The ensemble-average value of the mean-square pressure is often assessed by using the spatial-average technique, underlying an equivalence principle between spatial and ensemble estimators. Using the ideal-diffuse-field model, the accuracy of the spatial-average method has been studied theoretically forty years ago in the case of a single-tone excitation. This study is revisited in the present work on the basis of a more realistic description of the sound field accounting for a finite number of plane waves. The analysis of the spatial-average estimator is based on the study of its convergence rate. Using experimental data from practical examples, it is shown that the classical expression underestimates the estimator uncertainty even for frequencies greater than Schroeders frequency, and that the number of plane waves may act as lower bound on the spatial-average estimator accuracy. The comparison of the convergence rate with an ensemble-estimator shows that the two statistics cannot be regarded as equivalent in a general case.