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