ece & tcom 590 microwave transmission for telecommunications introduction to microwaves january...
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ECE & TCOM 590Microwave Transmission for
Telecommunications
Introduction to Microwaves
January 29, 2004
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
Brief Microwave History• Maxwell (1864-73)
– integrated electricity and magnetism– set of 4 coherent and self-consistent equations– predicted electromagnetic wave propagation
• Hertz (1873-91) – 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, ...
Ref: text by Pozar
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 0)
· Microwaves: L · propagation times not negligible
· Optics: L»
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
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
2
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 and inductance is 0.027 H– 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
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) {the 2 here
accounts for 2 leads}– a = radius of the wire– = length of the leads = skin depth = 1/ ( f o cond)1/2
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
Reference: Ludwig & Bretchko, RF Circuit Design
Reference: Ludwig & Bretchko, RF Circuit Design
Maxwell’s Equations
tDJH
tBE
B
D
/
/
0
• Gauss
• No Magnetic Poles
• Faraday’s Laws
• Ampere’s Circuit Law
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
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
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
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
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
conductor of surface the tonormaln where
conductorperfect of surfaceon 0Hor ,0Hn
JHn
/E n
conductorperfect of surfaceon 0Eor 0,En
n
s
t
s
Plane Waves in Lossless Medium
direction z in the movingconstantkztω
))kzt(cos(E))kzt(cos(E)t,z(E
:domain timein theor
eEeE)z(E0Ekz
E
0y/x/ and E E
medium lossless ain
real are and since real is ωk where0,EkE
x
jkzjkzxx
22x
2
x
22
Phase Velocity
cfv :space freein
fvor f
vv2
k
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maxima successive 2between distance :Wavelength
m/sec 103c1
vspace freein
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k
constant-t(
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d
dt
dzv
velocityaat elspoint trav phase Fixed
p
ppp
8
oo
p
p
Wave Impedance
E/Hor k
where
)eEeE(k
H
HjejkEejkE
yz
ExEz
z so ;0
yx
Hjt
H-E :eqn sMaxwell'By
jkzjkzy
yjkzjkz
xx
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
EEjH and HjE
22
22
2
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
22x
2
x
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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(Russian) ROTor Curl;)y
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