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Unformatted text preview: Cunningham ECE329 Lecture 38 TL With Initial Conditions Lecture 38 Cunningham ECE329 Lecture 38 Two kinds of initial conditions we will discuss in ECE329 Place a voltage and current distribution on the line that varies in magnitude along the length of the TL Charge the entire line to a constant nonzero voltage and current, and then open/close a switch Cunningham ECE329 Lecture 38 Initial Conditions Place an initial voltage and/or current distribution on the TL Z z=0 z=l T We will consider a transmission line that is opencircuited on both ends, and place a voltage distribution and a current distribution on the line at t=0. Cunningham ECE329 Lecture 38 Z z=0 z=l T z V(z,0) Arbitrary initial voltage distribution What happens to this initial voltage distribution on the TL for t>0? Cunningham ECE329 Lecture 38 Z z=0 z=l T z V(z,0) The voltage (made up of charges on the TL) will begin to dissipate by forming + and  waves. Cunningham ECE329 Lecture 38 Z z=0 z=l T=1 sec z V(z,0) Eventually the + and  waves will reach the ends of the TL, where they will be reflected back! Cunningham ECE329 Lecture 38 At t=0+ V ( z ,0) = V + ( z ,0) + V " ( z ,0) I ( z ,0) = I + ( z ,0) + I " ( z ,0) Initial distribution Initial + wave Initial  wave Also, as usual: I + = V + Z I " = " V " Z Cunningham ECE329 Lecture 38 Solving (still at t=0) I ( z ,0) = I + ( z ,0) + I " ( z ,0) Z I ( z ,0) = V + ( z ,0) " V " ( z ,0) V + ( z ,0) = 1 2 V ( z ,0) + Z I ( z ,0) ( ) V " ( z ,0) = 1 2 V ( z ,0) " Z I ( z ,0) ( ) Initial + and  voltage waves derived from initial voltage and current distribution on the TL. Cunningham ECE329...
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 Summer '08
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