192 IEEE TRANSACTIONS ONELECTROMAGNETIC COMPATIBILITY, VOL. 49, NO. 1, FEBRUARY2007 Short Papers Transmitting Antenna’s Reflected Power and its Influence on Reverberation Chamber Calibration X. C. Wei, Member, IEEE, and Er-Ping Li, Senior Member, IEEE Abstract—For the reverberation chamber operating at low frequencies, the reflected power at the transmitting antenna’s terminal is very large. In this paper, we analyzed the statistical property of this large reflected power. Furthermore, two different normalization methods used for cham- ber calibration are compared. Through measurement results, it is shown that using net power to do the normalization will give better chi-square and uniformity results than using transmission power to do the normaliza- tion. However, from the view of the practical testing, the later one greatly reduces the testing complexity and is accurate enough for the engineering application. Index Terms—Chi-square validation, high reflection, reverberation chamber. I. INTRODUCTION The reverberation chamber is an electrically large cavity consisting of highly conducting walls. By using mechanical stirrers to change the modes inside the chamber, it can provide a statistically isotropic and uniform field environment for electromagnetic (EM) measurement [1]–[3]. Recently, it has found more and more applications in EM testing, such as antenna measurement [4] and the simulation of mobile communication environment [5]. Before conducting any testing, the statistical property of the chamber must be validated. One often-used criterion is the chi-square validation; the power received by a linear antenna (or the square of any rectan- gular component of the electric field) during stirrer’s rotation follows the chi-square distribution with two degrees of freedom [6]. Another criterion is that the maximum values of the x, y, and z components of the electric field during the stirrer’s rotation are uniformly distributed within the working volume. Theoretically, for these two statistical prop- erties, it is assumed that the net power in the chamber is constant over the stirrer’s rotation, where the net power equals the transmission power delivered to the transmitting antenna minus the reflected power from the transmitting antenna. This assumption means that the chi-square distribution and uniformity are obtained mostly by changing the modes inside the chamber but not by changing the energy inside the cham- ber. According to this assumption, during the validation, the received power and field strength should be normalized by the net power for each stirrer position, which we call net-normalization method. However, this net-normalization method has some drawbacks in the practical calibration and testing. Due to the high Q value of the chamber, the reflected power at the terminal of the transmitting antenna is very large, and it can vary in range between zero and a value very near the transmission power during stirrer’s rotation. When the reflected power is only slightly less than the transmission power, the net power will be very sensitive to noise and calibration errors. On the other hand, during chamber calibration, the calibration factor is measured, Manuscript received September 28, 2006; revised November 14, 2006. This work was supported in part by the Institute of High Performance Computing Singapore under Project IHPC/EMC/02/211. The authors are with the Institute of High Performance Computing, National University of Singapore, Singapore 117528 (e-mail: weixc@ihpc.a-star.edu.sg; eplee@ihpc.a-star.edu.sg). Digital Object Identifier 10.1109/TEMC.2006.890222 Fig. 1. Horizontal and vertical stirrers mounted inside the reverberation cham- ber. (a) Top view. (b) Front view. which is used to calculate the power necessary for the desired field strength during later electromagnetic compatibility (EMC) testing. If this calibration factor is based on the net power, the calculated input power will also be the net power, which is accordingly required to be constant during stirrer’s rotation for following EMC testing. This means that the reflected power must be compensated for each stirrer’s position, which will make the practical testing complex and time consuming. Therefore, the transmission power instead of the net power is often used to normalize the received power and field strength during practical calibration [7], [8], which we call tran-normalization method. However, the chamber will give different calibration results under these two different normalization methods. This difference is not clearly studied yet, although there had been many results about the statistical properties of the field within the working volume. This issue becomes more important for a chamber working at low frequencies since chamber reflection increases significantly at low frequencies. In the following sections, first, the reflected power of the transmitting antenna inside the reverberation chamber is analyzed, and then, both the net-normalization and tran-normalization methods are used to validate the chi-square distribution and field uniformity, and their accuracies are compared. II. REFLECTED POWER OF TRANSMITTING ANTENNA INSIDE A REVERBERATION CHAMBER The reverberation chamber under study was built at NanYang Tech- nological University, Singapore, of which the dimension is 12.5 m × 8.5 m × 6 m. Two zigzag stirrers (one horizontal stirrer and one vertical stirrer) are mounted inside the chamber to efficiently change the modes. The dimension and geometry are shown in Fig. 1. The EM energy is injected into the chamber via a transmitting antenna, which is placed near a wall/corner. The reflected power of the transmitting antenna inside a chamber is larger than that in the free-space because of the highly conducting walls, and this reflected power varies for different stirrer positions. This makes the net power P net into the terminal of the transmitting antenna a random variable, although the transmission power P tran is constant. The relationship between P tran and P net at the terminal of the transmitting antenna is P net = P tran (1 −|Γ| 2 ) (1) 0018-9375/$25.00 © 2007 IEEE