IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 47, NO. 1, FEBRUARY 2005 61 Generalized Transmission-Line Model for Estimation of Cellular Handset Power Absorption in Biological Tissues Daniel Razansky, Diana F. Soldea, and Pinchas D. Einziger Abstract—Evaluation of cellular handset power absorption in biological tissues has recently received due public attention. Generally, the solution of even simple cellular phone-human head configurations, involves massive and time consuming excitation of numerical algorithms. Furthermore, an explicit dependence of numerical solution on the physical parameters as well as on the configuration geometry is usually difficult to achieve. Herein, we focus on a generalized one-dimensional transmission-line model, which is capable of establishing tight bounds and estimates on the actual power absorption and radiation for many realistic configu- rations. The solution is given by explicit closed-form expressions, which depend continuously on the physical and geometrical parameters of the problem and, thus, can be readily physically interpreted. The potential promise of our simplified model is numerically verified via alternative finite-difference time-domain and moment method data for cellular handsets closely coupled to human head. Index Terms—Absorption efficiency, biological tissues, cellular handsets, radiation efficiency. I. INTRODUCTION C ELLULAR handset power absorption in biological tissues has recently become of increased scientific and public in- terest (e.g., [1] and [2]). Generally, the solution of a specific cellular phone-human head configurations involves massive and time consuming excitations of numerical algorithms, e.g., the method of moments (MoM) [3], the finite-difference time-do- main (FDTD) technique [4], [5], the coupled integral equations (CIE) procedure [3], and the multiple multipole algorithm [6]. While numerical methods are capable of supporting geometri- cally precise models and achieving accurate results, an explicit dependence of the numerical solution on the physical parame- ters as well as on the configuration geometry is usually difficult to achieve. Herein, we focus on a simplified one–dimensional (1-D) transmission-line model, commonly utilized in first-order prototype problems (e.g., [7]–[9]). This model, being directly associated with the problem of a plane wave incidence upon a lossy half-space [10]–[12], is extended to incorporate a generalized dual mode (TE and TM) excitations, enabling to establish tight bounds and estimates on the power absorption and radiation efficiencies in realistic cellular phone—human Manuscript received December 20, 2003; revised May 7, 2004. The authors are with the Department of Electrical Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel (e-mail: danir@tx.technion.ac.il). Digital Object Identifier 10.1109/TEMC.2004.838229 head configuration. These bounds and estimates are a direct consequence of the (TE and TM) modes orthogonality property in conjunction with the fact that the TEM mode power absorp- tion efficiency is the least for handset radiating in close vicinity of the human head. However, they are shown to be valid only for electric type sources. The power absorption and radiation efficiencies for the generalized transmission-line model are given via explicit closed-form expressions, which depend continuously on the physical and geometrical parameters of the problem and, thus, can be readily physically interpreted. Finally, the potential promise of our simplified model is nu- merically verified via an alternative FDTD and MoM data for several numerical models of cellular handsets closely coupled to human head [3]–[5]. II. FORMULATION The physical configuration, depicted in Fig. 1(a), consists of a cellular handset in close vicinity of a human head. Assuming that both the “planar” cellular handset and the human “flat” head are confined to the plane and the lossy half-space , respectively, results in a simplified configuration, as depicted in Fig. 1(b). The current sheet at , corresponding to the electric current distribution of the cellular handset, gener- ates an electromagnetic field, which, in general, can be uniquely decomposed into TE and TM orthogonal plane-wave modes. Thus, upon representing the electric current-sheet, depicted in Fig. 1(b), via one of the two elementary excitations, namely (1) where , , and , the corresponding modes propagation is governed by the general- ized transmission-line model [13], [14], depicted in Fig. 1(c). To obtain tight estimates and bounds on the cellular handset power absorption in the human head [see Fig. 1(a)] we analyze herein the power relations associated with this generalized trans- mission-line (simplified) model. The model consists of a point current source [see Fig. 1(c)], located at in a semi-in- finite lossless line , exciting a semi-infinite lossy line , acting as a load. Both transmission lines are char- acterized by the parameters , , and , via , , , and , , where, assuming a harmonic time dependence , and . Since only transverse components of the electromagnetic field, and , are rele- 0018-9375/$20.00 © 2005 IEEE