Lecture 1 - web page for staff

Report
ENE 428
Microwave
Engineering
Lecture 1 Introduction, Maxwell’s
equations, fields in media, and
boundary conditions
1
RS
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)
2
RS
3
RS
Grading
Homework
Quiz
Midterm exam
Final exam
10%
10%
40%
40%
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.
4
RS
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
10-11/06/51
RS
5
Introduction
http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=52
• 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 ( H and E )
6
RS
Lumped circuit model and
distributed circuit model
7
RS
Introduction (2)
• From Maxwell’s equations, if the electric field E
is changing with time, then the magnetic field H
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
8
RS
9
RS
10
RS
Point forms of Maxwell’s equations
B
E  
H 
t
D
t
M
J
(1)
(2)
  D  v
(3)
B  0
(4)
11
RS
12
RS
The magnetic north
can never be
isolated from the
south.
Magnetic field lines
always form closed
loops.
13
RS
Maxwell’s equations in free space
•  = 0, r = 1, r = 1
  H  0
E
t
  E  0
H
t
Ampère’s law
Faraday’s law
0 = 4x10-7 Henrys/m
0 = 8.854x10-12 Farads/m
 = conductivity (1/ohm)
(“constitutive parameters”)
14
RS
Integral forms of Maxwell’s equations

 E  d l   t  B  d S
(1)
S
 H dl 

D d S  I

t
(2)
S
 D  d S    dV
S
 B d S
 Q enc
(3)
V
0
(4)
S
Note: To convert from the point forms to the integral forms, we need to apply Stoke’s
Theorem (for (1) and (2)) and Divergence theorem (for (3) and (4)), respectively.
15
RS
Fields are assumed to be sinusoidal or
harmonic, and time dependence with
steady-state conditions
• Time dependence form:
E  A ( x , y , z ) co s(  t   ) a x
• Phasor form:
E s  A ( x , y , z )e
j
ax
16
RS
Maxwell’s equations in phasor form
  E S   j B  M
(1)
  H S  j D  J
(2)
  D  v
(3)
B  0
(4)
17
RS
Fields in dielectric media (1)
• An applied electric field E causes the polarization of the
atoms or molecules of the material to create electric D
dipole moments that complements the total displacement
flux,
D  0 E  Pe
C /m
2
where P e is the electric polarization.
• In the linear medium, it can be shown that
Pe  0e E.
• Then we can write
RS
D   0 (1   e ) E   0  r E   E .
18
Fields in dielectric media (2)
•  may be complex then  can be complex and can be
e
expressed as
   ' j ''
• 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
  '' 
tan  
.
 '
RS
19
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
 D x    xx

 
D y    yx


 D z    zx

 xy
 yy
 zy
 xz   E x 
 Ex 
 
 
 yz  E y     E y .
 
 
 E z 
 zz   E z 
20
RS
Analogous situations for magnetic
media (1)
• An applied magnetic field H causes the magnetic
polarization of by aligned magnetic dipole moments
B  0 (H  P m )
Wb / m
2
where P m is the magnetic polarization or magnetization.
• In the linear medium, it can be shown that
Pm  m H .
• Then we can write
B   0 (1   m ) H   0  r H   H .
21
RS
Analogous situations for magnetic
media (2)
•  m may be complex then  can be complex and can be
expressed as
   ' j  ''
• Imaginary part is counted for loss in the medium due to
damping of the vibrating dipole moments.
22
RS
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
 B x    xx
  
B y    yx
 
 B z    zx

 xy
 yy
 zy
 xz   H x 
H x 




 yz  H y     H y .




 H z 
 zz   H z 
23
RS
Boundary conditions between two
media
n
Dn2
Bn2
Ht2
Et1
Ht1
Bn1
Et2
Dn1


n  D 2  D1  S
n  B 2  n  B1
E
2


 E1  n  M
n H
2
S

 H1  JS
24
RS
Fields at a dielectric interface
• Boundary conditions at an interface between two
lossless dielectric materials with no charge or
current densities can be shown as
n  D 2  n  D1
n  B 2  n  B1
n  E1  n  E 2
n  H 1  n  H 2.
25
RS
Fields at the interface with a perfect
conductor
• Boundary conditions at the interface between a
dielectric with the perfect conductor can be
shown as
nD  0
nB  0
n  E  M
S
n  H  0.
26
RS
General plane wave equations (1)
• Consider medium free of charge
• For linear, isotropic, homogeneous, and timeinvariant medium, assuming no free magnetic
current,
H  E 
  E  
H
t
E
t
(1)
(2)
27
RS
General plane wave equations (2)
Take curl of (2), we yield
    E  
    E  
From
then
 (  H )
t
E
2
)

E

E
 t   
 
2
t
t
t
 ( E  
 A  A A
2
  E   E   
2
E
t
 E
2
 
t
2
For charge free medium
E  0
RS
28
Helmholtz wave equation
For electric field
For magnetic field
 E  
2
E
t
 H  
2
 E
2
 
H
t
t
2
 H
2
 
t
2
29
RS
Time-harmonic wave equations
• Transformation from time to frequency domain

t
 j
Therefore
 E s  j  (  j  ) E s
2
 E s  j  (  j  ) E s  0
2
 Es  Es  0
2
2
30
RS
Time-harmonic wave equations
or
 H s  H
2
where
 
2
s
0
j  (  j  )
This  term is called propagation constant or we can write
 =  + j
where  = attenuation constant (Np/m)
 = phase constant (rad/m)
RS
31
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

E  E0 e
 z

cos( t   z ) a x  E 0 e
 z
cos( t   z ) a x
• Consider only the forward-propagating wave, we have
E  E0e
 z
cos( t   z ) a x
• Use Maxwell’s equation, we get
H  H 0e
RS
 z
cos( t   z ) a y
32
Solutions of Helmholtz equations in phasor
form
• Showing the forward-propagating fields without timeharmonic terms.
E s  E0e
 z
H s  H 0e
e
 z
 j z
e
 j z
ax
ay
• Conversion between instantaneous and phasor form
Instantaneous field = Re(ejtphasor field)
33
RS
Intrinsic impedance
• For any medium,
 
Ex
Hy

j 
  j 
• For free space
 
Ex
Hy

E0
H0

0
 120 
0

34
RS
Propagating fields relation
Hs 
1

a  Es
E s   a   H s
where a  represents a direction of propagation
35
RS

similar documents