The Role of Losses in the Definition of the Overmoded Condition for Reverberation Chambers and Their Statistics

Abstract

It is commonly acknowledged that in perfectly stirred reverberation chambers, the energy density of the electric field follows a X <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> law, as long as the overmoded condition applies. This concept, never defined properly, is often confused with the idea of a threshold on the modal density, regardless of the quality factor of the cavity. This interpretation is here proven to be inaccurate, as losses play a fundamental role in the nature of the field statistics and not, as often assumed, just in its scaling. In particular, it is shown how the overmoded condition should be stated mathematically, highlighting how the cavity quality factor and the number of eigenmodes excited cannot be regarded as quantities intervening independently on the field statistics, but should rather be considered jointly. These results are derived by means of a modal analysis, with a limited number of assumptions. A quantitative relationship is established between average modal overlapping and the rate of convergence of the electric energy density towards a X <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> law. Rather than setting an arbitrary threshold on modal overlapping as a necessary condition for an overmoded behavior, the statistical uncertainty due to the limited number of available field samples is shown to affect the very definition of the overmoded condition.