IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 40, NO. 2, MAY 1998 145 A Spectral Approach for the Determination of the Reverberating Chamber Quality Factor Paolo Corona, Fellow, IEEE, Giuseppe Ferrara, and Maurizio Migliaccio, Member, IEEE Abstract—In this paper, a simple and effective approach for the evaluation of the chamber quality factor is presented. It is based on the averaged periodogram and permits a complete spectral characterization of the efficiency of reverberating chambers. A meaningful set of experiments is performed and discussed. Index Terms— Electromagnetic compatibility, mode stirred chambers, reverberating chambers, statistical electromagnetic fields. I. INTRODUCTION S CATTERING from large rotating metal plates, i.e., stirrers, is able to generate a fluctuating electromagnetic field [1]–[4]. The nature of such fluctuating field relies on the aspect shape and dimensions of the stirrers as well as their rotating speed [1]–[3]. This occurrence can be exploited in order to generate large spatially uniform and isotropic fields [4]. In particular, within the mode-stirrer reverberating chamber, i.e., a large metal overmoded cavity wherein the electromagnetic field is continuously perturbed by electrically large stirrers, a fluctuating electromagnetic field stochastic in nature is gener- ated [2], [4] and a high chamber quality factor is obtained [4]–[8]. In brief, the general physical mechanism governing the electromagnetic field within the reverberating chamber can be seen as the filtering within the cavity bandwidth of a large number of randomly walking eigenmodes [2], [4]. Note, however, that it is possible to achieve such a fluctuating behavior also operating on the input field waveform [2], [9]. Use of reverberating chambers has gained more and more attention in the electromagnetic compatibility community be- cause to the contrary of open-area test sites it is capable of producing repeatable test conditions and at variance with anechoic chambers is capable of generating a more realistic test field [4], [10]. As a matter of fact, the NASA/SSP 30 238 [11] and the CISPR/A 16 [12] documents, which regulate the level of electromagnetic radiation electronic equipment may produce with applications to space stations and microwave ovens, suggest to expose the device under test (OUT) in a re- verberating chamber. Further, the recent CISPR/A 66-67 [13] and IEC 1000-4-3 [14] documents, which provide standards to test procedures related to radiated, radio frequency, and Manuscript received June 26, 1997; revised November 12, 1997. This work was supported in part by the Italian Ministry of University of Scientific Research and Technology under Contract M.U.R.S.T.40% 120116.05. The authors are with the Istituto Universitario Navale, Istituto Teoria e Tecnica delle Onde Elettromagnetiche, Napoli 80133, Italy. Publisher Item Identifier S 0018-9375(98)04009-5. electromagnetic fields, consider also the use of reverberating chambers. As a consequence, it is a relevant issue for both the synthesis and analysis of reverberating chambers to characterize their behavior simply, effectively, and possibly with only few parameters. Within this framework in a previous work [10], a first-order systematic characterization of the electromagnetic field in a reverberating chamber has been outlined and applied to the reverberating chamber of the Istituto Universitario Navale (IUN). In this paper, we outline a simple and effective second-order (i.e., spectral) characterization of the field. The spectral estimates are based on the averaged periodogram approach. Further, it is shown that such a characterization can be summarized by two fundamental parameters: the chamber quality factor , and the bandwidth enlargement factor . Application is accomplished over some time-series of fluctuat- ing electromagnetic field relevant to the reverberating chamber of the IUN. These experiments showed that the quality factor is practically constant and equal to 42 dB both if different stirrers or a set of them are operated at 10 GHz and if all the three stirrers are operated and the input time-harmonic operating frequency is set to 9, 10, and 11 GHz. At the contrary, the spectral density function (sdf) shapes may profoundly change and this is witnessed by the , which varies from few hundred of hertz up to above 1 kHz. The paper is organized as follows. In Section II, the ra- tionales and description of the employed spectral estimate is given. In Section III, some meaningful results are obtained and discussed aimed at showing the capability and simplicity of the procedure to characterize the electromagnetic field within a reverberating chamber. Finally, in Section IV, some conclusions are drawn. II. SPECTRAL ESTIMATES Spectral analysis is a tool of outstanding importance in the characterization of stochastic electromagnetic fields, in this section we present a classical nonparametric Fourier-based spectral estimator with special regards to the application of the reverberating chambers electromagnetic field. More specif- ically, the periodogram spectral estimator is briefly illustrated; it is also shown that some fundamental modifications are necessary in order to achieve a reliable spectral estimation of the field. Preliminarily, we note two fundamental aspects: in order to estimate any statistical characteristics from a time series the ergodicity assumption must be invoked, i.e., direct substitution 0018–9375/98$10.00  1998 IEEE