ECE4370 Spring 2015 HW2 Solution
Huan Yu
February 9, 2015
Problem 1
Az (r)
=
=
H(r)
I dl ejkr
z
4
r
I dl ejkr
I dl ejkr
cos
r
sin
4
r
4
r
=
=
=
E(r)
=
=
=
Az (r)
1 1 Ar
1 (rA )
(
+
)
r
r
r
jIdlk sin jkr
j
e
[1 ]
4r
kr
H(r)
j2f
1
1
(r sin H )
1 (r
ECE4370 Spring 2015 HW1 Solution
Huan Yu
January 27, 2015
Problem 1
(1)
The mismatch loss for dipole:
4RL RAdipole
= 0.418
|ZL + ZAdipole |2
The mismatch loss for folded dipole:
4RL RAf dipole
= 0.603
|ZL + ZAf dipole |2
Thus, the folded dipole couples th
Homework 3: ECE 4370
Solutions
1. Recall our procedure for calculating fields from a line-current antenna: find the vector
magnetic potential first and then translate into a Poynting vector:
The integral for the stacked array of dipoles is just the sum of
Lecture Notes
ANT2: Space and Line Current Radiation
In this lecture, we study the general case of radiation from z-directed spatial currents. The farfield radiation equations that result from this treatment form some of the foundational principles of
all
AAT2: Rician Fading
By Prof. Gregory D. Durgin
copyright 2009 all rights reserved
Rician Wave Model
copyright 2009 all rights reserved
1
Rician Derivation
copyright 2009 all rights reserved
Rician PDF
copyright 2009 all rights reserved
2
Note on Bessel Fu
Lecture Notes
ANT1: Basic Radiation Theory
In this module, we discuss the basic approach for solving electromagnetic field quantities given a
distribution of current in space Once the approach is established, the simplest radiative system
space.
establis
Lecture Notes
ANT3: Antennas in Circuits
In this module, we look treat and analyze an antenna in the context of circuit theory. One of the
key outcomes of our discussion is to understand how to model antennas with circuit theories, as
theories
well as how
ANT4: Vertical Dipole Arrays
By Prof. Gregory D. Durgin
copyright 2009 all rights reserved
Example Analysis: Cellular Base Station Antenna
copyright 2009 all rights reserved
1
Field Solution for the Half-Wave Dipole
copyright 2009 all rights reserved
Fiel
126 SpaceTime Wireless Channels
First-Order Channel Statistics
Chapter 5
dropping below this threshold, we setup and evaluate the following integral:
0.3162
Pr[0 R < 0.3162 Pdif ] =
Pdif
2
Pdif
2
exp
Pdif
0
= exp
2
Pdif
d
=0.3162
Pdif
0
= 0.0952
If we ass
Laboratory Assignment 3:
Small-Scale Fading and Diversity
Names:
_
_
_
_
Objective
This laboratory assignment will use the network analyzer as a channel sounder,
measuring small-scale fading between two antennas in the microwave bands. Student
teams will
AAT1: Rayleigh Fading
By Prof. Gregory D. Durgin
copyright 2009 all rights reserved
Example of Small-Scale Fading at 5.8 GHz
copyright 2009 all rights reserved
1
Wave Interference on a Transmission Line
copyright 2009 all rights reserved
Small-Scale Fadin
ECE 4370: Antenna Engineering
Solutions to TEST 2 (Fall 2011)
1. Linear Antenna Arrays: Below are the true patterns for each array factor. Full credit was
given for anything remotely close.
a
90
b
2
120
90
60
60
1.5
1
150
30
1
150
0.5
30
0.5
180
0
210
180
ECE 4370: Antenna Engineering
Solutions to TEST 2 (Fall 2012)
1. Linear Antenna Arrays: Below are the true patterns for each array factor. Full credit was
given for anything remotely close.
a
90
b
4
120
60
90
20
120
60
15
3
2
150
10
150
30
180
180
0
0
210
Solutions to Homework 1: ECE 4370
Introduction to Radiating Systems
1. Answers
2. Helmholtz wave equation, everywhere except the origin. This was a very mathematical
problem; students received full credit for any honest effort. Here is an example of how t
ECE 4370 Solution 5
1. Path Loss Exponent: To solve this problem, I simply entered all of the data into a spreadsheet:
R (m)
PL wrt 1m (dB)
(10 log10 R)^2
10 log10 R x PL
10.0
31.3
100.0
313.0
10.0
33.4
100.0
334.0
10.0
31.3
100.0
313.0
10.0
32.4
100.0
32
Homework 4: ECE 4370
Solution
1. Link Budgets and Fading
1. Received power at the fringe is -83.2 dBm
2. Occurs for 3.3% of locations at the fringe of coverage.
3. Received power at the location 6 km away is -96.1 dBm. The probability that this will
excee
Homework 2: ECE 4370
Solutions
Line Currents
1. Solution below:
Note that this is the same basic result as the Hertzian dipole, differing only by a constant of
proportionality. This leads to similar radiation parameters. Compare the table below:
2. Recall
Syllabus for Antenna Engineering
ECE 4370 Spring 2014
Class Description:
Course
ECE-4370
Title
Antenna Engineering
Cr Hrs Instructor Days
3
Greg Durgin
T Th
Time
Location
9:35 PM
10:55 PM
Van Leer
241
ECE 4370 Antenna Engineering
Understand and design ant
ECE 4370: Antenna Eng. (3-0-3)
ECE 4891: Antenna Eng. Lab (0-3-1)
urse
w Co 14
Ne
ring
for Sp
Prof. Gregory D. Durgin
Spring 2014, T-Th 9:35am
propagation.gatech.edu/ECE4370
Lecture Class (4370)
Basics of Antenna Eng.
Only Prereq. is ECE 3025
New Lab Clas
Laboratory Assignment:
S-Parameter Measurement
Names:
_
_
_
_
Objective
This laboratory assignment explores the measurement of s-parameters using the Network
Analyzer in the microwave laboratory. The exercises described here will help familiarize
or refre
Laboratory Assignment:
Exploring Spectrum
Names:
_
_
_
_
Objective
This laboratory assignment explores RF spectrum using the Spectrum Analyzer in the
microwave laboratory. The exercises described here will help familiarize students with
some of the basic
Homework 2: ECE 4370
Radiation and Line Currents
1. In class, we presented expressions for vector magnetic potential, magnetic field, and
electric field for a Hertzian dipole. Show that the vector magnetic potential for the
Hertzian dipole that we use in
ECE 4370: Antenna Engineering
Solutions to TEST 2 (Spring 2015)
1. Uniform Linear Antenna Arrays:
y
y
x
y
x
(b)
(a)
x
(c)
y
y
y
x
(d)
x
(e)
(f)
y
y
y
x
(g)
x
x
(h)
(i)
(1) b: N = 4,
= 90 , d =
4
(ordinary endre)
(5) i: N = 4,
= 112.5 , d = 3
16
(Hansen
Homework 3: ECE 4370
Line Currents and Link Budgets
1. Cellular base station antennas tend to focus power along the horizon
where all the paying customers operate. To do this, the antennas are
manufactured with stacked, in-phase half-wave dipoles (see the
Homework 1: ECE 4370
Introduction to Radiating Systems
1. Energy-Harvesting Circuit:
(15 points)
2. You are feeding an electrically short monopole transmit antenna that has an impedance
value of 5 j60 using a 50 transmission line. How much increase in tra