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FIGURE 8.6. The waveguide modes created by the corresponding image sources.
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Following Reference [2], we can also present the continuous spectrum of the total eld for x=d ) 1 as: c % p i 3p 1 jRn j eikx 2De 4 1 jRn j x 8:9
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For the case of a perfectly conductive waveguide, when jRn j 1, ZEM 0, we obtain that c 0, that is, in the case of the ideal conductive waveguide, the continuous part c of the total eld vanishes, and only the discrete spectrum of the normal waves propagates along the ideal waveguide without attenuation according to (8.8). Finally, the intensity of the total eld can be approximately obtained as I % b n c n c c where n c is the complex conjugate of n c . The path loss of the radio wave can be derived as [2] L % 32:1 20 log10 jRn j 20 log10 ( " 1 Rn 2 #
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1 jRn j2 ) pn x 17:8 log10 x 8:6 ln jRn j d r 0 d n
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where x is the distance between two terminals, receiver and transmitter, along the corridor. Analysis of the Waveguide Corridor Model. Let us present some examples of simulation of the total path loss L in decibels (dB) according to (8.10) versus
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FIGURE 8.7(a). Path loss for n 10 wave modes versus distance from the transmitter.
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distance between the transmitter and receiver. For our numerical computation, we considered the following parameters: the width of the corridor d 3 m, the conductivity of walls s 0:0133 S=m, and the signal frequency f 900 MHz [33]. The results of these path loss computations, according to (8.10), are shown in Figure 8.7a for the guiding modes with the number n varying from 1 to 10. For n > 3, the effect of these modes is negligible at ranges beyond 20 m, and we just have to subtract the attenuation from the rst two main modes of the original signal power in order to get the total power of a signal (in decibels) for each distance d between the transmitter and the receiver located along the corridor waveguide. This effect was also shown in Reference [2], where it was experimentally obtained that only one to two main modes are important in the range of ten and more meters from the transmitter. Therefore in Figure 8.7b, we present the total led attenuation, as a sum of the rst two waveguide modes, that fully describes the total path loss inside the corridor as a guiding structure versus the distance from the transmitter. We will compare this theoretical prediction of the path loss with the real experiment carried out in Reference [33] along the corridor. 8.2.3. Physical Model of Radio Propagation Between Floors and Walls Bertoni et al. [1,21,22] developed a theoretical model, based on the geometrical theory of diffraction (GTD), which explains the propagation between a transmitter and a
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FIGURE 8.7(b). Path loss for the rst modes versus distance from the transmitter.
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receiver located on different oors of a building. Depending on the structure of the building and the location of the antennas, either direct ray propagation through oors or diffraction outside the building will determine the propagation characteristics and the range dependence of the signal. There are two paths over which propagation can take place: (1) Paths that involve transmission through the oors; (2) Paths having segments outside the building and involving diffraction at window frames. The paths through the oors include the direct ray, the multiple-re ected rays, and the rays that are transmitted through semitransparent walls and oors. These rays are contained entirely within the building perimeter. The diffracted ray paths involve transmission outside the building through windows and diffraction into paths that run alongside the face of the building and then reenter through another window at a different oor. For propagation of the direct ray through semitrans-parent oors, as indicated by path T in Figure 8.8, extracted according to Reference [1], the electromagnetic eld strength in general reaching a receiving site is given by [21,22] jEj2 Y Z0 Pe Y 2 2 Tfloor;m Twall;n 2 4pL m n 8:11
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