Wave chaotic analysis of weakly coupled reverberation chambers

In this paper, we analyze the field fluctuations in weakly coupled complex cavities by using a random matrix theory to model the chaotic scattering within each cavity. Universal (chaotic) and non-universal are separated. In particular, non-universal are found to be conveniently described by the radiation impedance concept. Inherently, the development of the random field regime is accounted for by taking each mode of the cavity as a random plane wave expansion. Sources and sinks inside the cavities are assumed to be electrically small. A model for the cascaded cavities scenario is derived through the electric network theory and random matrix theory for both lossy and lossless cases. The adopted physical framework is a linear chain of two-port cavities terminated by a one-port cavity. The field flowing into this last cavity is related to the current excitation on the first cavity through the coupling radiation impedance. Closed-form expressions are derived for two interconnected cavities, mimicking the nested reverberation chamber scenario. Finally, the practical issue of measurements in a nested reverberation chamber is presented and discussed. Accordingly, based on physical arguments, the small fluctuations theory applies. Results are of interest in interference propagation through complex electromagnetic environment or planar circuits, EMC immunity tests, and reverberation chambers.