Engineering 6813 Tutorials 8 and 9 (Transmission Lines)
Fall, 2010
1. For the transmission line shown below, find 𝑉out if (a) 𝑓 = 60 Hz and (b) if 𝑓 = 500 kHz.
12 Ω
120 ∠0 V
°
+
–
+•
Vin
–•
Lossless, vP = 2c/3
Z0 = 50Ω
80 m
•+
Vout
•–
80 Ω
2. At a frequency of 80 MHz, a lossless transmission line has a characteristic impedance of 300 Ω and a wavelength
of 2.5 m. (a) Find 𝐿. (b) Find 𝐶. (c) If the line is terminated in a parallel combination of 200 Ω and 5 pF,
determine Γ and 𝑠.
3. Determine the average power dissipated in each resistor shown at the ends of the 50 Ω transmission line for
which the velocity factor is 2/3.
25
lossless, Z0 = 50Ω
5.3
100 V at 0o
100
4. The input impedance of a lossless air line operating at 500 MHz is (0.8 − 𝑗1.25)𝑍0 . Use analytic methods and
the Smith chart to find (a) the SWR; (b) 𝑧𝐿 if the load is located at the voltage minimum nearest to the input;
(c) the distance from the input to the load. (d) Repeat (b) if the voltage minimum is replaced with a voltage
maximum.
5. A 50 Ω lossless transmission line is terminated in a load impedance 𝑍𝐿 = (25 + 𝑗50) Ω. Use the Smith chart
to find (a) the voltage reflection coefficient, (b) the VSWR, (c) the distance of the first voltage minimum from
the load, (d) the input impedance of the line, given that the line is 3.3𝜆 long, and (e) the input admittance of
the line. (Taken from Fundamentals of Applied Electromagnetics by Ulaby, 1999, Prentice Hall.)
6. Given that the vswr is 3 on a 50 Ω line, the first voltage minimum occurs at 5 cm from the load, and that the distance between successive minima is 20 cm, find the load impedance. (Taken from Fundamentals of Applied Electromagnetics
by Ulaby, 1999, Prentice Hall.)
Also, do problems 11.20 and 11.30 from the text.