University of Illinois
Spring 2016
ECE 310: Problem Set 13
Due: 5pm, April 29, 2016
1. Complete the following signal flow diagram (butterfly structure) of a 4-pt, radix-2, decimation-intime FFT algorithm. Specify all the connection weights and determine t
ECE-329
Spring 2009
Homework 4 Solution
February 18, 2009
1. Curl and divergence exercises. a) F = x x + y y
2 1 y -axis 0
1 2 2 1 0 x -axis 1 2
Curl F= Divergence b) F = y x x y
2 1 y -axis 0
x x x
y y y
z z 0
= 0.
F=
(x) + (y ) = 1 + 1 = 2 . x y
1 2
ECE 329
Homework 3
1. Given that V (x, y, z) = 4x2 y
yz 2 and E =
Due: Fri, June 27, 2014, 5PM
rV , what is r E?
2. Is E = 2 + 4z 2 x a possible electrostatic eld? Discuss.
x
y
3. An important vector identity which is true for any vector eld A(x, y, z) is
ECE 329
Homework 6
Due: Tue, July 8, 2013, 5PM
1. In this problem we will compare the magnitudes of electrical force qE and magnetic force qv B on
a moving test charge q due to elds E and B produced by another charge Q at some distance r.
Q
. Also let B t
ECE 329
Homework 2
Due: Jan 28, 2008, 5PM
1. In this problem we will compare the magnitudes of electrical force qE and magnetic force qv B on a moving test charge q due to elds E and B produced by another charge Q at some distance r. a) Let E be
ECE 329
Homework 4 Solutions
Due: Tue, June 27, 2016, 5PM
1.
a) In vacuum, the displacement vector is D = o E + P. Thus, the displacement field between the
plates is
C
D = 4o z 2 ,
m
from which we obtain the polarization field as P = 0 mC2 .
b) Since D =
ECE 329
Homework 7 Solutions
Due: Fri, July 8 2016, 5PM
1.
a) The 2-D sketch of the described configuration is shown below.
y(m)
3
1
2
-1
x(m)
1
1
-1
4
b)
i. Case : |x| < 1, and |y| < 1
The magnetic field distribution of the system of current sheets in th
ECE 329
Homework 6 Solutions
Due: Wed, July 6, 2016, 5PM
1.
a) The capacitance of the capacitor will be
C=
A
o (2 102 )2
=
2.23 pF.
d
5 103
b) The conductance of the same capacitir will be
G=
A
103 (2 102 )2
= 8 105 S,
=
d
5 103
whereas corresponding res
ECE 329
Homework 5 Solutions
Due: Thu, June 30, 2016, 5PM
1.
S are fresh water, ground conductivity of
a) Examples of materials with conductivity near 103 m
S
S
S
3
4
Earth (10 m ), dry earth (10 m ), and wet earth (102 m
).
b) Examples of materials with
ECE 329
Homework 3 Solutions
Due: Fri, June 24, 2016, 5PM
1. In electrostatics, we generate a curl-free vector field E(x, y, z) if we take the gradient of a scalar
function V (x, y, z). Therefore, E = (V ) = 0.
2. Maxwell equations for electrostatics stat
ECE 329
Homework 8 Solutions
Due: Tue, July 12, 2016, 5PM
1. Since the closed paths are not varying in time and the magnetic field B is independent of position,
we can rewrite Faradays law as follows
E=
I
C
E dl =
dB
dt
Z
S
dS =
dB
n
Area,
dt
where n
ECE 329
Homework 6 Solutions
Due: Wed, July 9, 2013, 5PM
1.
a) Referring to the hint, we expect E, B, and Vs to be orthogonal to one another. Based on this
assumption, we can write
Q
|E| =
4o r2
for the magnitude of the electric eld, and
|B| =
o I|dl|
4r2
ﬂ: 66.?2/rr/ meniaéo , e/snrzq
ECE 329 Fields and Waves I Summer 16
Kudeki
Exam 1
Fri, July 1, 2016 — 11 AM - 11:50 AM
Name:
- 99 . rm
Please clearly PRINT your name in CAPITAL LETTERS and circle your section in the above boxes.
This is a closed book ex
ECE 329
Homework 8 Solutions
Due: Tue, July 15, 2014, 5PM
1.
a) Solution of the left-hand side of the Faradays law r E =
x
rE=
y
z
@
@x
@
@y
@
@z
0
cos(!t + x)
which must be equal to
@B
@t .
@B
@t
is given by
@
(sin(!t + x) z =
@x
=
0
sin(!t + x),
z
Thus,
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5411 I = lrlln- .II- n'J-n at I lll'HIIJIIIII-'a' .r "' HI" "I 1Ilr' H IIFIII IIr InI-mm-il rrr haw l rrLapurLLd- nl'
Eli .JL.-'
ECE 329
Homework 2 Solutions
Due: Tue, June 21, 2016, 5PM
1.
a) Expressing the equation
H
S
D dS =
R
V
dV in terms of its units, we write
D=
[ mC3 ] [m3 ]
c
= [ 2 ].
2
[m ]
m
This makes sense because electric displacement gives the electric flux density.
ECE 329
Homework 9 Solutions
Due: Thu, July 14, 2016, 5PM
1.
a) Referring to the hint, we should first find the divergence of the current density. Thus, we write
J=
2
3
4z +
3x y +
2z(y yo )2 = 3x3 + 2(y yo )2 .
x
y
z
Then, taking the integral of bot
ECE 385 Digital Systems Laboratory
Lecture 21 Sound on the DE2-115
Zuofu Cheng, Deming Chen
Spring 2016
Link to Course Website
Storage and Playback of Audio
Most straightforward way to
represent audio is LPCM
(Linear pulse-coded
modulation)
Constant num
University of Illinois
Spring 2016
ECE 310: Problem Set 7
Due: 5pm, March 11, 2016
1. Consider the LSI system y[n] = x[n] + x[n 4].
1. Compute and sketch the systems magnitude and phase response.
2. Determine the systems output for each of the following i
University of Illinois
Spring 2016
ECE 310: Problem Set 14
Due: 5pm, May 4, 2016
1. For the following bilinear transformation
s=
1 z 1
1 + z 1
or z =
1+s
1s
four points are given in the s-plane as follows: (a) s1 = j, (b) s2 = 2, (c) s3 = 2, and (d) s4 =
University of Illinois
Spring 2016
ECE 310: Problem Set 11
Due: 5pm, April 15th, 2016
N 1
1
1. Given N real input values cfw_ xn N
n=0 and corresponding real target values cfw_ tn n=0 , suppose
that we want to fit a line of the form
tn axn + b,
n = 0, 1,
University of Illinois
Spring 2016
ECE 310: Problem Set 6
Due: 5pm, March 4, 2016
1. Let X(z) be the z-transform of x[n]. Assume that x[n] = 0 for n < 0. Express the z-transform of the
following signals in terms of X(z).
a) x [n 2]
b) Recfw_x[n]
c) Given
University of Illinois
Spring 2016
ECE 310: Problem Set 9
Due: 5pm, April 1th, 2016
1. A signal xa (t) is assumed to be bandlimited to 15 kHz. It is desired to filter this signal with an
analog bandpass filter that passes all frequencies between 500 Hz an
ECE 329
Homework 13 Solutions
Due: Thu, July 28 2016, 5 PM
1. Bonus Problem :
The magnetic field of a plane wave propagating in a non-magnetic material ( = o = 4 107 H/m)
is given by
A
H = 25 ez cos(8 106 t 3z ) x
.
3
m
By inspection, we have the
frequen
ECE 329
Homework 12 Solutions
Due: Tue, July 26, 2016, 5 PM
1. Bonus Problem : Solution of this problem will be given within the solutions of HW13.
2.
a) Since
= 2103 49 109 = 89 106 1, we use the approximations for good conductors, i.e.
4
= = f . Theref
ECE 329
Homework 10 Solutions
Due: Tue, July 19, 2016, 5PM
1.
a) The vector wave field E(z, t) is given by
E(z, t) = 4(
t z/c
V
) y .
m
b) The associated wave field H(z, t) is
H(z, t) =
t z/c
4
A
(
)x
.
o
m
c) The Poynting vector is
S=EH=
16 2 t z/c
W
ECE 329
Homework 11 Solutions
Due: Fri, July 22, 2016, 5PM
A
1. The pulse of sheet current Js (t) = x
Jso cos(t) m
will produce magnetic and electric fields as shown
in the following figure.
z
S+ = E+ H+
y
E+
Js(t) = xJso(t)
H+
x
H
E
S = E H
a) The averag
ECE 329
Homework 14 Solutions
Due: Tue, Aug 02, 2016, 5 PM
1. This problem is similar to that given in Example 3 in Lecture 30.
a) The voltage in the first line will be a sum of incident V + and reflected voltages V , i.e. V1 =
V + + V whereas in the seco
ECE 329
Homework 1 Solutions
Due: Fri, June 17, 2016, 5PM
1. Review of vectors :
a) D = A + B = 2
x + 3
y 4
z.
b) A + B 4C = 2
x + 3
y 4
z 4(3
x y + 2
z ) = 10
x + 7
y 12
z.
p
c) |A + B 4C| = (10)2 + 52 + (10)2 = 293 17.12.
d) A + 2B C = 4
x + 5
y 8
z.
p