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Unformatted text preview: EEL 3472 EEL 3472 Transmission Transmission Lines Lines EEL 3472 EEL 3472 2 Crosssectional view of typical transmission lines (a) coaxial line, (b) two wire line, (c) planar line, (d) wire above conducting plane, (e) microstrip line. (a) Coaxial line connecting the generator to the load; (b) E and H fields on the coaxial line Transmission Lines Transmission Lines EEL 3472 EEL 3472 3 Electric and magnetic fields around single phase transmission line Stray field Triplate line Transmission Lines Transmission Lines EEL 3472 EEL 3472 4 Transmission Lines Transmission Line Equations for a Lossless Line Lh L h = Ch C h = The transmission line consists of two parallel and uniform conuductors, not necessarily identical. Where L and C are the inductance and capacitance per unit length of the line, respectively. Transmission Lines Transmission Lines EEL 3472 EEL 3472 5 By applying Kirchhoffs voltage law to N  (N + 1)  (N + 1)  N loop, we obtain If node N is at the position z , node (N +1) is at position z + h , and h v v dt di L v v dt di L N N N N N N h = = + + 1 1 ) ( z i i N = h z v h z v z i dt d L ) ( ) ( ) ( + = Definitions of currents and voltages for the lumpedcircuit transmissionline model. dt di L N h Transmission Lines Transmission Lines N (N+1) i NS EEL 3472 EEL 3472 6 Since h is an arbitrary small distance, we can let h approach zero Applying Kirchhoffs current law to node N we get from which L t i ( z ) =  lim h 0 v ( z + h )  v ( z ) h L t i ( z ) =  z v ( z ) ) ( ) ( 1 z i z z v t C i i dt dV C i N N N h NS  =  = = Transmission Lines Transmission Lines EEL 3472 EEL 3472 7 2 2 2 z v z t i L  = L i t =  V z C V t =  i z t z i t v C  = 2 2 2 Telegraphers Equations All crosssectional information about the particular line is contained in L and C 2 2 2 2 z v t v LC  = 1 2 2 2 2 = z v t v LC Wave Equation Transmission Lines Transmission Lines EEL 3472 EEL 3472 8 Waves on the Lossless Transmission Line Roughly speaking, a wave is a disturbance that moves away from its source as time passes. Suppose that the voltage on a transmission line as a function of position z and time t has the form V(z,t) = f(zUt) U = const This is the same function as f(z) , but shifted to the right a distance of Ut along the z axis. The displacement increases as time increases. The velocity of motion is U . f(x) has its maximum where x = z Ut = 0, and the position of maximum Z max at t = t o is given by Z max = Ut o x = ZUt...
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This note was uploaded on 09/26/2011 for the course EEL 3211 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff

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