Field Statistics in Nested Reverberation Chambers

Abstract

The electric field in nested reverberation chambers is Rayleigh distributed. Positioning an antenna in each of two nested reverberation chambers, the transmission amplitude coefficient between the two antennas is double Rayleigh distributed.Index Terms-Apertures, electromagnetic coupling, electromagnetic probability theory, reverberation chambers, shielding measurements.N ESTED reverberation chambers are two (or more) reverberation chambers connected by at least one aperture. They are often used to measure properties of the aperture, e.g., its shielding properties [1], [2]. In [3], the case of one reverberation chamber positioned inside another larger reverberation chamber is investigated (see Fig. 1).Here, we will first look upon the case when the exterior and interior reverberations chambers are connected by one aperture. We assume the power P t is transmitted into the exterior chamber, the power P a leaks through the aperture, and the power P r is received in an antenna in the interior chamber. The power values are in principal deterministic, but it is well known that for complex electrically large chambers, it is beneficial to treat P a and P r as random variables. The complete interior reverberation chamber can be looked upon as one antenna and the aperture can be seen as the antenna port. The received power by an antenna inside a reverberation chamber is exponentially distributed [4]- [6]. Hence, the power leaking through the aperture (P a ), or differently stated, received in the antenna port, is also exponentially distributed. By normalizing P a by its expectation value E {P a }, we define the normalized power leaking through the aperturehaving the probability density function (pdf)Assuming the exterior chamber is linear, the expected power leaking through the aperture is proportional (∝) to the power Manuscript Fig. 1. Nested reverberation chambers. The electric field is (spatially) Rayleigh distributed in both the exterior and interior chambers. The transmission amplitude coefficient (|S 21 |) between the two antennas in the figure is double Rayleigh distributed. By performing independent good stirring in both the exterior and interior chamber, samples from the double Rayleigh distribution can be measured using a network analyzer. transmitted into the exterior chamberand hence, it also follows from (1)The power leaking through the aperture (P a ) excites the interior chamber. We treat it as a random variable as we do not know its exact value. However, for every specific case, the power leaking through the aperture has a deterministic value, hence like in all reverberation chambers [4]:The electric field in the interior chamber, as well as in the exterior chamber, is spatially Rayleigh distributed.Hence, it follows that for every specific case of the power leaking through the aperture, the power received in the antenna positioned in the interior chamber can be seen as a sample from a random variable being exponentially distributed [4]- [6]. Similarly to the derivation of (4), the power received in the an...

Efficient Statistical Model for Predicting Electromagnetic Wave Distribution in Coupled Enclosures

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Latest developments on the shielding effectiveness measurements of materials and gaskets in reverberation chambers

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Probability distributions of three‐antenna efficiency measurement in a reverberation chamber

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