advertisement

Problem 2.75 Generate a bounce diagram for the voltage V (z,t) for a 1-m–long lossless line characterized by Z0 = 50 Ω and up = 2c/3 (where c is the velocity of light) if the line is fed by a step voltage applied at t = 0 by a generator circuit with Vg = 60 V and Rg = 100 Ω. The line is terminated in a load RL = 25 Ω. Use the bounce diagram to plot V (t) at a point midway along the length of the line from t = 0 to t = 25 ns. Solution: Rg − Z0 100 − 50 50 1 = = = , Rg + Z0 100 + 50 150 3 ZL − Z0 25 − 50 −25 −1 = = = . ΓL = ZL + Z0 25 + 50 75 3 Γg = From Eq. (2.149b), V1+ = Vg Z0 60 × 50 = = 20 V. Rg + Z0 100 + 50 Also, T= l 3 l = = = 5 ns. up 2c/3 2 × 3 × 108 The bounce diagram is shown in Fig. P2.75(a) and the plot of V (t) in Fig. P2.75(b). Voltage Γ = Γg = 1 3 z=0 Γ = ΓL = - 1 3 z = 0.5 m z=1m V1+ = 20V 5 ns -6.67 V 10 ns -2.22 V 15 ns 0.74 V 20 ns 0.25 V 25 ns -0.08 V t t Figure P2.75: (a) Bounce diagram for Problem 2.75. V(0.5 m, t) 20 V 20 V 13.34 V 5 10 11.12 V 11.86 V 12.10 V 15 20 25 Figure P2.75: (b) Time response of voltage. t (ns)