ELC 4383 – RF/Microwave Circuits I
Chapter 2 Supplemental Homework
S2.1. The voltage on a transmission line is given as v(t) = 2 cos (2 x 1010 t – 35z) Volts. Find
(a) the frequency.
(b) the wavelength.
S2.2. A transmission line has the following parameters (per unit length): L = 0.4 μH/m, C = 120 pF/m, R
= 0, and G = 0.
(a) Is the line lossless? Why or why not?
(b) What is the characteristic impedance of the line at 3 GHz?
(c) What is the propagation constant of the line at 3 GHz?
S2.3. A lossless transmission line with Z0 = 80 Ω is terminated with a 15 Ω load.
(a) Find the load reflection coefficient.
(b) Find the standing wave ratio (SWR) on the line.
S2.4. Consider the circuit given below with a Z0 = 100 Ω, lossless transmission line terminated in a 90 Ω
load. Do not use the Smith Chart to solve this problem; use the necessary formulas.
l = 0.2λ, Z0 = 100 Ω
ZL = 90 Ω
Zin, Γin
ΓL
(a) Find ΓL, the reflection coefficient at the load.
(b) Find the SWR on the line.
(c) Find Γin, the reflection coefficient at the input of the line.
(d) Find Zin, the input impedance to the line.
2
S2.5. Consider the circuit given below with a Z0 = 50 Ω, lossless transmission line terminated in a 30 Ω
load. Do not use the Smith Chart to solve this problem; use the necessary formulas.
8Ω
l = 0.25λ, Z0 = 50 Ω
5V
ZL = 30 Ω
(a) Find Zin, the input impedance to the transmission-line section.
(b) Find the power delivered to the 30 Ω load. Use the following equation and the methods discussed in
class:
𝑃=
|𝑉0+ |2
(1 − |𝛤𝐿 |2 )
2𝑍0
S2.6. Consider the circuit given below with a Z0 = 50 Ω, lossless transmission line terminated in a 90 Ω
load. Do not use the Smith Chart to solve this problem; use the necessary formulas.
8Ω
l = 0.25λ, Z0 = 50 Ω
7V
(a) Find Zin, the input impedance to the transmission-line section.
(b) Find the power delivered to the 90 Ω load.
ZL = 90 Ω
3
S2.7. Consider the circuit given below with a lossless transmission line terminated in a (60 + j30) Ω
load. Use the Smith Chart to find the following:
l = 0.20λ, Z0 = 50 Ω
ZL = (60 + j30) Ω
Γin
ΓL
(a) Find ΓL, the load reflection coefficient.
(b) Find Γin, the input reflection coefficient.
(c) Find Zin, the input impedance, in Ohms
(d) Find 𝑌𝑖𝑛 , the input admittance, in Siemens.
S2.8. Consider the circuit given below with a lossless transmission line terminated in a (30 + j25) Ω
load. Use the Smith Chart to find the following:
l = 0.15λ, Z0 = 50 Ω
ZL = (30 + j25) Ω
Γin
(a) Find ΓL, the load reflection coefficient.
(b) Find Γin, the input reflection coefficient.
(c) Find Zin, the input impedance, in Ohms.
(d) Find Yin, the input admittance, in Siemens.
ΓL