微波工程
Microwave Engineering
授課教師：蔡友遜
(03B0201,
3216)
課程大綱
I.
Introduction of Electromagnetic Theory
(1)
II.
Transmission Line Theory
(2)
III.
Transmission Line
(3, 10.5)
IV.
Microwave Network Analysis
(4)
V.
Impedance Matching and Tuning
(5)
VI.
Microwave resonators
(6)
ps.
括弧中之數字代表所對應教科書之章節
教學目標
以傳輸線理論為基礎，學習微波電路設
計所需之基本原理和技巧，包括微波網
路及諧振器分析和阻抗匹配方法，以期
應用在微波被動式與主動式元件及電路
系統設計上。
教科書
D.M. Pozar, Microwave Engineering,
3
nd
. Ed. John Wiley & Sons, 2005.
參考資料
Lecture Note by Prof.
T.S. Horng, E.E.
Dept. NSYSU.
T.C. Edwards and M.B. Steer, Foundations
of Interconnect and Microstrip Design, 3
nd
.
Ed. John Wiley & Sons, 2000.
考試重點
(Open Book)
1.
簡答題
重點敘述
課本內容之
Point of Interest
2.
設計及計算題
範例及問題
習題
評分標準
期中考
40%
期末考
40%
二次
(
模擬
)
作業
20%
The
term
microwave
(
微波
)
refers
to
alternating
current
signals
with
frequencies
between
300
MHz
(
3
8
Hz)
and
30
GHz
(
3
10
Hz),
with
a
corresponding
electrical
wavelength
between
1
m
and
1
cm
.
(Pozar
defines
the
range
from
300
MHz
to
300
GHz)
The
term
millimeter
wave
(
毫米波
)
refers
to
alternating
current
signals
with
frequencies
between
30
GHz
(
3
10
Hz)
to
300
GHz
(
3
11
Hz),
with
a
corresponding
electrical
wavelength
between
1
cm
to
1
mm
.
The
term
RF
(
射頻
)
is
an
abbreviation
for
the
“Radio
Frequency”
.
It
refers
to
alternating
current
signals
that
are
generally
applied
to
radio
applications,
with
a
wide
electromagnetic
spectrum
covering
from
several
hundreds
of
kHz
to
millimeter
waves
.
名詞解釋
Microwave Applications
Functional Block Diagram of a
Communication System
Input signal
(Audio, Video, Data)
Input
Transducer
Transmitter
Output
Transducer
Receiver
Output signal
(Audio, Video, Data)
Channel
Electrical System
Wire
or
Wireless
Antenna and Wave Propagation
Surface Wave
Direct Wave
Sky Wave
Satellite
communication
Microwave &
Millimeter Wave
Earth
Ionsphere
Transmitting
Antenna
Receiving
Antenna
Repeaters(Terrestrial communication)
50Km@25fts antenna
Wireless Electromagnetic Channels
Microwave
Millimeter
Wave
RF
Natural and manmade sources
of background noise
Absorption by the atmosphere
Communication
Windows:
35.94and 135
GHz , below 10
GHz
Remote
sensing:
20 or 55
GHz
Spacecraft
Communication:
60 GHz
IEEE Standard C95.1

1991 recommended power density limits for
human exposure to RF and microwave electromagnetic fields
Popular Wireless Transmission
Frequencies
Popular Wireless Applications
Wireline and Fiber Optic Channels
Wireline
Coaxial
Cable
Waveguide
Fiber
1 kHz
10 kHz
100 kHz
1 MHz
10 MHz
100 MHz
1 GHz
10 GHz
100 GHz
10
14
Hz
10
15
Hz
Microwave
Millimeter
wave
RF
Guided Structures at RF Frequencies
Planar Transmission Lines
and Waveguides
Good for Microwave Integrated
Circuit (MIC) Applications
Good for Long Distance
Communication
Conventional Transmission
Lines and Waveguides
Theory
Wireline
Coaxial
Cable
Waveguide
Fiber
1 kHz
10 kHz
100 kHz
1 MHz
10 MHz
100 MHz
1 GHz
10 GHz
100 GHz
10
14
Hz
10
15
Hz
l
<<
Conventional
Circuit Theory
l
l
>>
Microwave
Engineering
Optics
Transmission Line
Circuit Theory, Electronics, Electromagnetics
Microwave
Resonator
RF & Microwave
Background Build

Up
Transmission
Line
Impedance
Matching
Microwave
Network
RF and Microwave Passive Components
RF and Microwave Active and Nonlinear Components
RF and Microwave ICs and Systems
Goal for this course
Chapter 1
Electromagnetic Theory
History of Microwave Engineering
J.C. Maxwell (1831

1879) formulated EM theory in 1873.
O. Heaviside (1850

1925) introduced vector notation and
provided an analysis foundation for guided waves and
transmission lines from 1885 to 1887.
H. Hertz (1857

1894) verified the EM propagation along
wire experimentally from 1887 to 1891
G. Marconi
(1874

1937) invented the idea of wireless
communication and developed the first practical
commercial radio communication system in 1896.
E.H. Armstrong (1890

1954) invented superheterodyne
architecure and frequency modulation (FM) in 1917.
N. Marcuvitz,
I.I. Rabi
,
J.S. Schwinger
,
H.A. Bethe
,
E.M.
Purcell
, C.G. Montgomery, and R.H. Dicke built up radar
theory and practice at MIT in 1940s (World War II).
ps. The names underlined were Nobel Prize winners.
Maxwell’s Equations
Equations in point (differential) form of time

varying
0
,
,
,
B
D
J
t
D
H
M
t
B
E
Equation
Continuity
,
0
t
J
( 0,0)
E M
Generally, EM fields and sources vary with space (x, y, z) and time (t) coordinates.
Equations in integral form
, Faraday's Law
,Ampere's Law
, Gauss's Law
0, No free magnetic c
harge
C S
C S
S
S
B
E dl ds
t
D
H dl ds I
t
Dds Q
Bds
,
Divergence theorem
,
Stokes' theorem
v s
s c
A A ds
A A dl
Where MKS system of units is used, and
E
: electric field intensity, in V/m.
H
: magnetic field intensity, in A/m.
D
: electric flux density, in Coul/m
2
.
B
: magnetic flux density, in Wb/m
2
.
M
: (fictitious) magnetic current density, in V/m
2
.
J
: electric current density, in A/m
2
.
ρ
: electric charge density, in Coul/m
3
.
ultimate source of the electromagnetic field.
Q
: total charge contained in closed surface
S
.
I
: total electric current flow through surface
S
.
Time

Harmonic Fields
0
,
,
,
B
D
J
D
j
H
M
B
j
E
When steady

state condition is considered, phasor representations of
Maxwell’s equations can be written as : (time dependence by multiply
e

j
t
)
2
: Displacement current density, in A/m
EM wave propagatiom
D
t
Constitutive Relations
Question
:
2(6) equations are not enough to solve 4(12) unknown
field components
In free space
H
B
E
D
0
0
,
where
0
= 8.854
10

12
farad/m is the permittivity of free space
.
μ
0
= 4
10

7
Henry/m is the permeability of free space.
In istropic materials
(e.g. Crystal structure and ionized gases)
3 3 3 3
,
x x x x
y y y y
z z z z
D E B H
D E B H
D E B H
)
1
(
,
)
(
);
1
(
,
0
"
'
0
0
"
'
0
m
m
e
e
j
H
P
H
B
j
E
P
E
D
where
P
e
is electric polarization,
P
m
is magnetic polarization
,
e
is electric susceptibility, and
m
is magnetic susceptibility.
Complex
and
The negative imaginary part of
and
account for loss in medium (heat).
, Ohm's law from an EM field point of v
iew
=
='(")
= ('")
"
tan, Loss tangent
'
J E
H j D J
j E E
j E E
j j j E
where
is conductivity (conductor loss),
ω
’’
is loss due to dielectric damping,
(
ω
¶¶
+
)
can be seen as the total effective conductivity,
is loss angle.
In a lossless medium,
and
are real numbers.
Microwave materials are usually characterized by specifying the real
permittivity,
’=
r
0
,and the loss tangent at a certain frequency.
It is useful to note that, after a problem has been solved assuming a
lossless dielectric, loss can easily be introduced by replaced the real
with a
complex
.
Example1.1 :
In a source

free region, the electric field intensity
is given as follow. Find the signal frequency?
V/m
4
ˆ
)
3
(
y
x
j
e
z
E
Solution :
)
3
(
0
)
3
(
0
0
ˆ
4
ˆ
12
4
0
0
ˆ
ˆ
ˆ
1
y
x
j
y
x
j
e
y
x
e
z
y
x
z
y
x
j
H
H
j
E
)
3
(
0
0
2
)
3
(
0
)
3
(
0
0
0
ˆ
16
0
4
12
ˆ
ˆ
ˆ
1
y
x
j
y
x
j
y
x
j
e
z
e
e
z
y
x
z
y
x
j
E
E
j
H
rad/s
10
6
2
4
ˆ
16
8
0
0
0
0
2
z
Boundary Conditions
2
1
2
1
2
1
2
1
,
,
,
H
n
H
n
E
n
E
n
B
n
B
n
D
n
D
n
Fields at a dielectric interface
Fields at the interface with a perfect conductor
(
Electric Wall
)
S
S
J
H
n
E
n
B
n
D
n
,
0
,
0
,
Magnetic Wall
boundary condition (not really exist)
0
,
,
0
,
0
H
n
M
E
n
B
n
D
n
S
ty
conductivi
Assumed
It is analogous to the relations between voltage and current at the end of a short

circuited transmission line.
It is analogous to the relations between voltage and current at the end of a open

circuited transmission line.
Helmholtz (Vector) Wave Equation
In a source

free, linear, isotropic, and homogeneous
medium
0
,
0
2
2
2
2
H
H
E
E
is defined the wavenumber, or propagation constant
, of the medium; its unit are 1/m.
Plane wave in a lossless medium
( ),
1
( ) [ ],
jkz jkz
x
jkz jkz
y
E z E e E e
H z E e E e
k
Solutions of above wave equations
H
E
k
is wave impedance, intrinsic impedance of medium.
In free space,
0
=377
.
ˆ
Transverse Electromagnetic Wave
(TEM)
x y
E H z
,
E
j
H
H
j
E
)
tan
1
(
)
(
1
'
"
'
j
j
j
j
j
j
j
is phase velocity, defined as a fixed phase point on
the wave travels.
In free space,
v
p
=
c
=2.998
10
8
m/s.
1
k
dt
dz
v
p
f
v
v
k
p
p
2
2
is wavelength, defined as the distance between
two successive maximum (or minima) on the wave.
Plane wave in a general lossy medium or a good conductor
In wave equations,
=
j
k
.
1
:Complex propagation constant (m )
: Attenuation constant, : Phase cons
tant
2
1
s
is skin depth or
penetration depth
, defined as the
amplitude of fields in the conductor decay by an amount
1/e or 36.8%, after traveling a distance of one skin depth.
Good ( but not perfect) conductor
Condition: (1)
>>
ω
or (2)
’’>
>
’
Example1.2 :
The skin depth of several kinds of materials at a
frequency of 10GHz:
s
(10

7
m) 8.14 6.60 7.86 6.40
Aluminum Copper Gold Silver
Thin plating
Example1.3 :
A plane wave propagating in a lossless dielectric
medium has the electric field intensity given as follow.
Determine the wavelength, phase velocity, wave impedance,
and dielectric constant?
V/m
)
ˆ
6
.
61
10
cos(1.51
10
0
z
t
E
E
x
Solution :
8
.
307
5
.
1
377
impedance
wave
5
.
1
10
45
.
2
10
3
constant
dielectric
m/s
10
45
.
2
6
.
61
10
51
.
1
velocity
phase
m
102
.
0
6
.
61
2
2
wavelength
0
2
8
8
2
8
10
r
p
r
p
v
c
k
v
k
Analyzing
E
x
can find
=1.51
10
10
rad/s and
k
=61.6 m

1
. Then
Poynting’s Theorem
Energy (power) conservation for EM fields and sources
)
(
2
)
(
2
1
0
*
*
e
m
l
s
v
s
s
W
W
j
P
P
dv
M
H
J
E
P
s
s
s
d
S
s
d
H
E
P
2
1
2
1
*
0
*
,
H
E
S
dv
H
E
dv
E
P
v
v
l
)
(
2
2
2
"
2
"
2
v
e
dv
E
E
W
*
4
v
m
dv
H
H
W
*
4
Power transmitted through
the surface S
Power loss to heat in the
volume v (
Joule’s law
)
Net reactive energy
stored in the volume v
Power delivered by
the source
P
s
Time

averaged Poynting power
entering good conductor
where S is instantaneous Poynting vector
)
Re(
2
1
*
H
E
P
s
s
j
R
1
2
]
2
)
1
Re[(
)
Re(
s
s
t
s
s
s
s
t
R
E
ds
H
R
ds
J
R
P
2
0
2
2
2
2
2
2
Surface resistivity of conductor
Example1.4 :
The electromagnetic fields of an antenna at a
large distance are given as follow. Find the power radiated by
this antenna?
A/m
)
cos
2
cos(
sin
1
ˆ
)
,
(
V/m
)
cos
2
cos(
sin
120
ˆ
)
,
(
0
0
r
jk
r
jk
e
r
j
r
H
e
r
j
r
E
Solution :
W
5
.
1443
)
cos
2
(
cos
sin
60
sin
ˆ
W/m
)
cos
2
(
cos
sin
60
ˆ
)
Re(
2
1
0
2
0
2
2
0
2
0
radiated
2
2
2
2
*
d
d
d
d
r
r
P
P
r
r
H
E
P
Wave Reflection
2
1

field
ed
transmitt
;
ˆ
,
ˆ
field
reflected
;
ˆ
,
ˆ
field
incident
;
1
ˆ
,
ˆ
0
0
0
0
0
0
0
0
0
0
0
0
0
T
e
E
T
y
H
e
TE
x
E
e
E
y
H
e
E
x
E
e
E
y
H
e
E
x
E
jrz
t
jrz
t
z
jk
r
z
jk
r
z
jk
i
z
jk
i
Oblique incidence
Total reflection
Surface waves
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