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Definition
Websters Dictionary:
a usually metallic device forradiating or receiving radio waves
IEEE:
a means for radiating or receivingradio waves
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jarak
Bidangreferensi
Reactivenearfield
Mixture of
wave typesSinglewave type
Nearfieldregion
Far-Fieldregion
Antena
DE : diameter
aperture antenna
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This disturbance is created by
a time-varying current sourcethat has an accelerated charge
distribution associated with it.
If charges are accelerated back and forth (i.e. oscillate), a
regular disturbance is created and radiation is continuous
Antennas are designed to support charge oscillations
Radiation is a disturbance in the electromagneticfields that propagates away from the source of the
disturbance
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To createradiation,there must be
a time varyingcurrent or anacceleration(ordecceleration)
of charge.
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Since accelerated charge produces radiation, it follows from
this equation that time-changing current produces radiation
vq
I
Current :dtdzqI l
then : qvdt
dzlqIl l
vqdt
dv
qldt
dI
or
next
vqlI
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Given the distribution of time-varying current, findthe radiation characteristics of the antenna
S
Wire Antenna
Radiation
Pattern Reflector Antenna
Time varying
current element
creates
accelerated
charges and
radiation occurs
The overall antenna radiation performance can be
obtained by the superposition (in vector) sense of the
elementary current elements
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Maxwells equations in integral form are a setof FOUR LAWS resulting from several
experimental findings and a purely
mathematical contribution.Faradays Law
Amperes Circuital Law
Gausss Law for the Electrical Field
Gausss Law for the Magnetic Field
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The electromotive force around a closedpath is equal to the time rate of change of
the magnetic flux enclosed by the path
SC dSdtd
dl BE
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The magnetomotive force around a closed
path is equal to the algebraic sum of thecurrent due to the flow of charges and the
displacement current bounded by the path
S
SC
C
dSdtdIdl DH Displacement
current introducedby Maxwell
SSC dSI
JCurrent due to
flow of freecharges
SSC
dSdt
ddSdl DJH
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The magnetic flux emanating from a closedsurface is equal to zero
0S
dSB
Note that Gauss Law for
magnetic field is consistent
with Faradays Law
11
1
SC
dSdtddl BE
22
2
SC
dSdt
ddl BE
21
0SS
dSdt
dB
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The net current due to flow of charge emanatingfrom a closed surface is equal to the time rate of
decreases of the charge within the volume
bounded by the surface
VS
dvdt
ddS J
SS
VS
dSdSdt
d
dvdS
JD
D
Amperes Law
Gauss Law
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0
S
VS
SSC
SC
dS
dvdS
dSdt
ddSdl
dSdt
ddl
B
D
DJH
BE
Gauss Law
Amperes Law
Faradays Law
Gauss Law
VS
dvdt
ddS J Law of Conservation of Charge
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j
j
j
J
B
E
JEH
HE
0
known
AB ABH
11
Vector potential yet
to be determined
Time-harmonic Maxwells Eqs.in homogeneous and isotropic
medium
0 AVector
calculus
identity
observe that
0)( AE j
AEj
then
Vector
calculus
identity
observe
0
scalar potential yetto be determined
Find & !1
2
3
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JAAA )(22 j
AH 1
JEH jm.e.
2JEA
j
1
AAA2)(
vector calculus identity
Aj 3
then
AE j3
E
)( Aj
then2
2
4
5
m.e.
Aj2
Note: Equation (4) and (5) are coupled !!
vector calculus identity
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To uncouple previous equations Lorentz conditionis introduced:0 jA
then
122
22
JAA propagation
constant
These are vector andscalar wave equations !
Observation: these differential equations relate the
electromagnetic potentials to sources
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Vector wave eq.for vector potential JAA 22
vectorvector
In Cartesian Coordinates :
)
()
()
(22
zyxzyxzyx JzJyJxAzAyAxAzAyAx
zyx AzAyAx222
only true for Cartesian
coordinates
Equatingeach
component :zzz
yyy
xxx
JAA
JAA
JAA
22
22
22
three scalar
wave equations
Question : How to solve scalar wave eq. in unbounded space?
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Let us first seek
solution for the
source at origin :
)()()( 22 rrgrg
delta function
delta scalar
source at the
origin
Due to the obviousspherical symmetry:
x
)(),,()( rgrgrg
y
zdoes not
depend on
and
)()()( 22 rrgrg then :
Scalar Laplacian inspherical coordinates :
2
2
222
22
sin1)(sin
sin1)(1
g
rg
rg
rr
rrg
)()()(1 22 rrg
r
gr
rr
then :
x
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)()()(1 22
rrgr
gr
rr
From partial differential
eq. to ordinary
differential eq.
partial derivatives
Since is only afunction of (i.e. not ), then :r)(rg r dr
rdgrg )(
ordinary
derivatives
Finally: )()()(1 22 rrg
dr
dgr
dr
d
r
2
22
21
dr
gdr
dr
dgr
r
this is a second order linear
ordinary differential eq. with
variable coefficients
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)()())((1 22 rrgdrrdgr
drd
r Recall:
This second order
differential eq. canadmit two solutions:
r
erj
4
r
erj
4or
these two solutions are
linearly independent
Which one should
we use ?The one which gives outgoing wave for
time dependencetje
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Physical
quantity )cos(4
1)
4Re( rt
rr
ee
rj
tj
real partWave amplitude decays as
r
1
Note: characterizes an outgoing wave)cos( rt
Wave front:
1velocity.cost
dt
drrt
2
f
ccT
Note: characterizes an incoming wave
y
z
y
z)cos( rt
C, speed of light
wavelength period
We use outgoing wave for unbounded space !
x
x
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observation point
y
z
x
r
source at the origin
r
erg
rj
4)(
observation
point
y
z
x
r
Source not at the origin
'r 'rrR
'44)',(
'
rr
e
R
errg
rrjRj
Note : length of vector'rrR R
Therefore, )'()',()',( 22 rrrrgrrg
222
)'()'()'(' zzyyxxrr
Note:
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z
y
x
z
y
x
z
y
x
J
JJ
A
AA
A
AA
22Recall:
Recall: )'()',()',( 22 rrrrgrrg
three scalar
wave equations
usually called
Greens function
By the argument of
the superposition'
4dv
R
e
J
J
J
A
A
ARj
z
y
x
z
y
x
'rr
''4
)'(
ionsource_regover_the
'
dvrr
er
rrj
JAor in a
vector formy
z
x
r'r
R
source region
over the source region
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A
E H
Recall : )(1
)( rr
AH
)()(1
)( rrj
r
JHE
From M.E. :
Recall : ''4)'(
ionsource_reg
over_the
'
dvrr
er
rrj
JA
only exist at
the source
region
Observation: This is the answer to our BIG question !
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In many practical situation, the obervation point is typically
quite far away from the source region, simplified results canbe constructed.
y
z
x
r
'r
R
source region
rrrr
r
r
r
rrrrRR
''
'
'cos'
r
r
r
r
'
'
rrjrjrrrjRj
er
e
rrr
e
R
e'
)'(
4)'(44
much smaller thanr
')'(4
' dverr
e rrjrj
JA
Far field
approximation:Very important result !
E & H
fields: );
( AAj EEH r
1
b k
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Macam-macam bentukAntena
M
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Macam-macambentuk Antena
Macam macam
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Macam-macambentuk Antena
M k i di i d
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Mekanisme radiasi padapatch mikrostrip
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ON FREE-SPACE ENVIRONMENT,
THE CONSTITUTIVE RELATION :
D = 0 E
B = 0 H
WHERE :
0 = 1/36 x 10-9 F / m
0 = 4 x 10-7 H / m
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BOUNDARY CONDITION
PERFECT CONDUCTOR
n x E = 0 Surface tangential component of E iscontinuous across the
boundary
n . H = 0 No magnetic flux penetrates into theconductor
n x H = Js Surface current density flows on theconductor
n . D = Flux lines of D terminate on thecharge since there is no field
within the conductor
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IMPERFECT CONDUCTOR
INFLUENCED BY SKIN DEPTH AS:
s = (2 / 0)1/2
n x E = Zs n x Js
Where : Zs is surface impedance
Zs = (1 + j) / s [ ohm / square ]
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BOUNDARY BETWEEN TWO
DIELECTRIC MEDIA
At the boundary the tangential fieldcomponent are aqual on adjacent sides:
n x E1 = n x E2
n x H1 = n x H2
Normal electric flux is continuous :
n . D1 = n . D2
