IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 49, NO. 3, AUGUST 2007 719 Short Papers Maximum Working Volume and Minimum Working Frequency Tradeoff in a Reverberation Chamber Alyse Coates and Alistair P. Duffy Abstract—Mode stirred reverberation chambers are attractive as test facilities because the electric fields produced in them are statistically uni- form over a large volume. The field strengths generated can also be high for only a modest input power. These factors allow testing of representa- tive or actual equipment without the need to rotate the equipment or scan with antennae to obtain worst case illumination. Providing these optimum test conditions for a given system configuration will allow the results to be interpreted with confidence. Usually standard guidelines for mode stirred chamber operation involve estimating the minimum working frequency based on a mode density calculation or using measurements to calculate the field uniformity of a given working volume. This paper uses the trans- mission line matrix technique to investigate the relationship between the minimum working frequency (i.e., the lowest usable frequency) and the maximum working volume. The paper presents a straightforward test to determine this tradeoff and illustrates the exploitation in the analysis of stirrer design options. Index Terms—Numerical modeling, optimization, reverberation cham- bers, transmission line matrix (TLM). I. INTRODUCTION The lowest usable frequency (LUF) is a useful concept for consider- ing the operation of a reverberation chamber. It provides a “usability” gauge which determines the level of confidence in the results based on adequate stirring of the modes within the chamber. Here, of course, “adequate” refers to a level of statistical significance which is accepted by the community as a convention. As there is no immutable physi- cal law which governs this decision, it allows the user to work below this gauge or to set the minimum frequency above this gauge if it is appropriate to do so. This paper presents a method to determine the maximum working volume–minimum working frequency (or LUF) tradeoff, with partic- ular application to the use of modeling to design and analyze a given chamber. In setting the context for the work presented in this paper, a number of points are worth noting as the perceived need for more robust definitions of LUF have evolved over, approximately, the last decade. 1) Hatfield et al. [1] note that “one of the major problems with reverberation chambers has been the use of empirically derived guidelines or ‘rules of thumb’ to determine if the chamber is op- erating properly,” noting LUF being one of the most commonly used rules of thumb and based on the point at which the authors of the relevant NBS Technical Note [2] felt that the uniformity of the fields became unacceptable. They further note that the cham- ber may be used below the normally accepted LUF. Hatfield et al. [1] proposed a test based on field uniformity measurements in a chamber’s “usable test volume.” Manuscript received January 16, 2007; revised March 23, 2007. This work was supported in part by Brand-Rex Ltd., Glenrothes, Fife, U.K. A. Coates was with the Applied Electromagnetics Group, De Montfort Uni- versity, Leicester LEI 9BH, U.K. She is now with Lockheed Martin UK INSYS Ltd., Ampthil MK45 2HD, U.K. (e-mail: alyse.coates@ieee.org). A. P. Duffy is with the Applied Electromagnetics Group, De Montfort Uni- versity, Leicester LEI 9BH, U.K. (e-mail: apd@dmu.ac.uk). Digital Object Identifier 10.1109/TEMC.2007.902199 2) Arnaut [3] reiterates the fact that there is no true LUF but ac- knowledges the requirement for the concept because of the prac- tical need to attribute pass and fail limits in EMC testing. Further, Arnaut notes that “sufficient” stirring is dependent on a number of factors and puts limits on the minimum volume and quality factor of the chamber. 3) The difficulty in obtaining a useful metric to determine the cham- ber performance at low frequencies was reported in [4]. A work- ing definition of LUF was reported based on field uniformity. 4) The relevant standard, 61000-4-21 [5] presents the accepted tests for field uniformity, primarily for chambers used in measure- ments. It notes that if the “margin by which the chamber fails to meet the uniformity requirements is small, it may be possible to obtain the desired uniformity by: increasing [the number of tuner steps], normalizing the data or reducing the size of the working volume.” 5) A quality metric was proposed in [6] to interpret [5] en route to using genetic algorithms to optimize the stirrer design. 6) Hill [7] makes the point that electromagnetic boundary condi- tions preclude adequate statistical stirring in the vicinity of the chamber walls. Hill goes on to investigate the transition from a planar interface to a free-space behavior, i.e., where there is field uniformity. He notes that the fields become statistically uniform as the distances from the walls become large and that the working volume can be obtained from the analysis presented in [7], given a value of the field deviation. A particular conclusion is that the fields approximate to uniform values as the distance from the walls becomes greater than half a wavelength. 7) Arnaut and West [8] discuss the criterion (described in [5]) to place any equipment under test no (EUT) closer than a quarter to half a wavelength to any perfectly conducting wall, noting that this restricts the use of the chamber to relatively high frequencies. Their theoretical and experimental investigations confirmed that the field performance changed markedly below a distance of a quarter of a wavelength. These references [1]–[8] indicate that a general approach to deciding on the minimum frequency that a chamber can be operated at and how far from the walls the EUT should be placed would be useful. It is hoped that this general approach can encourage clarity and, if necessary, agreement between the parties involved in the selection of the criteria for uniformity. This paper presents such an approach to the analysis of reverberation chambers. The method is discussed and used to analyze the effect of stirrer configuration on working volume and LUF. II. APPROACH USED The LUF was obtained, for a given working volume, by recording the electric field outputs (in the x, y, and z directions) at each vertex, for each stirrer position. The total field at each point and the standard deviation of each component at a given frequency was calculated using all points, as in [5]. The minimum working frequency (lowest usable frequency) was determined by obtaining the frequency where 95% of the frequency points remaining (i.e., the higher frequencies) were within 3 dB for all field components considered. This approach results in a simple method that can be applied to both measurements and simulations which is empathetic to the origins of the rules of thumb, the method set out in [5] and other approaches to interpreting the working volume. 0018-9375/$25.00 © 2007 IEEE