rs 1 ene 428 microwave engineering lecture 1 introduction, maxwell’s equations, fields in media,...
TRANSCRIPT
![Page 1: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/1.jpg)
RS1
ENE 428Microwave
Engineering
Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions
![Page 2: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/2.jpg)
RS2
Syllabus•Assoc. Prof. Dr. Rardchawadee Silapunt (Ann), [email protected] •Dr. Ekapon Siwapornsathain (Eric), [email protected], Tel: 0814389024•Lecture: 9:00am-12:00pm Wednesday, AIT•Instructors at King Mongkut’s University of Technology Thonburi, BKK, Thailand•Textbook: Microwave Engineering by David M. Pozar (3rd edition Wiley, 2005)• Recommended additional textbook: Applied Electromagnetics by Stuart M.Wentworth (2nd edition Wiley, 2007)
![Page 3: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/3.jpg)
RS3
![Page 4: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/4.jpg)
RS4
Homework 10% Quiz 10% Midterm exam 40% Final exam 40%
Grading
Vision Providing opportunities for intellectual growth in the context of an engineering discipline for the attainment of professional competence, and for the development of a sense of the social context of technology.
![Page 5: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/5.jpg)
10-11/06/51
RS5
Course overview• Maxwell’s equations and boundary
conditions for electromagnetic fields• Uniform plane wave propagation• Transmission lines• Matching networks• Waveguides• Two-port networks• Resonators• Antennas• Microwave communication systems
![Page 6: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/6.jpg)
RS6
• Microwave frequency range (300 MHz – 300 GHz) ( = 1 mm – 1 m in free space)
• Microwave components are distributed components.
• Lumped circuit elements approximations are invalid.
• Maxwell’s equations are used to explain circuit behaviors ( and )
Introduction
DDDDDDDDDDDDDDE
DDDDDDDDDDDDDDH
http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=52
![Page 7: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/7.jpg)
RS7
Lumped circuit model and distributed circuit model
![Page 8: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/8.jpg)
RS8
• From Maxwell’s equations, if the electric field is changing with time, then the magnetic field varies spatially in a direction normal to its
orientation direction
• Knowledge of fields in media and boundary conditions allows useful applications of material properties to microwave components
• A uniform plane wave, both electric and magnetic fields lie in the transverse plane, the plane whose normal is the direction of propagation
DDDDDDDDDDDDDDEDDDDDDDDDDDDDDH
Introduction (2)
![Page 9: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/9.jpg)
RS9
![Page 10: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/10.jpg)
RS10
![Page 11: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/11.jpg)
RS11
Point forms of Maxwell’s equations
(1)
(2)
(3)
(4)0
B
D
Jt
DH
Mt
BE
v
![Page 12: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/12.jpg)
RS12
![Page 13: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/13.jpg)
RS13
The magnetic north can never be isolated from the south.
Magnetic field lines always form closed loops.
![Page 14: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/14.jpg)
RS14
Maxwell’s equations in free space
• = 0, r = 1, r = 1
0 = 4x10-7 Henrys/m0 = 8.854x10-12 Farads/ms = conductivity (1/ohm)(“constitutive parameters”)
0
0
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
EH
t
HE
t
Ampère’s law
Faraday’s law
![Page 15: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/15.jpg)
RS15
Integral forms of Maxwell’s equations
Note: To convert from the point forms to the integral forms, we need to apply Stoke’sTheorem (for (1) and (2)) and Divergence theorem (for (3) and (4)), respectively.
0
SdB
QdVSdD
ISdDt
ldH
SdBt
ldE
S
enc
VS
S
S
(1)
(2)
(3)
(4)
![Page 16: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/16.jpg)
RS16
Fields are assumed to be sinusoidal or harmonic, and time dependence with steady-state conditions
( , , ) cos( ) xE A x y z t a DDDDDDDDDDDDDD
• Time dependence form:
• Phasor form:
( , , ) js xE A x y z e a
DDDDDDDDDDDDDD
![Page 17: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/17.jpg)
RS17
Maxwell’s equations in phasor form
(1)
(2)
(3)
(4)0
B
D
JDjH
MBjE
v
S
S
![Page 18: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/18.jpg)
RS18
Fields in dielectric media (1)• An applied electric field causes the
polarization of the atoms or molecules of the material to create electric dipole moments that complements the total displacement flux,
where is the electric polarization. • In the linear medium, it can be shown that
• Then we can write
EDDDDDDDDDDDDDD
DDDDDDDDDDDDDDD
20 /eD E P C m
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
ePDDDDDDDDDDDDDD
0 .e eP E DDDDDDDDDDDDDDDDDDDDDDDDDDDD
0 0(1 ) .e rD E E E DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
![Page 19: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/19.jpg)
RS19
Fields in dielectric media (2)• may be complex then can be complex and
can be expressed as
• Imaginary part is counted for loss in the medium due to damping of the vibrating dipole moments.
• The loss of dielectric material may be considered as an equivalent conductor loss if the material has a conductivity . Loss tangent is defined as
' ''j
''tan .
'
e
![Page 20: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/20.jpg)
RS20
Anisotropic dielectrics
• The most general linear relation of anisotropic dielectrics can be expressed in the form of a tensor which can be written in matrix form as
.x xx xy xz x x
y yx yy yz y y
z zx zy zz z z
D E E
D E E
D E E
![Page 21: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/21.jpg)
RS21
Analogous situations for magnetic media (1)• An applied magnetic field causes the
magnetic polarization of by aligned magnetic dipole moments
where is the magnetic polarization or magnetization.
• In the linear medium, it can be shown that
• Then we can write
HDDDDDDDDDDDDDD
20 ( ) /mB H P Wb m
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
mPDDDDDDDDDDDDDD
.m mP HDDDDDDDDDDDDDDDDDDDDDDDDDDDD
0 0(1 ) .m rB H H H DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
![Page 22: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/22.jpg)
RS22
Analogous situations for magnetic media (2)• may be complex then can be complex and
can be expressed as
• Imaginary part is counted for loss in the medium due to damping of the vibrating dipole moments.
' ''j
m
![Page 23: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/23.jpg)
RS23
Anisotropic magnetic material
• The most general linear relation of anisotropic material can be expressed in the form of a tensor which can be written in matrix form as
.x xx xy xz x x
y yx yy yz y y
z zx zy zz z z
B H H
B H H
B H H
![Page 24: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/24.jpg)
RS24
Boundary conditions between two media
Ht1
Ht2
Et2
Et1
Bn2
Bn1
Dn2
Dn1
n
2 1
2 1
Sn D D
n B n B
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
2 1
2 1
S
S
E E n M
n H H J
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
![Page 25: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/25.jpg)
RS25
Fields at a dielectric interface
2 1
2 1
1 2
1 2.
n D n D
n B n B
n E n E
n H n H
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
• Boundary conditions at an interface between two lossless dielectric materials with no charge or current densities can be shown as
![Page 26: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/26.jpg)
RS26
Fields at the interface with a perfect conductor
0
0
0.
S
n D
n B
n E M
n H
DDDDDDDDDDDDDD
DDDDDDDDDDDDDD
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
DDDDDDDDDDDDDD
• Boundary conditions at the interface between a dielectric with the perfect conductor can be shown as
![Page 27: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/27.jpg)
RS27
General plane wave equations (1)
• Consider medium free of charge• For linear, isotropic, homogeneous, and
time-invariant medium, assuming no free magnetic current,
(1)
(2)
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD EH E
t
DDDDDDDDDDDDDDDDDDDDDDDDDDDD HE
t
![Page 28: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/28.jpg)
RS28
General plane wave equations (2)
Take curl of (2), we yield
From
then
For charge free medium
( )
DDDDDDDDDDDDDDDDDDDDDDDDDDDD HE
t
2
2
( )
DDDDDDDDDDDDDDDDDDDDDDDDDDDD DDDDDDDDDDDDDDDDDDDDDDDDDDDD
DDDDDDDDDDDDDDE
E E EtEt t t
AAA 2
0 E
2
22
t
E
t
EEE
![Page 29: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/29.jpg)
RS29
Helmholtz wave equation
22
2
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD E EE
t t
22
2
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD H HH
t t
For electric field
For magnetic field
![Page 30: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/30.jpg)
RS30
Time-harmonic wave equations
• Transformation from time to frequency domain
Therefore
j
t
2 ( ) DDDDDDDDDDDDDDDDDDDDDDDDDDDDs sE j j E
2 ( ) 0 DDDDDDDDDDDDDDDDDDDDDDDDDDDDs sE j j E
2 2 0 DDDDDDDDDDDDDDDDDDDDDDDDDDDDs sE E
![Page 31: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/31.jpg)
RS31
Time-harmonic wave equations
or
where
This term is called propagation constant or we can write
= + j
where = attenuation constant (Np/m) = phase constant (rad/m)
2 2 0 DDDDDDDDDDDDDDDDDDDDDDDDDDDDs sH H
( ) j j
![Page 32: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/32.jpg)
RS32
Solutions of Helmholtz equations
• Assuming the electric field is in x-direction and the wave is propagating in z- direction
• The instantaneous form of the solutions
• Consider only the forward-propagating wave, we have
• Use Maxwell’s equation, we get
0 0cos( ) cos( )
DDDDDDDDDDDDDDz z
x xE E e t z a E e t z a
0 cos( )
DDDDDDDDDDDDDDz
xE E e t z a
0 cos( )
DDDDDDDDDDDDDDz
yH H e t z a
![Page 33: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/33.jpg)
RS33
Solutions of Helmholtz equations in phasor form
• Showing the forward-propagating fields without time-harmonic terms.
• Conversion between instantaneous and phasor form
Instantaneous field = Re(ejtphasor field)
0
DDDDDDDDDDDDDD
z j zs xE E e e a
0
DDDDDDDDDDDDDD
z j zs yH H e e a
![Page 34: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/34.jpg)
RS34
Intrinsic impedance
• For any medium,
• For free space
x
y
E jH j
0 0
0 0
120 x
y
E EH H
![Page 35: RS 1 ENE 428 Microwave Engineering Lecture 1 Introduction, Maxwell’s equations, fields in media, and boundary conditions](https://reader036.vdocuments.us/reader036/viewer/2022081506/56649c755503460f949284b8/html5/thumbnails/35.jpg)
RS35
Propagating fields relation
1
DDDDDDDDDDDDDDDDDDDDDDDDDDDD
DDDDDDDDDDDDDDDDDDDDDDDDDDDDs s
s s
H a E
E a H
where represents a direction of propagationa