Transmission Line Problems Example 1 A 50 lossless

Transmission Line Problems

Example 1 • A 50 -Ω lossless transmission line is terminated in a load with impedance ZL = (30− j 50) Ω. The wavelength is 8 cm. Find: – (a) the reflection coefficient at the load, – (b) the standing-wave ratio on the line, – (c) the position of the voltage maximum nearest the load, – (d) the position of the current maximum nearest the load.

Example 1 • A) • B)

Example 1 • The maximum value of the standing-wave pattern of corresponds to the position on the line at which the incident and reflected waves are in-phase.

Example 1 • The minimum value of voltage occurs when the two waves interfere destructively, which means when the incident and reflected waves are in phase-opposition

Example 1 • D) The maximum value of the current occurs at a voltage minimum

Homework

Example 2 • Using a slotted line, the following results were obtained: distance of first voltage minimum from the load = 4 cm; distance of second voltage minimum from the load = 14 cm; voltage standing-wave ratio = 1. 5. If the line is lossless and Z 0 = 50 W, find the load impedance.

Example 2 • Distance between two minimums

Example 2 • Voltage minimum occurs at

Example 2

Example 3 • A lossless transmission line of electrical length l = 0. 35 l is terminated in a load impedance as shown in Fig. Find Γ, S, and Zin.

Example 3

Homework

Example 4 • Two half-wave dipole antennas, each with an impedance of 75 Ω are connected in parallel through a pair of transmission lines, and the combination is connected to a feed transmission line, as shown in Figure • All lines are 50 W and lossless. (a) Calculate Zin 1 , the input impedance of the antenna-terminated line, at the parallel juncture. (b) Combine Zin 1 and Zin 2 in parallel to obtain Z′L, the effective load impedance of the feedline. (c) Calculate Zin of the feedline.

Example 4

Example 4

Example 5 • A 100 -MHz FM broadcast station uses a 300 Ω transmission line between the transmitter and a towermounted half-wave dipole antenna. The antenna impedance is 73 Ω. You are asked to design a quarterwave transformer to match the antenna to the line. (a)Determine the electrical length and characteristic impedance of the quarterwave section. (b) If the quarter-wave section is a two-wire line with d=2. 5 cm, and the wires are embedded in polystyrene with εr = 2. 6, determine the physical length of the quarter-wave section and the radius of the two wire conductors.

Example 5 a) For quarter wavelength line b)

Example 5 • For two wire line

Example 6 • If the two-antenna configuration shown in Figure is connected to a generator with Vg = 250 V and Zg = 50 Ω, how much average power is delivered to each antenna?

Example 6 • λ/2 length means impedance does not change • Two parallel 75 Ω means 37. 5 Ω at CD • Same case for the AB because of λ/2

Example 6 each antenna receives

Homework