1.introduction to em radiation
TRANSCRIPT
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Electromagnetism: an introduction
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MAXWELL’s EQUATIONS
0B
D
JDt
H
Bt
E
e
e
GIVEN
• E, Electric field [V/m]
• H, Magnetic field [A/m]
• B, Magnetic Flux density, [T = Wb/m2]
• D, Electric Flux density [C/m2]
• Je, Current density [A/m2]
• e, Electric Charge density [C/m3]
Moreover, B and D fields depend on E and H fields through
constitutive relations of the media where they propagate.
In vacuum or in an isotropic media: D= ·E, B= ·H where [F/m]
is the permittivity while [H/m] is the permeability.
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When frequency = 0 (stationary fields), E field
and H field are uncoupled
CV
Only E field
inside capacitor induced by the Voltage V
V
I=V/R
Only B field
Induced by the
current loop
I
ee JJDt
H
0Bt
E
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I
P
FIELD SOURCES ARE ELECTRIC CURRENTS
Following Maxwell’s equations, a non stationary current I inside any wire
generates in P a Magnetic field H and an Electric field E
E, H
eJD
tH
Bt
E
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RADIATION PROPERTIES OF A SHORT
DIPOLE ANTENNA
Short dipole antenna = Short dl wire with a current I.
More complex wired antennas can be seen as a set of elementary dipole antennas
35
243
32
21
r
rrrjsineE
rrcose2E
3
5
2
43
3
2
2
1
rj2
0
2j
21
21
21
21
e2
Z4
Idle 0
Y
Z
X
Er
Er
dl
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For a given frequency, the structure of the Electric field radiated from a short dipole
antenna strictly depends on r/ value
(r/ )-1
(r/ )-2
(r/ )-3
35
243
32
21
r
rrrjsineE
rrcose2E
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(r/ )-1
(r/ )-2
(r/ )-3
35
243
32
21
r
rrrjsineE
rrcose2E
(r/ )-1
(r/ )-2
(r/ )-3
35
243
32
21
r
rrrjsineE
rrcose2E
For a given frequency, the structure of the Electric field radiated from a short dipole
antenna strictly depends on r/ value
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NEAR FIELD ZONE (r/ <<1) STATIONARY or NON RADIATIVE FIELD
Electrotecnics formulations to solve such problems… (think about to 50 Hz
electric sources: f = 50 Hz = 6000 km… the radiated field does not vary
inside typical circuits length!)
Electric Field and Magnetic field are independent
With reference to the small dipole antenna, both Er and E Electric field
components coexist
RADIATIVE FIELD (r/ > 1)
Raileigh zone (r<< D2/(2 ) )
Fresnel zone (D2/(2 ) <r< 2D2/ )
Fraunhofer or FAR FIELD zone (2D2/ << r)
With reference to the small dipole antenna, Er Electric
field component vanishes for r/ >> 1
DI1
I2
I3
P
r
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FAR FIELD or Fraunhofer zone
The following IMPEDANCE RELATION (planar wave) can be written
Conditions
r>>
r>2D2/
Ex. Microwave communications: f=1GHz, =30 cm
HrZE 0
E
B
r
120 impedance vacuumZ0
DI1
I2
I3
P
r
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RADIATED FIELD ZONES
for the feeder of a parabolic antenna
(HORN ANTENNA with d /2)
Zona di Rayleigh
Zona di Fresnel
Zona di Fraunhofer
d2/(2 ) 3 cm
2d2/ 15 cm f=1GHz
=30 cm
d
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RADIATED FIELD ZONES
for the PARABOLIC ANTENNA
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Attention: POLARIZATION ASPECTS
The radiated Electromagnetic field is a VECTORIAL FIELD.
Vertical linear
polarization
Clockwise
circular
polarization
E
B
B
E
E E
B B
Horizontal
linear
polarization
Anti
Clockwise
circular
polarization