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, 3nd. 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, 3nd. 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 (3108 Hz) and 30 GHz (31010 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 (31010 Hz) to 300 GHz (31011 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
ReceiverOutput signal
(Audio, Video, Data)
Channel
Electrical System
Wire orWireless
Antenna and Wave Propagation
Surface Wave
Direct Wave
Sky Wave
Satellitecommunicatio
n
Microwave & Millimeter Wave
Earth
Ionsphere
Transmitting Antenna
Receiving
Antenna
Repeaters(Terrestrial communication)
50Km@25fts antenna
Wireless Electromagnetic Channels
Mic
row
av
e
Millim
ete
rW
ave
RF
Natural and manmade sources of background
noise
Absorption by the atmosphere
Communication
Windows:35.94and
135GHz , below
10 GHz
Remote sensing:20 or 55
GHz
Spacecraft Communicatio
n: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
WirelineCoaxial Cable Waveguide Fiber
1
kH
z1
0
kH
z1
00
kH
z1
MH
z
10
MH
z
10
0
MH
z 1 G
Hz
10
GH
z
10
0
GH
z
10
14 H
z
10
15 H
z
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
WirelineCoaxial Cable Waveguide Fiber
1
kH
z1
0
kH
z1
00
kH
z1
MH
z
10
MH
z
10
0
MH
z 1 G
Hz
10
GH
z
10
0
GH
z
10
14 H
z
10
15 H
z
l <<
Conventional Circuit Theory
l l >>
Microwave Engineering
Optics
Transmission Line
Circuit Theory, Electronics, Electromagnetics
Mic
row
ave
Reson
ato
r
RF & Microwave Background Build-Up
Tra
nsm
issi
on
Lin
e
Imp
ed
an
ce
Matc
hin
g
Mic
row
ave
Netw
ork
RF and Microwave Passive Components
RF and Microwave Active and Nonlinear Components
RF and Microwave ICs and Systems
Goal fo
r th
is c
ou
rse
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
Jt
DH
Mt
BE
EquationContinuity ,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 charge
C S
C S
S
S
BE dl ds
tD
H dl ds It
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/m2. B : magnetic flux density, in Wb/m2. M : (fictitious) magnetic current density, in V/m2. J : electric current density, in A/m2. ρ: electric charge density, in Coul/m3.
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
JDjH
MBjE
When steady-state condition is considered, phasor representations of Maxwell’s equations can be written as : (time dependence by multiply e -jt )
2: Displacement current density, in A/m EM wave propagatiomD
t
Constitutive Relations
QuestionQuestion : 2(6) equations are not enough to solve 4(12) unknown field components
In free space
HB
ED
0
0 ,
where 0 = 8.85410-12 farad/m is the permittivity of free space.
μ0 = 410-7 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
mm
ee
jHPHB
jEPED
where Pe is electric polarization, Pm 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 view
=
= ' ( " )
= ( ' " )
"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, ’=r0,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 4ˆ )3( yxjezE Solution :
)3(
0)3(
00
ˆ4ˆ12
400
ˆˆˆ1
yxj
yxj
eyx
ezyx
zyx
jHHjE
)3(
002
)3(
0
)3(
0
0
0
ˆ16
0412
ˆˆˆ1
yxj
yxjyxj
ez
ee
zyx
zyx
jE
EjH
rad/s 1062
4ˆ16 8
00002
z
Boundary Conditions
2121
2121
,
, ,
HnHnEnEn
BnBnDnDn
Fields at a dielectric interface
Fields at the interface with a perfect conductor (Electric Wall)
S
S
JHnEn
BnDn
,0
,0 ,
Magnetic Wall boundary condition (not really exist)
0
,
,0
,0
Hn
MEn
Bn
Dn
S
ty conductivi AssumedIt 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
,022
22
HH
EE
is defined the wavenumber, or propagation constant
, of the medium; its unit are 1/m.
Plane wave in a lossless medium( ) ,
1( ) [ ],
jkz jkzx
jkz jkzy
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 yE H z
,
EjH
HjE
)tan1()(1 '"' jjjjjjj
is phase velocity, defined as a fixed phase point on the wave travels.In free space, vp=c=2.998108 m/s.
1
kdt
dzvp
f
vv
kpp
22is wavelength, defined as the distance between two successive maximum (or minima) on the wave.
Plane wave in a general lossy medium or a good conductorIn wave equations, =j k.
-1: Complex propagation constant (m )
: Attenuation constant, : Phase constant
21
sis 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 )ˆ6.6110cos(1.51 100 ztEEx
Solution :
8.3075.1
377 impedance wave
5.11045.2
103 constant dielectric
m/s 1045.26.61
1051.1 velocity phase
m 102.06.61
22 wavelength
0
2
8
82
810
r
pr
p
v
c
kv
k
Analyzing Ex can find =1.511010 rad/s and k=61.6 m-1. Then
Poynting’s Theorem Energy (power) conservation for EM fields and sources
)(2)(2
10
**emlsv ss WWjPPdvMHJEP
ss
sdSsdHEP2
1
2
1 *0
*, HES
dvHEdvEPvvl )(
222"2"2
ve dvEEW *
4
vm dvHHW *
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 bythe source Ps
Time-averaged Poynting power
entering good conductor
where S is instantaneous Poynting vector
)Re(2
1 *HEP
ss jR
1
2]
2)1Re[()Re(
s
st
s
s sst RE
dsHR
dsJR
P 20
222 2
22
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 )cos2
cos(sin
1ˆ),(
V/m )cos2
cos(sin
120ˆ),(
0
0
rjk
rjk
erjrH
erjrE
Solution :
W 5.1443)cos2
(cossin
60
sinˆ
W/m )cos2
(cossin
60ˆ)Re(
2
1
0
2
0
2
2
0
2
0radiated
2222
*
dd
ddrrPP
rrHEP
Wave Reflection
21
-
field ed transmitt;ˆ ,ˆ
field reflected ;ˆ ,ˆ
fieldincident ;1
ˆ ,ˆ
00
0
00
00
00
00
00
T
eET
yHeTExE
eEyHeExE
eEyHeExE
jrzt
jrzt
zjkr
zjkr
zjki
zjki
Oblique incidence
Total reflection
Surface waves