microwave

clappergappawpawΠολεοδομικά Έργα

16 Νοε 2013 (πριν από 3 χρόνια και 10 μήνες)

156 εμφανίσεις

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