Question

Problem 2 A transmission line configuration, shown below, is use in a communications system to divide power. The frequency is 100 MHz and all transmission lines are considered ideal and lossless. The values of 2,2 = 225Ω, 2, = 50Ω, Zo,3 = 50Ω, and L3 = 0.75 meters. (a) Determine the shortest line lengths for Li and L2 and their corresponding charac- teristic impedances Z2, Z1 to give equal power (Zi into the two loads (eg into Z2, and Z) and also have Zin-50 Ω. (Hint: Use L1 and L2 to be λ/4 transformers.) EE 330 Spring 2019 (b) Suppose the 225 2 resistor suddenly shorts out (02): then find the corresponding Zin for this situation. (Use the lengths Li and La and the characteristic impedances Zo.i and Zo2 that you found in part (a).) (c) Determine the VSWR on transmission line Ls, using the results of part (b). Solve this part using the Smith Chart. L1, Zo.1 L3, Zo,3 る Zin L2, Zo.2

Answer 1

Given that: A transmission line configuration shown below is use in a communications system to divide power lambda = c/f = 3 times 10^8/10^8 = 3m rightarrow c_3 = lambda/4 = 0.75 m due to z_1 in = z_01^2/z_1 = z_0^2/50 ohm z_in 1 = (z_03)^2/z_01^2/50 --- (1) rightarrow due to z_z rightarrow z_in^1_2 = (z_02)^2/z_2 = z_02^2/225 ohm z_in_ = (z_03)^2/(z_0z^2/225) --- (2) \r\n rightarrow z_in 1 = z_in 2 rightarrow (z_02)^2/225 = (z_01/50)^2 rightarrow z0^2/z0_1 = 2.121 --- (3) rightarrow calculating z_in z_in Vertical-bar Vertical-bar z_in^1_2 = z_01^2/50(z_02^2/225)/z_01^2/50 + z_02^2/225 = (z_01 z_02) /11250 = (z_01)^4/11250 (4.5)/z_01^2 (0.04) = z_01^2 (0.01) ohm z_in = z0^2[z_01^2(0.01)] 50 = 2500 times 10^2/(z01)^2 rightarrow z_01^2 = 5000