ECE 303 - Sum2017
1
Test 2 w/Answers
1. Let a signal source vs (t) = 5 cos( 5000 t ) have source resistance Rs = 75 . The source is
connected to a lossless line and load having Zin = 100 + j 50 , as s
Solutions - Set 4: Lossless Lines - Sinusoids
ECE 303 - Sum2014
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4-3. Let a transmission line be used to connect a source and a load. The source produces a
forward wave with amplitude A = 2 and the l
Solutions - Set 3: Lossless Lines - Pulses
ECE 303 - Sum2014
1
3-1. A signal source with Rs = 70 is located at x = 0 on a lossless transmission line. The
line is terminated at x = 40 m with a 100 load
Solutions - Set 8: Point Charges and Fields
ECE 303 - Sum2014
1
8-1. Assume the z coordinate is zero. A 50 nC charge is located at the origin in free space.
At any point the E-eld has the form | E | u
Solutions - Set 5: Line Impedance
ECE 303 - Sum2014
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5-1. A lossless transmission line operating at f = 1 MHz has per meter L = 6(10)7 H and
C = 3(10)11 F. The line is terminated at x = 0 m with RL =
1
Solutions Set 9: Voltage
ECE 303 - Sum2014
9-1. Let the vector A = 5 ux + 3 uy and let the vector B = 4 ux + 6 uy . Compute the following
quantities : (a) A B , (b) the angle between A and B .
DETAI
Solutions Set 10: Gauss Law
ECE 303 - Sum2014
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10-1. Let a vector eld in Cartesian coordinates be given by A. Compute A, the divergence
of A, if the vector eld is given by the following:
(a) A = x2 y
Solutions Set 11: Poisson/Laplace Equations
ECE 303 - Sum2014
1
11-1. Let a scalar eld G = G(x) over the region 0 x 2 in Cartesian coordinates be given
by the dierential equation
d2 G
=0
dx2
The bound
Solutions - Set 13: Curl Relations for Magnetic Field
ECE 303 - Sum2014
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13-3. A vector eld F is given by F = y 2 ux +3 z uy x y uz . (a) Compute X F . (b) Evaluate
the magnitude | X F | at the point
1
Solutions - Set 14: Time-Varying Magnetic Fields
ECE 303 - Sum2014
14-1. A magnetic ux density is given by B = 0.2 ux + 0.3 uy + 0.4 uz . Compute the magnetic
ux M through the closed path formed by
Solutions - Set 16: Wave Propagation in Lossy Media
ECE 303 - Sum2014
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16-1. A medium has parameters = 50 0 , = 0 , = 10. Compute the real () and imaginary
() parts of the propagation constant of thi
ECE 303 - Sum2014
Solutions - Set 15: Plane Wave Propagation
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15-6. An electromagnetic wave is propagating in free-space along the y-axis (Cartesian coordinates). The electric eld is given by E = 20
Solutions Set 7: Power Flow on Transmission Lines
ECE 303 - Sum2014
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7-1. Let the voltage across a 100 resistor be v(t) = 5 cos(2 1000 t) and let the current be i(t).
(a) Compute and plot the current
Solutions - Set 6: Lossy Lines - Sinusoids
ECE 303 - Sum2014
1
6-1. A lossy transmission line operating at f = 1 MHz has per meter parameters R = 0.6 , L
= 5(10)7 H, G = 2(10)7 S, and C = 0.5(10)10 F.
ECE 303 - Sum2017
1
Test 1 w/Answers
1. Let vp = 2(10)8 m/s and T = 0.4 sec, and let a waveform be defined by the math form
(
g(u) =
3 10 7 u ,
0,
0uT
else
x
.
vp
(b) Plot v(x) over 0 x 200.
Let time
Assignment 2: 2 June 2017
ECE 303 - Sum2017
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Problem 1. (10 pts)
A signal source with resistance RS = 40 is located at x = 0 on a lossless transmission line. The
line has characteristic resistance R0
ECE 303 - Sum2017
Turn-In Assignment 5
7 July 2017
1
Problem 1. ( 10 pts )
The charge density (x) in the space-charge region of a one-dimensional material having = 200
is given by
0.05 x 0
80 0 cos(
1
Turn-In Assignment 6: 14 July 2017
ECE 303 - Sum2017
Problem 1. (10 pts)
At t = 0, a mobile electron at point P = (x, y, z) = (3, 4, 5) in silicon is moving in the d v direction.
At t = 0 a magnetic
Problem 1.
1
Turn-In Assignment 1: 26 May 2017
ECE 303 - Sum2017
(10 pts)
Let a waveform f () be defined by the following function:
(
f () =
10 e 10
8
cos 5 (10) 8 ,
0,
0 8(10)9
else
Let the propagati
ECE 303 - Sum2017
Turn-In Assignment 3: 9 June 2017
1
Problem 1. ( 10 pts )
Let a source at x = 4 produce a forward wave vf (x, t) = A e j ( t x ) on a transmission line
having a load at x = 0. The so
ECE 303 - Sum2017
Turn-In Assignment 4:
1
30 June 2017
Problem 1. ( 10 pts )
Assume the z coordinate is zero in this problem. In free space, four positive charges and their
locations are given by:
Q1
ECE 303 - Sum2014
1
Test 1 w/Answers
1. Let vp = 2(10)8 m/s and T = 0.3 sec, and let a waveform be dened by the math form
g(u) =
2 10 7 u , 0 u T
0,
else
x
.
vp
(b) Plot v(x) over 0 x 300.
Let time t1
ECE 303: Electromagnetic Fields
SYLLABUS
Page 1 of 2 pages
Ten Week Summer Semester, 2014; Home Page: courses.ncsu.edu/ece303/lec/051
Instructor: Dr. S. T. Alexander; Oce: EB-2, Rm. 2094, Phone: 515-5
Solutions - Set 1: Transmission Lines and the Wave Equation
ECE 303 - Sum2014
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1-1. In this problem use the lumped parameter circuit model for the transmission line segment
of length x given on page
ECE 303 - Sum2014
Solutions - Set 2: Propagation on Transmission Lines
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2-1. A lossless transmission line having no reections is 2 meters long and the propagation
velocity is vp = 2(10)8 m/sec. With
Solutions - Set 17: Wave Reection and Transmission
ECE 303 - Sum2014
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17-1. Let medium 1 and 2 be dielectrics ( = 0). The parameters for medium 1 are ( 1 , 1 ) =
( 0 , 0 ) and the parameters for medi
Solutions - Set 12: Time-Invariant Magnetic Fields
ECE 303 - Sum2014
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12-1. Let three vectors A, B, and C in Cartesian coordinates be related by C = A X B. Additionally, let A = 4 ux + 2 uy + 2 uz an
ECE 303 - Sum2014
1
Problem Set 5 : Line Impedance
5-1. A lossless transmission line operating at f = 1 MHz has per meter L = 6(10)7 H and
C = 3(10)11 F. The line is terminated at x = 0 m with RL = 50
ECE 303 - Sum2014
Problem Set 15: Plane Wave Propagation
1
15-1. An electromagnetic wave propagates in a medium having permeability 0 = 4(10)7 and
permittivity . Compute the velocity of propagation if
ECE 303 - Sum2014
Problem Set 16: Wave Propagation in Lossy Media
1
16-1. A medium has parameters = 50 0 , = 0 , = 10. Compute the real () and imaginary
() parts of the propagation constant of this me
ECE 303 - Sum2017
Notes Set 18: Wave Reflection and Transmission
1
INTRODUCTION
This set of Notes considers the case when waves propagating in one medium are incident
upon the boundary containing anot
ECE 303 - Sum2017
Notes Set 10: Gauss Law
1
INTRODUCTION
A fundamental property we have seen is that charges create electric fields. Sometimes
the charges are discrete charges or point charges, as we
ECE 303 - Sum2017
Notes Set 9: Voltage
1
INTRODUCTION
Voltage is a type of Potential energy, which is the ability to do work. In fact, voltage is often
referred to as the electric potential. This set
ECE 303 - Sum2017
Notes Set 4: Lossless Lines - Sinusoids
1
INTRODUCTION
In an earlier set of Notes we studied the behavior of pulses transmitted on lossless lines. We
learned that for short pulses we
Problem Set 11: Poisson/Laplace Equations
ECE 303
1
11-1. Let a scalar field G = G(x) over the region 0 x 2 in Cartesian coordinates be given
by the differential equation
d2 G
= 0
dx 2
The boundary co