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Transcript
ECE 563 / TCOM 590
Introduction to Microwaves
and E&M Review
September 2, 2004
M. Black
Brief Microwave History
• Maxwell (1864-73)
– integrated electricity and magnetism
– set of 4 coherent and self-consistent equations
– predicted electromagnetic wave propagation
• Hertz (1886-88)
– experimentally confirmed Maxwell’s equations
– oscillating electric spark to induce similar
oscillations in a distant wire loop (=10 cm)
Brief Microwave History
• Marconi (early 20th century)
– parabolic antenna to demonstrate wireless
telegraphic communications
– tried to commercialize radio at low frequency
• Lord Rayleigh (1897)
– showed mathematically that EM wave
propagation possible in waveguides
• George Southworth (1930)
– showed waveguides capable of small
bandwidth transmission for high powers
Brief Microwave History
• R.H. and S.F. Varian (1937)
– development of the klystron
• MIT Radiation Laboratory (WWII)
– radiation lab series - classic writings
• Development of transistor (1950’s)
• Development of Microwave Integrated
Circuits
– microwave circuit on a chip
– microstrip lines
• Satellites, wireless communications, ...
Microwave Applications
–
–
–
–
–
–
–
–
–
–
Wireless Applications
TV and Radio broadcast
Optical Communications
Radar
Navigation
Remote Sensing
Domestic and Industrial Applications
Medical Applications
Surveillance
Astronomy and Space Exploration
Radar System Comparison
Radar Characteristic
tracking accuracy
identification
volume search
adverse weather perf.
perf. in smoke, dust, ...
wave mmwave optical
poor
fair
good
poor
fair
good
good
fair
poor
good
fair
poor
good
good fair
Microwave Engr. Distinctions
· 1 - Circuit Lengths:
· Low frequency ac or rf circuits
·
·
·
·
time delay, t, of a signal through a device
t = L/v « T = 1/f where T=period of ac signal
but f=v so 1/f= /v
so L «, I.e. size of circuit is generally much
smaller than the wavelength (or propagation
times or phase shift  0)
· Microwaves: L 
· propagation times not negligible
· Optics: L» 
Microwave Distinctions
· 2 - Skin Depth:
· degree to which electromagnetic field
penetrates a conducting material
· microwave currents tend to flow along the
surface of conductors
· so resistive effect is increased, i.e.
· R  RDC a / 2 , where
–  = skin depth = 1/ ( f o cond)1/2
– where, RDC = 1/ ( a2 cond)
– a = radius of the wire
• R waves in Cu >R low freq. in Cu
Microwave Engr. Distinctions
· 3 - Measurement Technique
· At low frequencies circuit properties
measured by voltage and current
· But at microwaves frequencies, voltages
and currents are not uniquely defined; so
impedance and power are measured rather
than voltage and current
Circuit Limitations
• Simple circuit: 10V, ac driven, copper wire,
#18 guage, 1 inch long and 1 mm in
diameter: dc resistance is 0.4 m,
L=0.027μH
–
–
–
–
–
f = 0; XL = 2  f L  0.18 f 10-6 =0
f = 60 Hz; XL  10-5  = 0.01 m
f = 6 MHz; XL  1 
f = 6 GHz; XL  103  = 1 k 
So, wires and printed circuit boards cannot be
used to connect microwave devices; we need
transmission lines, waveguides, striplines, and
microstrip
High-Frequency Resistors
• Inductance and resistance of wire resistors
under high-frequency conditions (f  500
MHz):
–
–
–
–
–
L/RDC  a / (2 )
R /RDC  a / (2 )
where, RDC =  /( a2 cond)
a = radius of the wire
 = skin depth = 1/ ( f o cond)-1/2
Reference: Ludwig & Bretchko, RF Circuit Design
High Frequency Capacitor
• Equivalent circuit consists of parasitic lead
conductance L, series resistance Rs
describing the losses in the the lead
conductors and dielectric loss resistance Re
= 1/Ge (in parallel) with the Capacitor.
• Ge =  C tan s, where
– tan s = (/diel) -1 = loss tangent
Reference: Ludwig & Bretchko, RF Circuit Design
Reference: Ludwig & Bretchko, RF Circuit Design
Transit Limitations
• Consider an FET
• Source to drain spacing roughly 2.5 microns
• Apply a 10 GHz signal:
– T = 1/f = 10-10 = 0.10 nsec
– transit time across S to D is roughly 0.025 nsec
or 1/4 of a period so the gate voltage is low and
may not permit the S to D current to flow
Ref: text by Pozar
Wireless Communications
Options
• Sonic or ultrasonic - low data rates, poor
immunity to interference
• Infrared - moderate data rates, but easily
blocked by obstructions (use for TV remotes)
• Optical - high data rates, but easily
obstructed, requiring line-of-sight
• RF or Microwave systems - wide bandwidth,
reasonable propagation
Cellular Telephone Systems (1)
• Division of geographical area into nonoverlapping hexagonal cells, where each
has a receiving and transmitting station
• Adjacent cells assigned different sets of
channel frequencies, frequencies can be
reused if at least one cell away
• Generally use circuit-switched public
telephone networks to transfer calls between
users
Cellular Telephone Systems (2)
• Initially all used analog FM modulation and
divided their allocated frequency bands into
several hundred channels, Advanced Mobile
Phone Service (AMPS)
– both transmit and receive bands have 832, 25
kHz wide bands. [824-849 MHz and 869-894
MHz] using full duplex (with frequency
division)
• 2nd generation uses digital or Personal
Communication Systems (PCS)
Satellite systems
• Large number of users over wide areas
• Geosynchronous orbit (36,000 km above earth)
– fixed position relative to the earth
– TV and data communications
• Low-earth orbit (500-2000 km)
– reduce time-delay of signals
– reduce the need for large signal strength
– requires more satellites
• Very expensive to maintain & often needs
line-of sight
Global Positioning Satellite
System (GPS)
• 24 satellites in a medium earth orbit (20km)
• Operates at two bands, L1 at 1575.42 and
L2 at 1227.60 MHz , transmitting spread
spectrum signals with binary phase shift
keying.
• Accurate to better that 100 ft and with
differential GPS (with a correcting known
base station), better than 10 cm.
Frequency choices
• availability of spectrum
• noise (increases sharply at freq. below 100
MHz and above 10 GHz)
• antenna gain (increases with freq.)
• bandwidth (max. data rate so higher freq.
gives smaller fractional bandwidth)
• transmitter efficiency (decreases with freq.)
• propagation effects (higher freq, line-of sight)
Propagation
• Free space power density decreases by 1/R2
• Atmospheric Attenuation
• Reflections with multiple propagation paths
cause fading that reduces effective range, data
rates and reliability and quality of service
• Techniques to reduce the effects of fading are
expensive and complex
Antennas
• RF to an electromagnetic wave or the inverse
• Radiation pattern - signal strength as a function
of position around the antenna
• Directivity - measure of directionality
• Relationship between frequency, gain, and size
of antenna,  = c/f
– size decreases with frequency
– gain proportional to its cross-sectional area \ 2
– phased (or adaptive) array - change direction of
beam electronically
Math Review


Misalkan A dan B interseksi on vectors
   
A  B  A B cos  : scalar atau dot product,
projeksi satu vecto r terhadap lainnya
   

A  B  A B sin  C
Perubahan yg didefisika n oleh partial /x menghasilk an
     

x y z
x
y
z
Untuk systems coordinate berikutnya
jika sebuah field memiliki scalar u  u(x, y, z)
bervariasi dalam ruang (Space)
u  u  u 
z ; gradient : rate of change
y
x
u 
z
y
x
 Ax Ay Az
; Divergence : net outward flow


A 
z
y
x

Ay Ax
) z ; Curl or ROT (Russian)

(  A) z  (
y
x
rotation (pusaran daun yg mengalir di sungai)
 
A  A  0;   u  0 or curl of gradient  0
  
  


A  ( B  C )  ( A  B)  C ;   (  C )  (  )  C  0
or div of curl  0
 

 A  ds   ( A)dV ; Divergence theorem
v
s
 
 
 A  d   (  A)ds; Stokes (batu) theorem

s
Maxwell’s Equations
  D  
B  0
  E  B / t
  H  J  D / t
•
•
•
•
Gauss
No Magnetic Poles
Faraday’s Laws
Ampere’s Circuit Law
Characteristics of Medium
Constitutive Relationships
D  E,   ro , Dielectric Permitivit y
B  H,   or, Magnetic Permeabili ty
Jc  E, J  Jc  Jv, Jv  Convective Current
Assumption s
J    0, in the medium itself, not so on surfaces
, , scalars except ferrites, plasma
E, H proportion al to exp(j t - z)
where     j,   attentuati on constant
  phase constant, z  direction of propagatio n
Fields in a Dielectric Materials
Assume D  oE  P, and non  magnetic, so   o
and J    0 (D  electric flux or displaceme nt density)
P  dipole moment density   e oE,  e  dielectric suceptibil ity
D  o(1   e )E  E
  o(1   e )    j
  , for good dielectric (3 or 4 orders of magnitude)
 accounts for loss in the medium (heat)
negative due to entergy conservati on   0
Fields in a Conductive Materials
J  J c  E, where E fields vary as e jt
H  J 
D
E
 E  
 E  jE
t
t

 )E  (  j  j( j))E
j




 j(  j  j )E  [ j  (  )]E

where    is the effective conductivi ty
  
effective loss tangent  tan 

 j(
Wave Equation
Consider /t  j
   E  -jH,   H  jE
  (  E)  (  E) -  2 E    ( jH)
 ( j )( j )E
  2 E  -  2 E;
similarly  2 H  -  2 H;
define : k   2   propagatio n constant of waves
in medium described by  and 
General Procedure to Find Fields
in a Guided Structure
• 1- Use wave equations to find the z
component of Ez and/or Hz
–
–
–
–
–
note classifications
TEM: Ez = Hz= 0
TE: Ez = 0, Hz  0
TM: Hz = 0, Ez  0
HE or Hybrid: Ez  0, Hz  0
General Procedure to Find Fields
in a Guided Structure
• 2- Use boundary conditions to solve for any
constraints in our general solution for Ez
and/or Hz

n̂  E  0, or E t  0 on surface of perfect conductor

n̂  E   s /

n̂  H  J s

n̂  H  0, or H n  0 on surface of perfect conductor
where n̂  normal to the surface of conductor
Plane Waves in Lossless Medium
 2 E  k 2 E  0, where k  ω  is real since  and  are real
in a lossless medium
E  E x and /x  /y  0
 2E x
2
  jkz
  jkz


k
E

0

E
(
z
)

E
e

E
e
x
x
2
z
or in the time domain :
E x (z, t )  E  (cos( t  kz))  E  (cos( t  kz))
ω t  kz  constant  moving in the  z direction
Phase Velocity
Fixed phase point trav els at a velocity
dz d t - constant


vp 
 (
) 

dt dt
k
k  
in free space v p 
1
 o o
1


 c  3  108 m/sec
Wavelength : distance between 2 successive maxima
(t - kz) - (t - k(z   ))  2  k
2 2v p v p
 


or v p  f
k

f
in free space : v p  f  c
Wave Impedance
H
By Maxwell' s eqn :   E  -
  jH
t



E x

 0; so
ẑ  E x x̂ 
ŷ
x y
z
z
 jkE  e  jkz  jkE  e  jkz   jH y
k
Hy 
( E  e  jkz  E  e  jkz )


where  
or   E/H
k
Plane Waves in a Lossy Medium
  E   jH and   H   jE  E
    E   j(  H)   j( jE  E )
    E  (  E)   2 E

2
2
  E   (1  j )E  0


2
 (1  j )    2  wave number , now complex


    j  j  (1  j ) note   0,   0

and   j and   k
Wave Impedance in Lossy
Medium
as before E  E x x̂ and /x  /y  0
 Ex
 2   2 E x  0  E x (z)  E  e  z  E  e  z
z
 z
  z  j z
 z
e  e e  time domain  e cos(t   z)
2
 j   z
Hy 
(E e  E  e  z )

j
where  
 wave impedance with losses

Plane Waves in a good
Conductor
practical case   
  j   j /   j  j 2 / 
 (1  j)  / 2     / 2
s  1 /   2 /   skin depth
at 10 GHz, s  1m for most metals (Al, Cu, Ag, Au)
 at microwave frequencie s, currents flow on the surface
Energy and Power
A source of electromag netic energy sets up fields that
store electric and magnetic energy and carry power
that may be transmitt ed or dissipated as loss
We  1 / 4 Re  E  D *dv   / 4  E  E *dv
v
v
Wm  1 / 4 Re  H  B*dv   / 4  H  H *dv
v
v
Ps  power generated by sources
 Po  P  2 j( Wm  We )
Po  1 / 2 Re  E H  ẑds  power transmitt ed
*
s