Question

(4) A voltage source of V40-V cos (ot) (o-2 π. 106 rad/s) drives a transmission line (Zo -100 Ω, length λ/8) terminated with a resistor R1 00 Ω in parallel with an inductor L -16 μΗ. What are the input impedance, the input voltage Vin (t) and load voltage VL(t)? What power is dissipated in resistor R? 2 -100

Answer 1

Given: A transmission drives with a voltage source V_s (t) = V cos (omega t) where: (omega = 2 pi times 10^6 rad/sec) Z_0 = 100 Ohm length = lambda/8 Resistor, R = 100 Ohm in parallel with an Inductor L = 16 mu H. Now, we determine the input impendence, input voltage V_in (t), and load voltage V_L (t) and what power is dissipated in resistor R. The impedance of inductor at 1 MHZ is jwL = j (2 pi times 10^6) (16 times 10^-6) almostequalto j 100 Ohm The parallel combination of the inductor and the resistor gives a total load impedance of Z_L = R (jwL)/R + jwL = 100 (100 j)/100 + j 100 Z_L = 50 \r\n Let us calculate the input impedance of the transmission line Z_in = Z_0 [Z_L + j Z_0 tan kl/Z_0 + j Z_L tan kl] substitute Z_0, Z_L values in above equation. Z_in = 100 p50 (1