Statistics of the quality factor of a rectangular reverberation chamber

The mean and standard deviation of the theoretical quality (Q) factor of a rectangular reverberation chamber are considered. Different averaging methods are investigated for deriving alternative expressions for its bandwidth-averaged value. Alternative basic assumptions are made regarding the distribution of the total energy density inside the cavity across the participating eigen-modes, thus providing alternatives for the assumption of equipartition of excitation energy. The physical reasons for such possible departures are explained on the basis of the stored and dissipated modal energy. For a given volume-to-surface ratio of a rectangular cavity, the theoretical arithmetic average Q (unlike the harmonic average) exhibits an explicit asymptotic dependence on the aspect ratios of the cavity. In the asymptotic high-frequency limit, the first-order dependence of the arithmetic Q on inverse frequency is governed by the imbalance between the TM and TE quality factors and by the aspect ratios of the cavity. Simulation results indicate better agreement between actual and smoothed theoretical arithmetic averages, particularly at lower frequencies, in comparison with those for the harmonic mean values. An expression for the distribution function of the arithmetic Q is formulated based on its statistical moments. We furthermore analyze the Q of a chamber with dynamically varying walls but constant average mode density. Such a chamber may serve as a model for mode stirring using flexible walls. The existence of a mode bunching effect which varies with tuner state but stabilizes with increasing frequency is shown. Effects of continuous dynamics of the cavity deformation on Q are discussed.