Download hw2-s04 - Rensselaer Polytechnic Institute

Fields and Waves I
ECSE 2100 Spring 2004
Name
Section
Homework 2
Due 5 February 2004
Note: You will need to use PSpice for this homework. Information regarding PSpice and
where to obtain it is provided on the course website. Click on “Class Information” and
then, on the left side, click on “Projects”. In the main frame, there is a link to a pdf-file
“Design with PSpice”. At the beginning of this file is link on where to get an evaluation
copy of PSpice. Alternatively, the computers in the classroom have PSpice. The pdf-file
provides a detailed description on implementing PSpice for problems in this course.
ZS1
75
T1
Z0 = 150
V
V
V
1. Input Impedance
Zl
VS
300
0
0
The above poorly designed lossless transmission line circuit has a length of 300 [m] and
the velocity of propagation is 3E8 [m/s]. Assuming a 1E6 [Hz] source frequency and a
10 [V] source amplitude, determine the input voltage, Vin, and load voltage, Vl.
Include a phase term relative to the source phase. The phase of the source is zero. Express
your solution in time domain form.
Hint: This problem is identical to the one in lesson 1.5. You need to find Zin and V+, both
of which are complex.
Verify your solution by implementing the circuit in PSpice. Include the plots in your
homework.
L.T.Ergene and D.Michael
Rensselaer Polytechnic Institute
Page 1
1/18/03
Troy,New York, USA
1
Fields and Waves I
ECSE 2100 Spring 2004
Name
Section
2. Lossy Lines
Consider a high speed microstrip transmission line of length 30 cm used to connect a 1.5
V amplitude 1 GHz, 50 [Ω] sinusoidal voltage source to a digital logic gate having a
input impedance of 1 [kΩ], as shown below. Based on measurements, the transmission
line parameters at 1 GHz are approximately given by R′=5 [Ω/cm], L′=6 [nH/cm],
C′=0.5 [pF/cm] an G′=0.
a) Find the propagation constant γ and characteristic impedance Z0 of the line.
b) Find the voltages at the source and the load ends of the line.
c) What is the power dissipation along the line?
50Ω
Microstrip
V1
20 cm
j0° (V)
1e
1 kΩ
0
1 GHz
0
3. Load Matching
A 50 [Ω] lossless line is to be matched to an antenna with ZL=(75-j20) [Ω] using a
shorted stub. Use the Smith Chart to determine the stub length and distance between the
antenna and stub.
Solve the same problem for a load with ZL= (150+j50) [Ω].
Include your Smith Chart drawings in your homework.
L.T.Ergene and D.Michael
Rensselaer Polytechnic Institute
Page 2
1/18/03
Troy,New York, USA
1
Fields and Waves I
ECSE 2100 Spring 2004
Name
Section
4. Transients on Transmission Lines
In response to a step voltage, the voltage waveform shown below is observed at the
sending end of a shorted line with Z0=50 [Ω] and εr=4. Determine Vg, Rg, and the line
length.
V (0,t)
16 V
4V
1V
t
0
L.T.Ergene and D.Michael
Rensselaer Polytechnic Institute
7 μs
14 μs
Page 3
1/18/03
Troy,New York, USA
1