AP03_5.vp FDTD requires the computational domain to be lim- ited by boundary conditions. Two boundary conditions are used here, perfectly-electric conductors (PEC) and perfectly- -matched layers (PML). PEC’s are implemented by forcing the tangential component of the electric field along the boundaries to be zero (Etangential = 0). In the PML-technique, an artificial layer of absorbing material is placed around the outer boundary of the computational domain. The goal is to ensure an electromagnetic wave incident into the PML region at an arbitrary angle to be absorbed without reflection. The PML region is realized by implementing a new degree of freedom into the formulas of the FDTD code, which is done by splitting the field components [1]. Fig. 1 shows the dimensions of the house spacing under consideration from a top and side view. The house space under consideration is restricted to a volume of V � 4 2 8 2 5m m m. . . Five boundaries are consid- ered to be walls of ferroconcrete and therefore good reflectors for high-frequency signals, as used for mobile communica- tion. Hence these walls are simulated by PEC’s. The 6th boundary is considered to be a window/door combination and therefore electromagnetically transparent. In order to simulate the incidence of electromagnetic waves from radiat- ing antennas far away from the housing, the window/door boundary is simulated as source plane. For calculation, the direction of propagation needs to be taken into account, so the electric field vector of the incident wave is simulated on the source plane by decomposition into components. Simula- tion is performed by setting the components of the electric field strength Einc(z) and Einc(y) on the source plane according to the electric fieldstrength Einc of the incident electromag- netic wave on the window/door combination. The time-de- pendence is taken into account by setting the values of the components of the electric field strength on the source plane sinusoidally. Setting of the magnetic component was omitted, as magnetic and electric fields are related by the impedance of free space. Impedance-matched simulation of free space along the window/door combination (source plane) is assured by implementing PML’s. The PML structure numerically ab- sorbs the energy of the electromagnetic wave traveling from the interior of the housing space towards the environment. 2 Results As shown in Fig. 1a, numerical calculation was performed for an electromagnetic wave with magnetic and electric field vectors Hinc and Einc and direction of propagation k related to the dimensions of the defined Cartesian system. Investigation of the electric field strength inside the housing space was based on different angles of incidence within a range of 5 85� � � �� in steps of � step � �5 . For each angle of incidence a calculation was performed, until a steady state of the electric field inside the housing space could be observed. Data analysis was restricted to the last time inverval in a steady state. The last time interval was divided into 10 time- -points with equal time spacing. Fixing the angle of incidence of the propagating electro- magnetic wave, the maximum absolute value of the electric field strength Emax was detected within the housing space and within the chosen time points for steady state. In addition Emax was referred to the amplitude of the incident electric field strength Einc. Fig. 2 shows Emax /Einc over �. As may be seen, the maxi- mum electric field strength depends strongly on the angle of the incident electromagnetic wave, and the maximum value of the electric field strength inside the housing exceeds the value of the electric field strength of the incident wave. The maximum may be observed for � � �20 with a ratio E Einc max .� 2 5. This may be explained by reflections and superposition on the perfectly conducting walls of the housing space, particulary in corners and edges where supercomposition with reflected electric fields from several walls may occur. Taking into account the density of the electromagnetic energy being quadratically dependent on the electric field strength, it may be argued that the density of the energy may be in the worst case about 5 times higher than the energy density of the incident electromagnetic wave on the source plane. Conclusion From Fig. 2 it may be concluded that the effects of electro- magnetic radiation from antennas for mobile communication should not only be judged by their electric field strength in free-space or boundaries between free-space and housings. As electromagnetic waves with high frequencies may have nega- tive effects on humans, attention should be paid to legal limits for electromagnetic radiation from radio transmitters for mobile communication in the vicinity of housings. Legal lim- its referring to free space propagation of electromagnetic waves should be regarded with care, as under unfavourable conditions humans inside housings may be subjected to elec- tric field strengths which exceed the allowed limits. It should be taken into account that the effects of electromagnetic radi- ation on humans are quadratically dependent on the electric field strength, as these effects are mainly related to the ener- getic density of the electromagnetic waves, and therefore the negative impacts on humans increase disproportionately with electric field strength. © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 45 Acta Polytechnica Vol. 43 No. 5/2003 0 20 30 40 50 60 70 80 90 0 1 2 3 E Emax / inc 10 Angle of incidence [°] Fig. 2: Dependency of maximum electric field strength inside a housing space referred to incident electric field strength (Emax /Einc) over angle of incidence (�) References [1] Berenger, J. P.: A Perfectly Matched Layer for the Absorption of Electromagnetic Waves. Journal of Computational Phys- ics 114, 1994, p. 185–200. [2] Sadiku, M.: Numerical Techniques in Electromagnetics. CRC-Press, 2001, Second Edition, ISBN 0-8493-1395-3, p. 121–186. [3] Simonyi, K.: Theoretische Elektrotechnik. Deutscher Verlag der Wissenschaften, 10. Auflage, ISBN 3-335-00375-6. Dr. Ing. H.-P. Geromiller phone: +493 715 313 354 fax.: +49 3 715 313 417 email: hans-peter.geromiller@e-technik.tu-chemnitz.de Prof. Dr. Ing. habil. A. Farschtschi Technical University of Chemnitz Chair of Fundamentials of Electromagnetics 09111 Chemnitz, Germany 46 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ Acta Polytechnica Vol. 43 No. 5/2003