A plane wave integral representation is presented for well-stirred fields in a reverberation chamber. The representation automatically satisfies Maxwell's equations in a source-free region and the statistical properties of the fields are introduced through the angular spectrum, which is taken to be a random variable. Starting with fairly simple and physically appropriate assumptions for the angular spectrum, a number of properties of the electric and magnetic fields and the power received by an antenna or a test object are derived. Many of these properties and test object responses are in agreement with other theories or with measured results. An important result for radiated immunity testing is that the ensemble (stirring) average of received power is equal to the average over plane wave incidence and polarization.

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Plane wave integral representation for fields in reverberation chambers

An analytical formulation has been developed for the shielding effectiveness of a rectangular enclosure with an aperture. Both the magnetic and electric shielding may be calculated as a function of frequency, enclosure dimensions, aperture dimensions and position within the enclosure. Theoretical values of shielding effectiveness are in good agreement with measurements. The theory has been extended to account for circular apertures, multiple apertures, and the effect of the enclosure contents.

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Analytical formulation for the shielding effectiveness of enclosures with apertures

With the proliferation of wireless devices in recent years, there is a growing need to test the operation and functionality of these various devices in different multipath environments, ranging from line-of-sight environment to a pure Rayleigh environment. In this paper we discuss how a reverberation chamber can be used to simulate a controllable Rician radio environment for the testing of a wireless device. We show that by varying the characteristics of the reverberation chamber and/or the antenna configurations in the chamber, any desired Rician K-factor can be obtained. Expressions for the desired K-factor as a function of the chamber and antenna characteristics will be presented. Experimental results are presented to illustrate the validity of these expressions, to show how the reverberation chamber can be used to simulate different multipath environments, and to show the realization of a controlled K-factor test facility. We present both a one-antenna and a two-antenna test configuration approach

On the Use of Reverberation Chambers to Simulate a Rician Radio Environment for the Testing of Wireless Devices

The paper deals with reverberation chambers for over-the-air (OTA) testing of wireless devices for use in multipath. We present a formulation of the S-parameters of a reverberation chamber in terms of the free space S-parameters of the antennas, and the channel matrix in the way this is known from propagation literature. Thereby the physical relations between the chamber and real-life multipath environments are more easily explained. Thereafter we use the formulation to determine the uncertainty by which efficiency-related quantities can be measured in reverberation chamber. The final expression shows that the uncertainty is predominantly determined by the Rician K-factor in the reverberation chamber rather than by the number of excited modes, assumed by previous literature. We introduce an average Rician K-factor that is conveniently expressed in terms of the direct coupling between the transmitting and receiving antennas (corresponding to a line-of-sight contribution) and Hill's transmission formula (corresponding to a multipath or non-line-of-sight contribution). The uncertainty is expressed in terms of this average K-factor and geometrical mode stirring parameters, showing strong reduction by platform and polarization stirring. Finally the formulations are verified by measurements, and the new understanding of uncertainty is used to upgrade an existing reverberation chamber to better uncertainty.

https://publications.lib.chalmers.se/records/fulltext/local_164015.pdf

Characterization of Reverberation Chambers for OTA Measurements of Wireless Devices: Physical Formulations of Channel Matrix and New Uncertainty Formula

/pdf/electromagnetic-theory-of-reverberation-chambers-nzgxgzj26y.pdf

Electromagnetic Theory of Reverberation Chambers

We present a theory based on power balance for aperture excitation of electrically large, lossy cavities. The theory yields expressions for shielding effectiveness, cavity Q, and cavity time constant. In shielding effectiveness calculations, the incident field can be either a single plane wave or a uniformly random field to model reverberation chamber or random field illumination. The Q theory includes wall loss, absorption by lossy objects within the cavity, aperture leakage, and power received by antennas within the cavity. Extensive measurements of shielding effectiveness, cavity Q, and cavity time constant were made on a rectangular cavity, and good agreement with theory was obtained for frequencies from 1 to 18 GHz. >

M. T. Ma

Papers

Aperture Excitation of Electrically Large, Lossy Cavities

Aperture excitation of electrically large, lossy cavities