Philadelphia University
Faculty of Engineering Communication and Electronics Engineering
Part 1 Dr. Omar R Daoud 1
ANTENNAS and MICROWAVES
ENGINEERING
(650427)
2/26/2018 Dr. Omar R Daoud 2
Introduction
Electromagnetic Waves (EM)
Static EM (Electrostatic/ Magnetostatic) Fields Electric (stationary charges) and magnetic (steady current)
fields are independent each other
Dynamic/Time varying EM Fields (Waves) Electric and magnetic fields are interdependent
The current is time varying (moving/accelerated charges)
They can be represented as
E(x,y,z,t)
H(x,y,z,t)
Introduction
Faraday’s Law
A static magnetic field produces no
current flow,
In a closed loop, a time varying field
will produce an electromotive force
(emf) which leads to a flow current.
An increasing magnetic field out of the
page induces the current or an emf.
The continuous-conductive-loop
distributed resistance is modeled as a
series resistor Rdist
2/26/2018 Dr. Omar R Daoud 3
Introduction
Transformer and motional emf
Stationary Loop in Time Varying B
Field
A stationary conducting loop is in a
time varying magnetic B field.
Applying Stokes theorem
Thus,
2/26/2018 Dr. Omar R Daoud 4
S
BSE d
tdVemf
t
BE
Introduction
Transformer and motional emf
Stationary Loop in Time Varying B
Field
Thus,
The time varying electric field is not
conservative, or not equal to zero.
The work done in taking a charge about
a closed path in a time varying electric
field, for example, is due to the energy
from the time varying magnetic field.
2/26/2018 Dr. Omar R Daoud 5
Introduction
Transformer and motional emf
Moving Loop in static B Field
Due to the conducting loop movement
with u velocity, an emf is induced (the
force on a charge moving with uniform
velocity in magnetic field)
2/26/2018 Dr. Omar R Daoud 6
Fundamentals of Electromagnetics With Engineering Applications by Stuart M. Wentworth
Copyright © 2005 by John Wiley & Sons. All rights reserved.
Figure 4-12 (p. 185)Conductive bar moving along a pair of parallel conductive rails.
L
memf ddV LBuLE
Introduction
Transformer and motional emf
Moving Loop in Time Varying Field
2/26/2018 Dr. Omar R Daoud 7
LS
memf ddt
dV LBuSB
LE
Introduction
Transformer and motional emf
Example
The loop shown is inside a uniform
magnetic field B = 50 ax mWb/m2 . If
side DC of the loop cuts the flux lines
at the frequency of 50Hz and the loop
lies in the yz plane at time t = 0, find
the induced emf at t = 1 ms.
2/26/2018 Dr. Omar R Daoud 8
Introduction
Transformer and motional emf
Example
Since the B field is time invariant, the
induced emf is motional, that is:
2/26/2018 Dr. Omar R Daoud 9
L
memf ddV LBuLE
zDC dzdd aLL
aaL
u
dt
d
dt
d loopmoving
1002,4 fcm
Introduction
Transformer and motional emf
Example
Transforming the B field into
cylindrical coordinate, since u and dL
is in cylindrical coordinates:
B0 = 0.05
2/26/2018 Dr. Omar R Daoud 10
a-aaB sincos00 BB x
z
z
B
BB
a
aaa
Bu
cos
0sincos
00 0
00
dz
dzdzBd
cos2.0
cos05.010004.0cos0
LBu
Introduction
Transformer and motional emf
Example
To determine recall that,
To calculate C, since the loop is in
the yz plane, then at
2/26/2018 Dr. Omar R Daoud 11
mVdzV
z
emf cos6cos2.0
03.0
0
Ctdt
d
2,0 t
Introduction
Transformer and motional emf
Example
Therefore,
At t = 1 ms,
2/26/2018 Dr. Omar R Daoud 12
mVt
tVemf
100sin6
2cos6cos6
mV.Vemf 8255)001.0(100sin6
Introduction
Displacement Current
At Static field
A conduction current density (related
to electric field Ohm’s Law) could be
defined
The divergence of curl of a vector is
identically zero, thus it is clearly
invalid for time varying fields since it
violates the law of current continuity,
Maxwell resolved this issue by
introducing the displacement current density.
2/26/2018 Dr. Omar R Daoud 13
dc JJH
Introduction
Displacement Current
At low frequencies, Jd (rate of change of the electric flux density)
is usually neglected compared with
Jc. But at radio frequencies, the two
terms are comparable.
2/26/2018 Dr. Omar R Daoud 14
tc
DJH
dcc iidt
dd
SDSJLH
Introduction
Displacement Current
The generated i(t) according to
apply the sinusoidal voltage source
v(t) in the circuit is the conduction
current.
Consider the loop surrounding the
plane surface S1.
By static form: the circulation of H
must be equal to the current that cuts
through the surface. But, the same
current must pass through S2 that
passes between the plates of
capacitor.
2/26/2018 Dr. Omar R Daoud 15
Introduction
Displacement Current
The generated i(t) according to
apply the sinusoidal voltage source
v(t) in the circuit is the conduction
current.
Consider the loop surrounding the
plane surface S1.
But, there is no conduction current
passes through an ideal capacitor,
(where J=0, due to σ=0 for an ideal
dielectric ) flows through S2. This is
contradictory in view of the fact that
the same closed path as S1 is used.
2/26/2018 Dr. Omar R Daoud 16
Introduction
Displacement Current
The generated i(t) according to
apply the sinusoidal voltage source
v(t) in the circuit is the conduction
current.
Consider the loop surrounding the
plane surface S1.
But to resolve this conflict, the
current passing through S2 must be
entirely a displacement current,
where it needs to be included in
Ampere’s Circuital Law.
2/26/2018 Dr. Omar R Daoud 17
Introduction
Displacement Current
The generated i(t) according to
apply the sinusoidal voltage source
v(t) in the circuit is the conduction
current.
Consider the loop surrounding the
plane surface S1.
So we obtain the same current for
either surface though it is conduction
current in S1 and displacement
current in S2.
2/26/2018 Dr. Omar R Daoud 18
122SSS
d dIt
Qd
tdd SJSDSJLH
Introduction
Maxwell Equations
Gauss’s Law
Gauss’s Law for Magnetic Field
Faraday’s Law
Ampere’s Circuital Law
2/26/2018 Dr. Omar R Daoud 19
v D encQd SD
0 B 0 SB d
t
BE
tc
DJH
SDSJLH d
tdd c
SBLE d
td
Introduction
Lossless TEM waves
A Transverse Electromagnetic wave
mode (TEM) means:
Both fields magnetic and electric are
always normal or perpendicular to each
other.
TEM Waves has no E field or H field
components along the direction of
propagation.
Consider an x-polarized wave
propagating in the +z direction in some
ideal medium characterized by µ and ε, with σ = 0 (medium lossless).
2/26/2018 Dr. Omar R Daoud 20
Fundamentals of Electromagnetics With Engineering Applications by Stuart M. Wentworth
Copyright © 2005 by John Wiley & Sons. All rights reserved.
A plot of the equation E(z,0) = E0cos(z)ax at 10
MHz in free space with E0 = 1 V/m.
xztEtz aE cos, 0
1pu
pu
Introduction
Lossless TEM waves
By applying Faraday’s Law
2/26/2018 Dr. Omar R Daoud 21
Fundamentals of Electromagnetics With Engineering Applications by Stuart M. Wentworth
Copyright © 2005 by John Wiley & Sons. All rights reserved.
A plot of the equation E(z,0) = E0cos(z)ax at 10
MHz in free space with E0 = 1 V/m.
tt
HBE
yy
zyx
ztEztEz
ztE
zyx
aa
aaa
E
sincos
00cos
00
0
dtztE
d
ztEt
y
y
aH
aH
sin
sin
0
0
CztE
y aH
cos0
Fundamentals of Electromagnetics With Engineering Applications by Stuart M. Wentworth
Copyright © 2005 by John Wiley & Sons. All rights reserved.
If no conduction current, C must be zero.
Introduction
Lossless TEM waves
Example
Suppose in free space that:
E(z,t) = 5.0 e-2zt ax V/m.
Is the wave lossless?
Find H(z,t).
2/26/2018 Dr. Omar R Daoud 22
Introduction
Lossless TEM waves
Example
Since the wave has an attenuation term (e-2zt) it
is clearly not lossless.
To find H
2/26/2018 Dr. Omar R Daoud 23
2 2
2
5 10
5 0 0
x y z
zt zt
o y y
zt
e tex y z zt
e
a a a
HE a a
2 210 10, =zt zt
y y
o o
td e dt te dt
H a H a
2 2
2
10 10
2 4
zt zt
y
o o
t Ae e
z z m
H a
udv uv vdu 2 and .ztu t dv e dt
Introduction
EM waves: Fundamental and Equations
For the source point in a space of time
varying E field, a H field is induced in the
surrounding region.
For a changing H field with time, an induced
E field will be found.
Energy is pass back and forth between E and
H fields as they radiate away from the source
at the speed of light.
In a free space, the constitutive parameters
are σ = 0, µr = 1, εr = 1, so the Ampere’s Law
and Faraday’s Law equations become :
2/26/2018 Dr. Omar R Daoud 24
ttc
EH
DJH 0
tt
HE
BE 0
Introduction
EM waves: Fundamental and Equations
The EM waves radiates spherically, but at a
remote distance away from the source they
resemble uniform plane wave.
In a uniform plane wave, the E and H fields
are orthogonal, or transverse to the direction
of propagation ( to propagate in TEM mode ).
Consider
2/26/2018 Dr. Omar R Daoud 25
xz zteEtz aE cos, 0
zeE
E
0
0Initial amplitude at z = 0
exponential terms attenuation
Angular frequency
Phase constant
Phase shift
f 2f
T12
2 f
dt
dzu p
Introduction
EM waves: Fundamental and Equations
Using Maxwell’s equation, the Helmholtz
wave equation can be derived as
where is the propagation constant (consists of
attenuation and phase constants) and defined as
2/26/2018 Dr. Omar R Daoud 26
2
22
tt
EEE
ss jj EE 2
022 ss EE
jjj )(
112
112
2
2
Introduction
EM waves: Fundamental and Equations
The general solution for the Helmholtz wave
equation can be expressed as
The magnetic field can be found by applying
Faraday’s Law :
The intrinsic impedance can be defined as
2/26/2018 Dr. Omar R Daoud 27
zzxs eEeEzE 00)(
xz
xz zteEzteEtz aaE coscos, 00
yzz
s ej
Ee
j
EaH
00
j
H
E
0
0
nj
n ej
j
0
0
H
E
2tan
Introduction
EM waves: Fundamental and Equations
The loss tangent is the ratio of magnitude of
conduction current density to displacement
current density in a lossy medium and can be
expressed as:
tan δ is used to determine how lossy a
medium is
Good (lossless or perfect) dielectric if
Good conductor if
2/26/2018 Dr. Omar R Daoud 28
tan
jj s
s
d
c
E
E
J
J
,1tan
, 1tan
Introduction
EM waves: Fundamental and Equations
To determine the E, H and propagation
direction, the Fleming’s Left Hand Rule is
used.
By knowing the EM wave’s direction of
propagation, given as unit vector ap, is the
same as the cross product of Es with unit
vector, aE and Hs with unit vector aH :
2/26/2018 Dr. Omar R Daoud 29
SS
SSP
HE
HEa
SPS
SPS
HaE
EaH
1
HE
EH
HE
aaa
aaa
aaa
P
P
P
Introduction
EM waves: Fundamental and Equations
Example
Suppose in free space that:
H(x,t) = 100 cos(2π x 107t – βx + π/4) az mA/m.
Find E(x,t).
2/26/2018 Dr. Omar R Daoud 30
Introduction
EM waves: Fundamental and Equations
Example
Since
H(x,t) = 100 cos(2π x 107t – βx + π/4) az mA/m.
So then,
Since free space is stated,
2/26/2018 Dr. Omar R Daoud 31
0.100 , , 4
120 0.100 12
j x j
s z P x
j x j j x j
s P s x z y
e e
e e e e
H a a a
E a H a a a
12 cos yt x E a2 2
2 30 rad mc f
7 212 cos 2 10
30 4y
Vx t x
m
E a
Introduction
EM waves: Fundamental and Equations
Example
Suppose in free space that:
E (x,y,t) = 5 cos(π x 106t – 3.0x + 2.0y) az V/m.
Find
H(x,y,t)
The direction of propagation, ap
2/26/2018 Dr. Omar R Daoud 32
Introduction
EM waves: Fundamental and Equations
Example
Since
E (x,y,t) = 5 cos(π x 106t – 3.0x + 2.0y) az V/m.
2/26/2018 Dr. Omar R Daoud 33
3 25 j x j y
s ze eE a3 2 3 210 15j x j y j x j y
s s x yj j e e j e e E H a a
3 2 3 2 3 2 3 210 152.53 3.8j x j y j x j y j x j y j x j y
s x y x y
o
j je e e e e e e e
j j
H a a a a
6 6 A( , , ) 2.53cos 10 3 2 3.80cos 10 3 2
mx yx y t x t x y x t x y H a a
So that,
Introduction
EM waves: Fundamental and Equations
Example
Since
where
and then,
2/26/2018 Dr. Omar R Daoud 34
s sP
s s
E Ha
E H
6 4 6 419 12.65j x j y j x j y
s s x ye e e e E H a a
y
yjxj
x
yjxj
p aeeaeea 4646 55.083.0
Introduction
EM waves: Propagations in different media
Lossless, Charge – Free
Charge free, ρv=0, medium has zero conductivity,
σ=0.
This is the case where waves traveling in vacuum
or free space (free of any charges).
Perfect dielectric is also considered as lossless
media.
2/26/2018 Dr. Omar R Daoud 35
, 0
1pu
jjj )(
jjjjj 22)0(
j
j
0 1200
Introduction
EM waves: Propagations in different media
Example (Lossless, Charge – Free) In a lossless, nonmagnetic material with :
εr = 16, and H = 100 cos(ωt – 10y) az mA/m.
Determine :
The propagation velocity
The angular frequency
The instantaneous expression for the electric field intensity.
2/26/2018 Dr. Omar R Daoud 36
Introduction EM waves: Propagations in different media
Example (Lossless, Charge – Free)
2/26/2018 Dr. Omar R Daoud 37
883 10
0.75 1016
p
r
c x mu x
s
The propagation velocity:
The angular frequency:
8 80.75 10 10 7.5 10p
radu x x
s
From given H field :
8( , ) 100cos 7.5 10 10 z
mAy t x t y
m H a
So, the time harmonic H field is:
0.100 ,
1200.100 3
j y
s z
j y j y
s P s y z x
r
e
e e
H a
E a H a a a
8( , ) 9.4cos 7.5 10 10 x
Vy t x t y
m E a
Finally, the instantaneous expression for E field is:
Introduction
EM waves: Propagations in different media
Dielectric
It is treated as a lossless approximation,
It has a complex permittivity, complex
propagation constant with attenuation constant
greater than zero.
The intrinsic impedance is also complex,
resulting a phase difference between E and H
fields.
2/26/2018 Dr. Omar R Daoud 38
Introduction
EM waves: Propagations in different media
Conductor
In any decent conductor, the loss tangent,
σ/ωε>>1 or σ>>ωε so that σ ≈ ∞, so that:
2/26/2018 Dr. Omar R Daoud 39
j
j
j
045)1(2
jej
2pu
f2
Introduction
EM waves: Normal Incidence
Consider a plane wave that are normally
incident which means the planar boundary
separating the two media is perpendicular to
the wave’s propagation direction.
Generally, consider a time harmonic x-
polarized electric field incident from medium 1
(µr1, εr1, σr1) to medium 2 (µr2, εr2, σr2)
2/26/2018 Dr. Omar R Daoud 40
xzii zteEtz aE 10 cos),( 1
y
zjzt
t
s
x
zjztt
s
y
zjzr
r
s
x
zjzrr
s
y
zjzi
i
s
x
zjzii
s
eeE
eeE
eeE
eeE
eeE
eeE
aH
aE
aH
aE
aH
aE
22
22
11
11
11
11
2
0
0
1
0
0
1
0
0
tri EEE 000 ,,
The E field intensities
at z=0
i
riir
E
EEEE
0
0
12
1200
12
120 ,
i
tiit
E
EEEE
0
0
12
200
12
20
2,
2
1
Introduction
EM waves: Normal Incidence
Consider a plane wave that are normally
incident which means the planar boundary
separating the two media is perpendicular to
the wave’s propagation direction.
Generally, consider a time harmonic x-
polarized electric field incident from medium 1
(µr1, εr1, σr1) to medium 2 (µr2, εr2, σr2)
2/26/2018 Dr. Omar R Daoud 41
xzii zteEtz aE 10 cos),( 1
y
zjzt
t
s
x
zjztt
s
y
zjzr
r
s
x
zjzrr
s
y
zjzi
i
s
x
zjzii
s
eeE
eeE
eeE
eeE
eeE
eeE
aH
aE
aH
aE
aH
aE
22
22
11
11
11
11
2
0
0
1
0
0
1
0
0
tri EEE 000 ,,
The E field intensities
at z=0
i
riir
E
EEEE
0
0
12
1200
12
120 ,
i
tiit
E
EEEE
0
0
12
200
12
20
2,
2
1
Introduction
EM waves: Normal Incidence
Standing wave pattern for an incident wave in
a lossless medium reflecting off a second
medium at z=0 where = 0.5.
SWR is a measure of mismatch of the load to
the line.
SWR=1 (matched)
SWR →∞ (total mismatch)
2/26/2018 Dr. Omar R Daoud 42
1
1
min
max
E
ESWR
Introduction
EM waves: Normal Incidence
Example
A uniform planar waves is normally incident from media
1 (z < 0, σ = 0, µr = 1.0, εr = 4.0) to media 2 (z > 0, σ =
0, µr = 8.0, εr = 2.0). Calculate the reflection and
transmission coefficients seen by this wave.
2/26/2018 Dr. Omar R Daoud 43
2 11 2
2 1
120 8; 60 , 120 240
24
240 60 30.60
240 60 5
1 1.60
Introduction
EM waves: Normal Incidence
Example
Suppose media 1 (z < 0) is air and media 2 (z > 0) has
εr = 16. The transmitted magnetic field intensity is
known to be:
Ht = 12 cos (ωt - β2z) ay mA/m.
Determine the instantaneous value of the incident
electric field.
2/26/2018 Dr. Omar R Daoud 44
2 2
2
12t
j z j zt os y y
EmA mAe e
m m
H a a
2t t
2 o s
2
30 , so 12 , E 0.36 , and 1.13t
j zox
E mA V Ve
m m m
E a
Introduction
EM waves: Normal Incidence
Example
Since we know the relation between transmitted E field
and incident E field,
2/26/2018 Dr. Omar R Daoud 45
2 1
2 1
3 21 ; , 1
5 5
t i i
o o oE E E
12.83, so 2.83t
j zi ioo s x
EE e
E a
1( , ) 2.83cos .x
Vz t t z
m E a
Introduction
EM waves: Oblique Incidence
Plane of incidence plane containing both a normal to the boundary and the incident’s wave propagation.
The propagation direction is ai and the normal is az, so the plane incidence is the x z plane. The angle of incidence, reflection and transmission is the angle that makes the field a normal to the boundary.
When EM Wave in plane wave form obliquely incident on the boundary, it can be decomposed into:
Perpendicular Polarization, or transverse electric (TE) polarization The E Field is perpendicular or transverse to the plane of incidence.
Parallel Polarization, or transverse magnetic (TM) polarization The E Field is parallel to the plane of incidence, but the H Field is transverse.
2/26/2018 Dr. Omar R Daoud 46
We need to decompose into its
TE and TM components
separately, and once the reflected
an the transmitted fields for each
polarization determined, it can be
recombined for final answer.
Introduction
EM waves: Oblique Incidence (TE polarization)
2/26/2018 Dr. Omar R Daoud 47
ztxtzxj
tts
yzxjtt
s
zrxrzxj
rrs
yzxjrr
s
zixizxj
iis
yzxjii
s
tt
tt
rr
rr
ii
ii
eE
eE
eE
eE
eE
eE
aaH
aE
aaH
aE
aaH
aE
sincos
sincos
sincos
cossin
2
0
cossin0
cossin
1
0
cossin0
cossin
1
0
cossin0
2
2
1
1
1
1
ri
i
t
sin
sin
2
1
iTE
i
ti
tir EEE 0012
120
coscos
coscos
iTE
i
it
it EEE 0021
20
coscos
cos2
TETE 1
By applying Snell’s Law,
Introduction
EM waves: Oblique Incidence (TM polarization)
2/26/2018 Dr. Omar R Daoud 48
y
zxjt
ts
ztxtzxjtt
s
yzxj
rrs
zrxrzxjrr
s
yzxj
iis
zixizxjii
s
tt
tt
rr
rr
ii
ii
eE
eE
eE
eE
eE
eE
aH
aaE
aH
aaE
aH
aaE
cossin
2
0
cossin0
cossin
1
0
cossin0
cossin
1
0
cossin0
2
2
1
1
1
1
sincos
sincos
sincos
iTM
i
it
itr EEE 0012
120
coscos
coscos
iTM
i
ti
it EEE 0021
20
coscos
cos2
t
iTMTM
cos
cos1
For TM polarizations, there exists an incidence angle at
which all of the wave is transmitted into the second
medium Brewster Angle, θi = θBA , where:
22
21
21
22
21
22
22 )(
sin
BA
2
11
1sin
r
rBA
When a randomly polarized wave such as light is
incident on a material at the Brewster angle, the TM
polarized portion is totally transmitted but a TE
component is partially reflected.
Introduction
EM waves: Oblique Incidence
Example A 100 MHz TE polarized wave with amplitude 1.0 V/m
is obliquely incident from air (z < 0) onto a slab of
lossless, nonmagnetic material with εr = 25 (z > 0). The
angle of incidence is 40. Calculate:
the angle of transmission,
the reflection and transmission coefficients,
the incident, reflected and transmitted for E fields.
2/26/2018 Dr. Omar R Daoud 49
Introduction
EM waves: Oblique Incidence
Example the angle of transmission,
the reflection and transmission coefficients
2/26/2018 Dr. Omar R Daoud 50
1
2 2
1 1 1; sin sin 40 ; 7.4
5 5t t
r
o o
6
1 28
2 100 102.09 , 10.45 .
3 10
rx rad rad
c x m c m
1 2
120120 ; 24
25
2 1
2 1
cos cos0.732; 1 0.268
cos cos
i tTE TE TE
i t
Introduction
EM waves: Oblique Incidence
Example the incident, reflected and transmitted for E fields.
2/26/2018 Dr. Omar R Daoud 51
2.09 sin 40 cos40 1.34 1.601 1j x zi j x j z
s y y
Ve e e
m
E a ao o
( , ) 1cos 1.34 1.60i
y
Vz t t x z
m E a
0.732r i
o TE oE E
1.34 1.600.732r j x j z
s y
Ve e
m
E a ( , ) 0.732cos 1.34 1.60r
y
Vz t t x z
m E a
0.268t i
o TE oE E
2 sin cos 1.35 10.40.268 0.268t tj x zt j x j z
s y y
Ve e e
m
E a a
m
Vzxttz y
raE 4.1035.1cos268.0),(
Introduction
Microwaves: General Description
Related History 19th century
1846 - earliest talk on EM wave, “Thoughts on ray vibrations,” Michael Faraday (1791-1867)
1864 - “Maxwell’s equations,” James Clark Maxwell (1831-1879)
1887 - first microwave-like experiment, “electric spark at λ~10cminduces at a distant wire loop,” Heinrich Rudolf Hertz (1857-1894)
1895 - wireless telegraphic communication and 1900 trans-Atlantic Ocean telegraph, Guglielmo Marconi (1874-1937)
20th century 1921 - magnetron, A. W. Hull
1930 - wave propagation in waveguide, George C. Southworth
1937 - klystron, Russell Varian, Sigurd Varian and William Hansen World War II – radar, MIT Radiation Laboratory
~1950 - coaxial cables for radio communication
~1960 - satellite communication
~1980 - remote sensing satellite, DBS (direct broadcast satellite)
~1990 - PCN/PCS (personal communications network/personal communication services), GPS (global positioning system), VSAT (very small aperture terminals)
~2000 - Digital DBS, WLL (wireless local loop), GII (global information initiative) using mobile satellite network, fibers, cables and wireless
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Introduction
Microwaves: General Description
Frequency Band
Commercial Broadcasting
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Introduction
Microwaves: General Description
Frequency Band
RF Bands
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Introduction
Microwaves: General Description
Frequency Band
Microwave Bands
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Introduction
Microwaves: General Description
Important Factors
Antenna Size
as antenna size ~ λ, it radiates efficiently
f, λ , size , radiation efficiency
Channel Bandwidth
as f available spectrum bandwidth
f for wider information bandwidth transmission, especially digital
video transmission e.g.,
1% BW of AM radio @1MHz gives 1channel of 10kHz audio
bandwidth
0.1% BW of C-band satellite communication @6GHz gives 1
channel of 6MHz video bandwidth
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Introduction
Microwaves: General Description
Important Factors Propagation through Atmosphere
ground wave (LF band, 30-300KHz) travels over and near the earth surface
ground absorption loss, especially for h-polarization
AM radio uses vertical polarization,
sky wave (HF band, 3-30MHz) performs refraction (signal bending) in ionosphere, plasma frequency ~ 9MHz
short-wave radio
space wave (VHF, UHF and microwave, 30M-300GHz) direct wave (line-of sight, LOS) and reflected wave
interference or multi-path phenomenon
low atmospheric attenuation and unaffected by rain and cloud
wireless, mobile, terrestrial and satellite communication
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Introduction
Microwaves: General Description
Devices In general, input/output matching is inherently required for microwave
components over the operating band.
passive devices (without DC bias): diplexer, filter, coupler, power
divider/combiner, isolator, circulator, attenuator, adapter, terminator, cable,
transmission line, waveguide, resonator, detector, mixer, phase shifter, lumped
R, L, C, antenna,…
active devices (with DC bias): amplifier, oscillator, switch, mixer, frequency
multiplier, active antenna, ….
vacuum tube devices
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Introduction
Microwaves: General Description
Devices Solid state devices
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HBT: heterojuction bipolar transistor
MESFET: metal-semiconductor field-effect transistor
HEMT: high electron mobility transistor
MOSFET: metal-oxide-semiconductor field-effect transistor CMOS:
complementary metal-oxide-semiconductor transistor IMPATT diode:
impact ionization avalanche transit-time diode
TRAPATT diode: trapped plasma avalanche triggered transit-time diode
BARITT diode: barrier injected transit-time diode
maser: microwave amplification by stimulated emission of radiation
LSA diode: limited space-charge accumulation mode of the Gunn diode
Introduction
Microwaves: General Description
Devices
Vacuum tube technology finds its applications in
high power (W-MW) and high frequency
(200MHz-200GHz)
e.g., magnetron: kW CW source in microwave oven,
MW pulsed source in radar, traveling wave tube
amplifier: >10 W power amplifier in satellite, klystron:
local oscillator in receiver.
Microwave solid-state devices are :
low cost, low power supply, low noise, small, light
weight, easy cooling, reliable and long life time
compared with microwave tubes.
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Introduction
Microwaves: General Description
Applications Growth and expansion of microwave technology move
from military and satellite applications into information
and entertainment applications.
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Introduction
Microwaves: General Description
Transmission Lines
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Introduction
Concept of Radiation
Radiation Mechanism
Vibration of EM waves from radiation source.
Vibration produced from electric time varying
current source, which is in form of scattering
electrical charges.
Mismatch between the characteristic impedance
of transmission line and open circuit at the other
end produces or generates reflected waves (as
static wave)
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Introduction
Concept of Radiation
Radiation Source- Single Wire
The current density, Jz over the cross section of
the wire:
If the wire is ideal conductor, the current density
Js resides on the surface as:
Where qs is the surface charge density. If the
wire is very thin (ideally zero radius), the current
in the wire:
Where ql is the charge per unit length.
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zvz vqJ
zsS vqJ
zlz vqI
Introduction
Concept of Radiation
Radiation Source- Single Wire
The basic relation between current and charge, and
it also serves as the fundamental relation of EM
radiation.
It states that to create radiation, there must be a
time varying current or an acceleration or
deceleration of charge.
To create charge acceleration or deceleration, the
wire must be curved, bent, discontinuous or
terminated.
To create periodic charge acceleration or
deceleration or time varying current, charge must be
oscillating in a time harmonic motion as for a λ/2
dipole.
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zlz
lz alq
dt
dvlq
dt
dIl
Introduction
Concept of Radiation
Radiation Source- Single Wire
Important Notes:
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Introduction
Concept of Radiation
Radiation Source- Single Wire
Configurations:
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Introduction
Concept of Radiation
Radiation Source- Single Wire
Important Notes:
Consider a pulse source attached to an open
ended conducting wire, connected to ground
through a discrete load at its open end:
When the wire energized, free
electron/charges are in motion due to
electrical lines of force created by the source.
The charges accelerate in the source end of
the wire, and decelerated during reflection
from its end
It is suggested that radiated fields are
produced at each end and along the
remaining part of the wire.
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Introduction
Concept of Radiation
Radiation Source- Single Wire
Important Notes:
Stronger radiation with a more broad frequency
spectrum occurs if the pulses are of shorter or
more compact duration.
Continuous time-harmonic oscillating charge
produces, ideally, radiation of single frequency
determined by f oscillation.
Pulses radiates a broad bandwidth of radiation.
The shorter the pulse width, the broader the
spectrum.
A sinusoidal waveform of current or charge leads
to a narrow spectrum of radiation; ideally zero
bandwidth at the frequency of the sinusoid if it
continues indefinitely.
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Introduction
Concept of Radiation
Radiation Source- Two Wires
Consider a voltage source connected to a two
conductor transmission line which connected to an
antenna.
It creates an E field between the conductors.
The E field has associated with it electric lines of force
that tangent to the E field at each point and its strength
is due to its intensity.
Have tendency to act on free electrons (easily
detachable from atoms) and force them to be
displaced.
The movement creates currents and in turn creates H
field intensity.
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Introduction
Concept of Radiation
Radiation Source- Two Wires The creation of time varying electric and magnetic fields
between the conductors forms EM waves which travel
along the transmission line.
The EM waves enter the antenna and associated with them
electric charges and corresponding currents. If remove part
of the antenna, free space waves can be formed by
connecting the open ends of the E lines.
The free space waves are also periodic but a constant
phase point P0 moves outwardly with the speed of light and
travels a distance of λ/2 (to P1) in the time of one half of
period.
Close to the antenna the constant phase point P0 moves
faster than the speed of light but approaches the speed of
light at points far away from the antenna.
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Introduction
Concept of Radiation
Radiation Source- Two Wires
The water waves created by the dropping of pebble in a
calm body of water, where once the disturbance initiated,
water waves are created which begin to travel outwardly.
When the EM waves are within the transmission line and
antenna, their existence is associated with the presence of
the charges inside the conductors.
When the waves are radiated, they form closed loops and
there are no charges to sustain their existence.
This leads us to conclude that electric charges are required
to excite the fields but are not needed to sustain them and
may exist in their absence. This is direct analogy with water
waves.
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Introduction
Concept of Radiation
Radiation Source- Two Wires
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Introduction
Concept of Radiation
Current Distribution- a Thin Wire
For a lossless two wire TLs, movement of charges creates a
traveling wave current, I0/2 along each wires.
At the end, it undergoes a complete reflection (equal
magnitude and 1800 phase reversal).
When it combines with incident traveling wave, forms a pure
standing wave pattern.
Radiation for each wire occurs time varying nature of
current and the termination of the wire.
For two-wire balanced (symmetrical) TL, the current in a half
cycle of one wire is the same magnitude but 1800 out of
phase for corresponding half cycle other wire.
If the spacing between two wires is very small (s<<λ) , the
fields radiated by the current of each wire are cancelled each
other. The net result is an almost ideal non-radiating
transmission line.
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Introduction
Concept of Radiation
Current Distribution- a Thin Wire
As the section begins to flare, it can be assumed
that the current distribution is essentially unaltered
in form in each of the wires. But due to the two
wires of the flared section are not close to each
other, the fields radiated by one do not cancel
those of the other. Ideally, there is a net radiation
by the TL system.
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Introduction
Concept of Radiation
Current Distribution- a Thin Wire
This is the geometry of widely used
dipole antenna.
If l<λ, the phase of current standing wave
pattern in each arm is the same
throughput its length.
Spatially it is oriented in the same
direction as that of the other arm.
The field radiated by the two arms of the
dipole (vertical parts of a flared TL).
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Introduction
Concept of Radiation
Current Distribution- a Thin Wire
The fields radiated will primarily reinforce each
other toward most directions of observation
If the diameter of each wire is very small (d<<λ)
, the ideal standing wave pattern along the
arms of dipole is sinusoidal with a null at the
end. For center-fed dipoles, the current patterns
are:
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