Hollow Waveguides
55
Then, Pd becomes
Pd =
and
kz
00
! 2 2
4
2 ks
I
C
dl|rs Ez |2 ,
H
dl|rs Ez |2
k2
C
R
=
.
2
4kz ks
dS|Ez |2
(2.4.38)
(2.4.39)
S
The above method of computing the attenuation of a waveguide is also known as the powerloss method. It is in
Submitted to the Annals of Applied Probability
HIGH DIMENSIONAL SPARSE COVARIANCE ESTIMATION:
ACCURATE THRESHOLDS FOR THE MAXIMAL DIAGONAL ENTRY
AND FOR THE LARGEST CORRELATION COEFFICIENT
By Aharon Birnbaum and Boaz Nadler
The Hebrew University and Weizm
The Annals of Statistics
2008, Vol. 36, No. 1, 199227
DOI: 10.1214/009053607000000758
Institute of Mathematical Statistics, 2008
REGULARIZED ESTIMATION OF LARGE
COVARIANCE MATRICES
B Y P ETER J. B ICKEL AND E LIZAVETA L EVINA1
University of California, B
This article was downloaded by: [Academy of Mathematics and System Sciences]
On: 21 June 2012, At: 23:53
Publisher: Taylor & Francis
Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer
House, 37-41 Mortimer S
ECE 531 Theory of Guided Waves
Homework 9
Due Nov 8, 2012
Reading Assignment: Lecture Notes Chapters 5 and 6
Do Problems 5-6.
Additional Problem:
(a) Convince yourself that if the LHM slab is matched to the RHM free
space, it can amplify evanescent waves.
ECE 531 Theory of Guided Waves
Take Home Exam 1
Due October 11, 2012
Problem 1:
Show that for a cold, collisionless plasma consisting of freely moving
electrons, that the dispersion relation for permittivity is given by
2
p
( ) 0 1 2
(1.1)
Deduce wh
ECE 531 Theory of Guided Waves
Take Home Exam 2
Due November 27, 2012
Problem 1:
Assume that you have a circular microstrip patch antenna with radius a and thickness d ,
use a magnetic wall model:
(a) Find the cavity modes of the microstrip patch. Assume
ECE 531 Theory of Guided Waves
Homework 2
Due September 13, 2012
Reading Assignment: Lecture Notes Chapter 2
Do Problems 2-1, 2-2, 2-3, 2-8 of lecture notes
Additional Problem:
Please give the physical reason why the attenuation constant k z" in a metalli
ECE 531 Theory of Guided Waves
Homework 3
Due September 20, 2012
Reading Assignment: Lecture Notes Chapter 2
Do Problems 2-12, 2-13, 2-17 of lecture notes
Addition problem:
Explain physically why an electrically small loop source can be modeled as
a magne
ECE 531 Theory of Guided Waves
Homework 6
Due October 18, 2012
Reading Assignment: Lecture Notes Chapter 4
Do Problems 4-1
New Problem:
Let us assume that the waveguide in Fig. 4.1 of the notes is of arbitrary
shape so that there is no closed form dyadic
190
Theory of Microwave and Optical Waveguides
The above is a matrix equation of the form
b=Aa
(5.2.34)
where,
[b]m = hfm , Hinc i, [A]mn = i!hfm , 2 G2m
1 G1m , fn i, [a]n = an
(5.2.35)
and
hfm , G, fn i =
hfm , Hinc i =
Z
Z
Z
dS 0 G(r, r0 ) fn (r0 )
Sa
136
Theory of Microwave and Optical Waveguides
l
y
^
n
Sp
V
Sa
d
So
S
Figure 4.1: Excitation of a cylindrical, hollow waveguide by a probe.
A dyadic Greens function is dened to be a solution to the following equation, i.e.,
r r G(r, r0 )
k 2 G(r, r0 ) = I
28
Theory of Microwave and Optical Waveguides
Exercises for Chapter 1
Problem 1-1: The fundamental units in electromagnetics can be considered to be meter,
kilogram, second, and coulomb.
(a) Show that 1 volt, which is 1 watt/amp, has the dimension of (kil
82
Theory of Microwave and Optical Waveguides
Exercises for Chapter 2
Problem 2-1: Many transmission line systems have more than two conductors, like your
home telephone line, computer bus etc. If you have an N conductors (a general cylindrical
waveguide
Chapter 1
Preliminary Background
1.1
Introduction
Waveguiding phenomena occur naturally or are man made. For instance, waveguides are
a fundamental component of radio wave, microwave and optical circuits [15]. They are
indispensable in modern technology i
Inhomogeneously Filled Waveguides
109
where d is the thickness of the slab. In etalon application, regions 1 and 3 are free space while
region 2 is dielectric. Specializing to the case when regions 1 and 3 have the same parameters,
we have
T12 T21 eik2x d
Coupling of Waveguides and Cavities
163
Now, if we lay another waveguide on top of the rst waveguide, the radiating electric and
magnetic dipoles couple most e ciently into the TE10 mode of the top waveguide if the top
guide is oriented at an angle with r
Discontinuities in Waveguides
217
I (z
I ( z ), V ( z )
z ), V ( z
z)
Z
Y
Figure 5.26: Lumped element model for deriving the CRLH transmission line equations.
@ 2 I(z)
= ZY V (z)
@z 2
(5.8.12)
or
2
=
YZ
p
= j Y Z
If
(5.8.13)
(5.8.14)
Z=
1
j!CL
(5.8.15)
Y
Microwave Integrated Circuits
325
Figure 7.22: Equivalent circuit for a T junction.
+
V1
V1
1
2
l
0
0
V2
Plane of symmetry
1
A
A
1
V3
0
0
4
3
V4
Figure 7.23: A directional coupler made of microstrip lines.
The directional coupler is a four-port network. W
244
Theory of Microwave and Optical Waveguides
Hs =
i
[k r H + ! rs Ez ],
z
2 z s z
ks
(6.6.7b)
we deduce that in region 1,
1
X
E1s =
n (k1s , rs )
!1 bn z rs <g
n (k1s , rs )],
(6.6.8a)
1
X
n (k1s , rs )
+ !1 an z rs <g
n (k1s , rs )],
(6.6.8b)
n (k0s ,
298
Theory of Microwave and Optical Waveguides
y
z
r
x
r
Slot Line
Microstrip Line
r
r
Coplanar Strips
Coplanar Waveguide
Figure 7.1: Dierent kinds of microwave integrated circuits waveguides.
rs Hs =
@
z Es
@z
ik
1
Ez ,
(7.1.2)
z rs Ez = ikHs ,
(7.1.3)
@
ECE 531 Theory of Guided Waves
Homework 7
Due October 25, 2012
Reading Assignment: Lecture Notes Chapter 4
Do Problems 4-7
New Problem:
Go through the mode-matching solution in Section 4.2.3 and make sure that
you understand it. Then show that if only one