IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 50, NO. 1, FEBRUARY 2008 175 Multiconductor Reduction Technique for Modeling Common-Mode Currents on Cable Bundles at High Frequency for Automotive Applications Guillaume Andrieu, Lamine Kon´ e, Fr´ ed´ eric Bocquet, Bernard D´ emoulin, and Jean-Philippe Parmantier Abstract—This paper presents the fundamentals of the so-called “Equivalent Cable Bundle Method” for the calculation over a large frequency range of common-mode currents induced on cable bun- dles by an electromagnetic (EM) perturbation. In particular, the method aims at overcoming the limitation of the multiconductor transmission line theory (MTLN), which is based on the propaga- tion of the quasi-transverse EM (TEM) mode and efficiently used only at “low frequencies.” The purpose of the method described here is to reduce the computation time by reducing the complex- ity of the cable bundle models. After a short presentation of the “high frequency” coupling problem, first, the theoretical basis of the method, and, second, the numerical and experimental valida- tions performed on prototypal cable bundles, in order to illustrate the efficiency and the advantages of the method, are presented. The method described in this paper is considered as a required first step in order to prepare wider applications on real systems in the near future. Index Terms—Cable bundle, cable harness, electromagnetic topology, numerical modeling. I. INTRODUCTION A S FOR many industrial domains such as aeronautics, the capability to generate a full numerical model of a car has become a strategic challenge in the automotive industry in order to improve the design and the production of future automobiles. To reach this goal, a huge effort is made in parallel to elaborate operative modeling techniques and to provide the required system input data (geometry, wiring, electrical circuits, etc.) to the models in the most efficient way. This paper addresses the particular aspect of cable bundle modeling techniques, which we call later “high frequencies (HFs),” typically above some gigahertz. Indeed, this frequency region is of particular interest for the possible interference generated by new HF sources such as Bluetooth or global system for mobile communication (GSM) devices. Manuscript received June 18, 2007; revised September 20, 2007. This work was supported in part by the IEMN Laboratory, University of Lille, Villeneuve d’Ascq, France, and in part by the RENAULT Company, Guyancourt, France. G. Andrieu was with the IEMN Laboratory, Group Telice, University of Lille, 59655 Villeneuve d’Ascq Cedex, France, and also with Renault Technocentre, 78288 Guyancourt, France. He is now with the Xlim Laboratory, University of Limoges, 87000 Limoges, France (e-mail: guillaume.andrieu@xlim.fr). L. Kon´ e and B. D´ emoulin are with the IEMN Laboratory, Group Telice, University of Lille, 59655 Villeneuve d’Ascq Cedex, France (e-mail: lamine.kone@univ-lille1.fr; bernard.demoulin@univ-lille1.fr). F. Bocquet is with Renault Technocentre, 78288 Guyancourt, France (e-mail: frederic.bocquet@renault.com). J.-P. Parmantier is with the Office National d’Etudes et de Recherches A´ erospatiales (ONERA), 31055 Toulouse, France (e-mail: jean- philippe.parmantier@onecert.fr). Digital Object Identifier 10.1109/TEMC.2007.911914 The multiconductor transmission line network (MTLN) the- ory provides efficient models to estimate electromagnetic (EM) coupling on a cable harness due to an electromagnetic excitation. The main advantages of the MTLN formalism applied on mul- ticonductor cable models are the calculation accuracy and the computation time reduction compared to numerical techniques that solve Maxwell’s equations (3-D codes). In the past 15 years, thanks to the use of electromagnetic topology formalism [1]–[3] for decomposing a complex elec- tronic system such as a car into elementary subsystems, the MTLN theory has led to efficient and encouraging calculations of complex systems [4], [5]. In the automotive domain, the field-to-TL approach is widely applied at the design level [6]–[8]. The 3-D computer codes are used to calculate tangential electric fields along the cable paths as a first step. As a second step, they are introduced as source terms in the MTLN cable harness models [9]–[11]. Moreover, over the last few years, automobile constructors have made efforts to develop precise numerical models of vehicles in which cable bundle models are the most accurate as possible. Unfortunately, the MTLN models become deficient when the height of the cable above a ground reference increases, with an averaged limit commonly set at a fifth of the wavelength. Various techniques have been proposed with success in order to extend their field of application [12]–[15]. However, in our study, we choose to keep using 3-D codes at “high frequen- cies.” Despite the constant progress in computer performance, it is still impossible to perform an accurate calculation on a realistic 3-D code model of an entire car including its metal- lic parts and its complete cable harness. This is mainly due to the computation time and the memory required for this kind of problem. Consequently, this paper presents a method that allows one to overcome this limitation with a methodology based on the reduction of the multiconductor cable complexity already addressed in several previous papers [16]–[18]. The so-called “Equivalent Cable Bundle Method” that we propose here only provides the common-mode current induced at the extremity of simplified cable structures. The main assumption is that, as far as EM coupling to the cable is concerned, the common-mode response is more critical than the differential-mode response. II. PROBLEM OF HF COUPLINGS ON CABLE BUNDLES A. Frequency Limitation of MTLN Formalism 1) Appearance of Additional Phenomena: It is well known that the MTLN theory is based on the propagation of a 0018-9375/$25.00 © 2008 IEEE