ECE 329
Homework 1
Due: Sept. 2, 2014, 5PM
1. Consider the 3D vectors
A = 2 y + 4,
x
z
B = + y + z ,
x
C = 4 2,
y
z
where
x (1, 0, 0), y (0, 1, 0),
and
z (0, 0, 1)
constitute an orthogonal set of unit vectors
directed along the principal axes of a right
ECE 329
Homework 13 Solutions
Due: Tuesday, Dec 2, 2014, 5 PM
1.
a) Considering that the lossless TL has no electrical connection to any elements at either end, each
resonant mode (or standing wave) will have a resonance frequency
f=
where
n1
n,
2
. There
ECE 329
Homework 12 Solutions
Due: Tue, Nov. 18, 2014, 5PM
1. The associated circuit is shown in the following gure:
a) In this circuit, the
injection coecient
is found as
g =
1
Zo
=
Rg + Zo
2
The load voltage reection coecient is given by
LV =
RL Zo
10
ECE 329
Homework 11
Due: November 11, 2014, 5PM
1. A monochromatic plane wave propagating in a vacuum in the region z < 0 has an electric eld phasor
given by
Ei = (j x y )e j2z V/m
The wave encounters a planar boundary at z = 0 which separates the vacuu
ECE 329
Homework 8 Solutions
Due: October 21, 2014, 5PM
1.
a) The vector wave eld E(x, t) is given by
E(x, t) = 5(
t + y/c V
)z .
m
b) The associated wave eld H(x, t) is
H(x, t) =
5
t + y/c
A
(
)x .
o
m
c) The Poynting vector is
S=EH=
25 2 t + y/c
W
(
)
ECE 329
Homework 9 Solutions
Due: Tues, October 28, 2014, 5PM
1.
a) Assuming the material is a perfect dielectric,
i. Impedance is given by
=
and the velocity
r
=
r
o
o
= p = 108.83
r o
12
1
c
m
v = p = p = 8.66 107
s
12
ii. Wavelength in the medium can
ECE 329
Homework 10 Solutions
Due: Tue, November 4, 2014, 5PM
1. The electric eld phasor of a plane wave is given by
E = 2e(0.00005+j0.1)z y m .
V
a) We know that the propagation velocity, also called phase velocity, is
wave frequency
b) Wavelength is
0.1
ECE 329
Homework 9
Due: TUESDAY, October 28, 2014, 5PM
1. Give the requested for the three electromagentic waves described in (a), (b), and (c):
a) = o and " = 12"o , electric eld linearly polarized in the x direction, poynting vector in the
y direction,
ECE 329
Homework 10
Due: November 4, 2014, 5PM
1. A plane TEM wave propagating in a material medium has an electric eld phasor
V
E = 2e
y .
m
Clearly, = + j = 0.00005 + j0.1 1/m, with .
When is true, then all the wave parameters , , v , and expressed in t
ECE 329
Homework 8
Due: October 21, 2014, 5PM
1. A z -polarized plane TEM wave is propagating in vacuum (i.e., v = c 3 108 m/s and =
o 120 ) in the direction. If in the wave eld varies at y = 0 with time according to
y
t
t
Ez (0, t) = 5( ) V/m, where = 40
ECE 329
Homework 11 Solutions
Due: November 11, 2014, 5 PM
1. For a wave propagating in a vacuum in z < 0, we are given an incident electric eld phasor
Ei = (j x
y )e
j2z
V
.
m
The wave encounters a boundary at z = 0 with = o and the reected phasor is giv
ECE 329
Homework 13
Due: Tuesday, December 2, 2014, 5PM
1. Consider a lossless TL which is open circuited at both ends. If
v = 1 c = 1.5 108
2
l=6
m is the length of the line, and
m/s for the line,
a) What are all the resonance frequencies of the line fre
ECE 329
Homework 12
Due: Nov. 18, 2014, 5PM
Zo = 50 , length l = 900 m, and propagation velocity
f (t) with an internal resistance Rg = Zo is connected to
one end of the T.L. (at z = 0) and the other end (z = l) is terminated by a load resistance RL = Zo
ECE210 - Spring 2011 - Homework 01 Solutions
Kudeki and Munson, Chapter 1, Problems 1,3,5,7,8,10,11,and 14
1. Problem 1.1 from text
Solution:
2. Problem 1.3 from text
Solution:
1
3. Problem 1.5 from text
2
Solution:
4. Problem 1.7 from text
Solution:
5. P
ECE 329
Homework 14 Solutions
Due: Tuesday, Dec. 9, 2014, 5 PM
1.
a) The direct approach is to nd the voltage and current at the load. Knowing the voltage and
impedance at the load, we can nd:
VL = j20 V
VL
j20
IL =
=
= j0.16 A
RL
125
1
PL =
Recfw_VL IL
ECE 329
Homework 14
Due: TUESDAY, Dec. 9, 2014, 5PM
VL = j20 V with source
RL = 125, and
Zo = 50 with wave velocity
1. In the transmission-line circuit shown below the voltage at the load is
impedance
Zg = 25.
The operating frequency is 200 MHz, the load
ECE 329
Homework 5
Due: Sept. 30, 2014, 5PM
1. Gausss law for magnetic eld B states that the surface integral S BdS = 0 over any closed surface S
2
enclosing a volume V . Given that B = 5R2 x + R2 sin(y) + R2 z and L=4R, determine the magnetic
2
y 3
ux
ECE 329
Homework 7 Solutions
Due: Tue, Oct 14, 2014, 5PM
1.
a) Seeing that this is an RC circuit, the time constant, , is equal to R C . We know that slab =
1.3air and and have some slab of width d and area A. Then, we can nd the time constant.
= RC
= R(
E CE 210
Analog Signal Processing
University o f Illinois
Spring 2009
Basar, Franke, Beauchamp
Exam 3
Thursday, April 23, 2009 - 7:00-8:15 PM
Name:
Section:
(circle one)
9 AM
1 PM
2 PM
Please clearly PRlNT your name IN CAPITAL LETTERS and circle your sect
MATH 286 G1 and X1 Ordinary Dierential Equations Fall 2010
PROFESSOR: Jared C. Bronski ([email protected])
OFFICE HOURS: To be arranged rst week of class, or by appointment1 . 375 Altgeld Hall 244 x 8218 LECTURES: MTWTh 12:00 12:50 ( 156 Henry Admin Bui
Problem 1 (25 points)
a) Given J(t) = a e-atu(t) B F(OJ) =
1 a. . Find the bandwidth W defined as IF(W)12 = 2 a + Jm (half power bandwidth) [your result will be in terms of a].
_
\ F~ )12- :
Ti IbJ-YJ- en. Z;:' 2-1
I + ~)'
Explain.
!.-
~
I +-L~'~; W:= 0/
ECE 2l0t2tl Universityo f I llinois
Analog S ignal P rocessing
Spring2 008
Basar, H asegawa-Johnson, rick T
Exam2
Thursday, arch1 3,2 008 7 :00-8:15 M M P
Name:
Section: circle o ne Class:
9AM
lPM
2PM
ECE2 IO
ECE 2II
circle one Please learlyPRINT your nam