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Lect38TLInitConds

# Lect38TLInitConds - TL With Initial Conditions L e c tu r e...

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Cunningham ECE329 Lecture 38 TL With Initial Conditions Lecture 38

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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 0 z=0 z=l T We will consider a transmission line that is open-circuited on both ends, and place a voltage distribution and a current distribution on the line at t=0.

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Cunningham ECE329 Lecture 38 Z 0 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 0 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.

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Cunningham ECE329 Lecture 38 Z 0 z=0 z=l T=1 μ 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 0 I " = " V " Z 0

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Cunningham ECE329 Lecture 38 Solving (still at t=0) I ( z ,0) = I + ( z ,0) + I " ( z ,0) Z 0 I ( z ,0) = V + ( z ,0) " V " ( z ,0) V + ( z ,0) = 1 2 V ( z ,0) + Z 0 I ( z ,0) ( ) V " ( z ,0) = 1 2 V ( z ,0) " Z 0 I ( z ,0) ( ) Initial + and - voltage waves derived from initial voltage and current distribution on the TL.
Cunningham ECE329 Lecture 38 Example. TL w/ Z 0 =50 Ω

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