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Unformatted text preview: 39 Lossy lines z C z z + z z L +- z C z z + z V ( z ) I ( z ) z L +- I ( z + z ) z R z G IDEAL LOSSLESS T.L.: REALISTIC LOSSY T.L.: I ( z + z ) I ( z ) V ( z ) Lossless TLs we have been studying so far are idealizations of real TLs which are invariably lossy . Here, we are making reference to Ohmic energy losses in the conducting wires of the TL, as well as to losses in the imperfect dielectric separating the two conductors. The effect of wire losses in TLs is modelled by adding a z R resis- tance in series with z L inductor in the equivalent circuit model of an infinitesimal ( z ) TL section as shown in the margin. In addition, a shunt conductance z G in parallel with capacitance z C accounts in the lossy model for dielectric losses. Using perturbation theory, it can be shown that for a coax of inner and outer radii a and b , R = f ( 1 a + 1 b ) , while for a parallel-plate transmis- sion line of width W , R = 4 W f , in terms of conductivity and per- meability of the T.L. conductors....
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- Summer '10