Estimate of the Probability Density Function of the Quality Factor of Mode Tuned, Source Stirred and Mode Stirred Reverberation Chambers

The probability density function (PDF) of the quality factor Q of well-stirred mode tuned, source stirred, and mode stirred reverberation chambers (STRCs, SSRCs and MSRCs, respectively) is derived. The approach is based on the volumetric number of independent field samples, and a new physical model is introduced to estimate the ratio between the stored energy and the dissipated power, so that the stirring speed is taken into account for MSRCs. The ergodicity of the spatial-correlation function of the energy density in the chamber volume is initially assumed; in other words, the independent sample number of the energy density, which contributes to the Q, is assumed to initially be constant for each field distribution across the volume. Then, this assumption is relaxed and the theory is enhanced to the case where the size of the independent volumetric samples is considered random, as well as their number. By invoking the central limit theorem, the Q PDF is achieved. It is shown that the Q PDF is basically normal, and its standard deviation decreases with the increasing of the independent variables that contribute to the Q itself. The Doppler effect tends to increase the standard deviation of the Q PDF.