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ECE 563 / TCOM 590Introduction to Microwaves
and E&M Review
September 2, 2004
M. Black
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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)
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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
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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, ...
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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
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Radar System Comparison
Radar Characteristic wave mmwave optical
tracking accuracy poor fair good
identification poor fair good
volume search good fair poor
adverse weather perf. good fair poor
perf. in smoke, dust, ... good good fair
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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»
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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
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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
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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
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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
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Reference: Ludwig & Bretchko, RF Circuit Design
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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
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Reference: Ludwig & Bretchko, RF Circuit Design
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Reference: Ludwig & Bretchko, RF Circuit Design
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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
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Ref: text by Pozar
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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
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Cellular Telephone Systems (1)• Division of geographical area into non-
overlapping 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
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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)
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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
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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.
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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)
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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
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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
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berikutnya coordinate systemsUntuk
zx
anmenghasilkx / partialoleh n didefisika ygPerubahan
C sinABA
lainnya r terhadapsatu vecto projeksi
product,dot atau scalar : cosABA
on vectorsinterseksi Bdan AMisalkan
Review
zyy
x
B
B
Math
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sungai) dimengalir ygdaun (pusaran rotation
(Russian) ROTor ;)()A(
flow outwardnet :Divergence ; A
change of rate :gradient ;u
(Space) ruang dalam bervariasi
z)y,u(x,uscalar memiliki fieldsebuah jika
z Curly
A
x
A
z
A
y
A
x
A
zz
uy
y
uxx
u
zxy
zyx
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theorem(batu) Stokes ;)(
theoremDivergence ;)(
0 curl of divor
0)()( ;)()(
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s
vs
dsAdA
dVAdsA
CCCBACBA
uAA
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Maxwell’s Equations
tDJH
tBE
B
D
/
/
0
• Gauss
• No Magnetic Poles
• Faraday’s Laws
• Ampere’s Circuit Law
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Characteristics of MediumConstitutive Relationships
npropagatio ofdirection z constant, phase
constanton attentuati ,j where
z)-texp(j toalproportion HE,
plasma ferrites,except scalars,,
surfaceson sonot itself, medium in the 0,J
sAssumption
Current ConvectiveJJJJ E,J
tyPermeabili Magnetic ,H,B
yPermitivit Dielectric,ED
v v,cc
ro
,or
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Fields in a Dielectric Materials
0on conservatientergy todue negative
(heat) medium in the lossfor accounts
magnitude) of orders 4or (3 dielectric goodfor ,
j)1(
EE)1(D
itysuceptibil dielectric ,E density moment dipole P
density)nt displacemeor flux electric(D 0J and
so magnetic,non and ,PED Assume
eo
eo
eoe
oo
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Fields in a Conductive Materials
tan tangent loss effective
tyconductivi effective theis where
E)](j[E)jj(j
E))j(jj(E)j
(j
EjEt
EE
t
DJH
e as vary fields E where,EJJ tjc
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Wave Equation
and by described mediumin
wavesofconstant n propagatio :
;H - H
;E - E
E))((
)H( E -E)(E)(
EjH H,-jE
jt/Consider
2
22
22
2
kdefine
similarly
jj
j
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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
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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
conductor of surface the tonormaln where
conductorperfect of surfaceon 0Hor ,0Hn
JHn
/E n
conductorperfect of surfaceon 0Eor 0,En
n
s
t
s
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Plane Waves in Lossless Medium
direction z in the movingconstantkztω
))kzt(cos(E))kzt(cos(E)t,z(E
:domain timein theor
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E
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medium lossless ain
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x
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Phase Velocity
cfv
fvf
vv
c
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8p
p
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Wave Impedance
E/Hor k
where
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yz
ExEz
z so ;0
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jkzjkzy
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xx
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Plane Waves in a Lossy Medium
k and j and
0,0 note)j1(jj
complex now,number ewav)j1(
0E)j1(E
E)E(E
)EEj(j)H(jE
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22
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Wave Impedance in Lossy Medium
losses with impedance wavej
where
)eEeE(j
H
)ztcos(edomain timeeee
eEeE)z(E0Ez
E
0y/x/ and xEE before as
zzy
zzjzz
zzxx
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2
x
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Plane Waves in a good Conductor
surface on the flow currents s,frequencie microwaveat
Au)Ag,Cu,(Al, metalsmost for m1 GHz, 10at
depth skin/2/1
2/2/)j1(
/jj/jj
case practical
s
s
2
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Energy and Power
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