Compound exponential distributions for undermoded reverberation chambers

Novel theoretical first-order probability density functions are derived for the energy density and magnitude of electromagnetic fields inside mode-tuned or mode-stirred reverberation chambers operated at relatively low frequencies. Deviations of physical characteristics for fields in undermoded chambers from those for ideal reverberation are quantified. These deviations are then used as parameters of the distributions. The distribution parameters can be easily and independently calculated from the measured tuner sweep data functions. The derivation is based on an eigenvalue decomposition of the 3×3 polarization matrix for the stir-averaged local field, followed by a polarization decomposition of the principal components. The theoretical distributions are compared with measured data, showing improved agreement and a significantly lower mismatch at lower frequencies compared to ideal χ₆⁽²⁾ distributions. The previously observed "flattening" of the cumulative distribution function is confirmed, resulting in a now calculable decrease of the mean value and an increase of the uncertainty for field statistics as frequency is lowered.