Evaluation Method for the Probability Distribution of the Quality Factor of Mode-Stirred Reverberation Chambers

Abstract

An efficient experimental technique is presented for determining the empirical probability distribution of the quality factor ( ) of a mode-stirred reverberation chamber. The method is based on triplets of S-parameters that are measured at three locations of the receiver and spectrally averaged across a narrow frequency interval. It avoids the need for detailed spatial mechanical scanning of a field sensor. Statistics of the fluctuations of the stored and dissipated energy can be deduced individually. The effective number of excited cavity modes per stir state at a selected frequency serves as a degrees-of-freedom parameter of the distribution. The value of is estimated with the method, by fitting the empirical distribution of to a Fisher-Snedecor theoretical distribution using nonlinear minimization. Measurement results across 0.1-6.1 GHz support the validity of the theoretical distribution and the experimental technique, indicating that spectral averaging over a band as narrow a few MHz is sufficient within this frequency range to obtain good agreement. For a chosen averaging bandwidth, is found to increase rapidly with frequency below approximately 1 GHz in our chamber, followed by a slow decrease at higher frequencies. This frequency dependence is interpreted physically.Index Terms-Maximum likelihood estimation, mode-stirred reverberation chamber (MSRC), moment method estimation, probability distribution, quality factor, uncertainty quantification.

Elliptic Stochastic Fields in Reverberation Chambers

“…Although the antennas exhibit considerable impedance mismatch at the lowest and highest measurement frequencies over these wide bands, previous analysis has shown that this mismatch is of little significance in considering the ratios of S-parameter-based quantities [20], pertinent to the present analysis. …”

“…Complex S-parameter data were measured in a 8.7 × 3.7 × 2.9 m 3 mode-stirred reverberation chamber [20] (first resonance at f 110 43.8 MHz), from 40 MHz to 5.040 GHz with a 125-kHz sampling step, using a pair of identical log-periodic antennas (M = 1000 equiangular stir steps), and again from 100 MHz to 12 GHz, now with a 150-kHz sampling step using a pair of identical broadband dipole antennas (1400 stir steps). Although the antennas exhibit considerable impedance mismatch at the lowest and highest measurement frequencies over these wide bands, previous analysis has shown that this mismatch is of little significance in considering the ratios of S-parameter-based quantities [20], pertinent to the present analysis.…”

Probability Distribution of the Coherence Bandwidth of a Reverberation Chamber

“…μw,rf πμ0σw (18) in which Q∞ Δ = 3hV /(2μw,rδwS) represents the asymptotic quality factor for f → +∞ [14]. In summary, the limit distribution of Δ is a normal distribution N (μΔ, σΔ), i.e.,…”

“…The resulting empirical cdf FΔ(δ) is compared with the theoretical F (4M, 6M ) cdf (9). Multivariate spectral averaging for evaluating FQ(q) based on measured S-parameters has previously been described, developed, and validated in [18]. It is applied here to the empirical determination of F Δ(δ).…”

“…Measured (blue dots)[18], analytically simulated (black dots), and theoretical estimated Fisher-Snedecor F (4M, 6M ) (red line) cdfs of δ/ Δ at 1 GHz, based on three-point spectral averaging, using 1000 rotational stir states for measurement and 270 translational wall stir states for simulation. The inset lists the estimated value of M and the coefficient of determination R for the curve match between the measured and theoretical distributions.…”