IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 48, NO. 4, NOVEMBER 2006 701 Equivalent Circuit Model of a Bundle of Cables for Bulk Current Injection (BCI) Test Antonio Orlandi, Senior Member, IEEE, Giulio Antonini, Senior Member, IEEE, and Romeo Michele Rizzi, Student Member, IEEE Abstract—A “simulation program with integrated circuit em- phasis” (SPICE) model for the evaluation, in frequency and time domain, of the coupling of a bundle of shielded coaxial cables with an external electromagnetic source such as a bulk current injection clamp, is developed. The proposed equivalent circuit takes into ac- count the presence of the transfer impedance and the presence of the transfer admittance, and it does not need the subdivision in elementary cells. Intermediate results are validated by comparing the exact numerical solutions with the output of the SPICE circuit, and the final results are validated by means of comparison with measurements carried out on an experimental setup. The feature selective validation (FSV) technique is used as a measure of the comparisons. Index Terms—Bundles, coaxial cables, feature selective valida- tion (FSV), simulation program with integrated circuit emphasis (SPICE) model, transfer admittance, transfer impedance. I. INTRODUCTION I N recent years, an ever-growing importance has been given to the analysis and characterization of electromagnetic (EM) performances and properties of data cables. This is due to their irreplaceable role in large computing and telecommunication systems, connecting together physical parts that are often placed far apart. The high bit rate of today’s data streams, the large-frequency spectra associated with wide- and ultra-wideband applications, the small amplitude of digital and analog signals, and their decreasing signal-to-noise ratio (SNR) margins due to energy consumption limitations make the EMC/EMI characterization of cables a critical issue in the overall design process of the system. The need of these performances’ characterizations should also meet the stringent requirements imposed by the reduction of the time-to-market of the products and the associated reduction of costs. This implies that engineers should use reliable models that allow one to predict (well before the actual manufacturing) the cable’s (or even the system’s) properties and performances in a short time and also carry out parametric analysis (such as the worst-case one). In this context, the scientific literature greatly emphasizes the development of cables’ models from different perspectives. Works such as [1]–[4] can be considered to be recent significant Manuscript received June 8, 2005; revised June 22, 2006. This work was sup- ported in part by the Ministry of Education, Italy, under Project COFIN 2004 and in part by the Italian Ministry of University (MIUR) under a Program for the Development of Research of National Interest under PRIN Grant 2004093025. The authors are with the UAq EMC Laboratory, Department of Elec- trical Engineering, University of L’Aquila, L’Aquila 67040, Italy (e-mail: orlandi@ing.univaq.it; antonini@ing.univaq.it; rmrizzi@ing.univaq.it). Digital Object Identifier 10.1109/TEMC.2006.882850 contributions containing complete reference lists. A growing interest in bulk current injection (BCI) [5] as a test for the sus- ceptibility of shielded cables toward the EM field radiation [6] has drawn attention toward the modeling of cables during such a test. In [7] and [8], a full simulation program with integrated circuit emphasis (SPICE) model is described for a single coaxial cable, taking into account the presence of the transfer impedance Z t and admittance Y t . This inclusion is done based on the cir- cuit models developed and tested in [9]. The equivalent model for a shielded coaxial cable (with a single internal conductor) has been generalized in [10] for cables with multiple internal conductors. The SPICE circuit models of the cable along with that of the current injection clamp have been validated by com- paring their results with the experimental data [11] and used for a parametric analysis of the effects of the length [12] and electri- cal imbalance [13] on the induced voltages at the terminations. In [14], the developed circuit model has also been used to evalu- ate the values of Z t and Y t of actual portions of cables by means of a model-tuning procedure based on simple measurements. This paper completes the above-mentioned approach by ex- tending the model and its circuit implementation to a bundle of shielded coaxial cables running parallel to each other and to the reference plane going through the BCI clamp. The structure of the paper resembles that of [7] and [8] in order to facilitate the connection of concepts and formulas among these three papers and to easily reuse the already developed parts of the model. In Section II, the governing equations are derived and applied to the case of two cables for the sake of clarity. In Section III, the circuit implementation of the equations is proposed, and in Sec- tion IV, the numerical and experimental validation of the results is presented. In Section V, some concluding remarks are given. II. TRANSMISSION LINE (TL) EQUATIONS FOR A BUNDLE OF SHIELDED CABLES An equivalent circuit model is developed in order to predict the voltages and currents at the terminations of the cables when they form a bundle, due to the current injected by the BCI clamp. The development of each part of this circuit requires an analytical solution of currents and voltages along the cables. Because of this, the following assumptions are needed. 1) The conductors in the bundle all run parallel to each other and to the reference plane. 2) Dielectric and internal conductor’s losses are neglected for all cables in the bundle. This approximation allows a closed-form solution of the integrals and a worst-case analysis because the attenuation due to these losses is not considered in the results. 0018-9375/$20.00 © 2006 IEEE