ECE 6130 LECTURE 5 Text Section: 2.5,6 Portfolio: For a terminated lossless transmission line: 1) Describe how to find the voltage at any point on the line as a function of time 2) Describe how to find the voltage along the line at any point in time. TRANSIENTS ON TRANSMISSION LINES Note definition of z axis is different from previous work. Equivalent circuit at initial time (t=0) The switch is closed, no voltage has moved down the transmission line. All the generator “sees” is Zo … ZL is too far away. I1+ = Vg / (Rg + Zo) Å + means positive-traveling wave, “1” means first wave V1+ = I1+ Zo = Vg Zo/ (Rg + Zo)Velocity of wave vp = 1/ sqrt(εμ) Wave moves down TL with no reflections until it reaches the load … Time to reach load: T = L / vp Wave reflects off load and starts back. V1- = ΓL V1+ ΓL = (ZL – Zo) / (ZL + Zo) (For ZL = 2 Zo, ΓL = 1/3 Å This is real … what happens if it is complex? Get phase change as well as reflection.) Wave V1- now reflects off generator. New +-traveling wave is produced: V2+ = = Γg V1- Γg = (Zg – Zo) / (Zg + Zo) Notice that reflections are getting progressively smaller.Waves keep reflecting until STEADY STATE is reached: (additional reflections are negligibly small) V∞ = Vg ZL / (Rg + ZL) Å Voltage on line at steady state. This is the SAME as we would have observed in the DC case! I∞ = V∞ / ZL = Vg / (Rg + ZL) BOUNCE DIAGRAMS Axes: Time and distance V1- = Γ L V1+ V2+ = Γ g V1- = Γ g Γ L V1+ V2- = Γ L V2+ = Γ g Γ L2 V1+ How to find V(z,t) for any z and t: 1. Find the point (z,t) on the bounce diagram (eg. Z= L/2, t = 3T) 2. Draw a line back to T=03. Add up all of the V traces you cross V(L/2,3T) = V1+ + V1- + V2+ Example :