TransmissionLines - EEL 3472 EEL 3472 Transmission...

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Unformatted text preview: EEL 3472 EEL 3472 Transmission Transmission Lines Lines EEL 3472 EEL 3472 2 Cross-sectional 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 lumped-circuit transmission-line 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 cross-sectional 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(z-Ut) 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 = Z-Ut...
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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.

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TransmissionLines - EEL 3472 EEL 3472 Transmission...

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