Post on 08-Dec-2016
Linear (wire) antennas 1P. Hazdra, M. Mazanek,….hazdrap@fel.cvut.czDepartment of Electromagnetic FieldCzech Technical University in Prague, FEEwww.elmag.org
v. 7.3.2016
Linear (wire) antennas
• Current distribution on a wire antenna, natural resonances
• Radiation pattern, input impedance• The dipole• The folded dipole• Symmetrization, baluns• Monopole antennas
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Linear (wire) antennas• Approximate solutions based on assumption that the
current distribution is only 1D, i.e. we go from surface density to ′ (1D integrals).
• Travelling wave / resonant.
3
Linear (wire) antennas - currentAt first we have to find the current on antenna• Numerical solutions based on variational principles (Method of Moments)• Approximate solutions in analytical form
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Transmitting thin‐wire antenna
/Δ
⋅
Perfectly Electrically Conducting surfaces: Tangential E field on PEC = 0
known feeding
Unknown current function hidden inside the vector potential 4 ′
Assuming only z‐directed current (hence only component), this leads to integro‐differential equation for thin‐wire antenna
, /
/Interchanging integration with differentiation
′R
Current on linear antenna (dipole)
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Center feeding
.
Whole dipole length
.
.
I 12
I sin 2
Triangular distribution
Sine distribution
small dipole
half-wavelength dipole
Linear (wire) antennas - current
6
sin12
I sin 2
Linear (wire) antennas - current
7
We have very good approximation for current flowing along linear dipole in the form of
It follows from understanding the dipole as two‐wire open‐circuited transmission line – in other words the radiation is neglected in this model.
valid for thin dipoles only
I sin 2
Linear (wire) antennas - current
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+
+
+
+
++ + ++ + +
-
- - -
- -
+
out‐of phase currents sidelobes
Complete fields from linear antenna
9
, , 4 ′ ′/
/
Near field requires complete evaluations
Electric field (magnitude) of / dipole
Region separation (Rayleigh, Fresnel, Fraunhofer)
is expanded into series
• Linear term only: Fraunhofer (far field)
• Quadratic: Fresnel 0.62 /,
Radiation from linear dipole antenna
10
, sin
, , 4 ′ ′/
/
Far‐field approximation of the radiation integral
Δ cos ⋅Δ
R Δ ≅
, , 4 ′ ′/
/
The radiated field is proportional to Fourier transform of the source current!!
, , 4 sin ′ ′/
/
space factorelementary dipole! (element factor)
⋅
Radiation from linear dipole antenna
11
, , 30 sin sin 2 ′ 60cos 2 cos cos 2
sin
/
/
, , , ,
Radiation pattern – changes withdipole length
Sinusoidal current distribution assumed
Radiation patterns
12
/2
2.15dBi
1.5
“maximal dipole”
1.25
3.82dBi 5.16dBi 3.48dBi
current:
“One of the goals of antenna design is to place lobes at the desired angles.”
Directivity of a dipole
13
The dipole
14
• Its radiation pattern is omnidirectional in the H‐plane, which is required by many applications (including mobile communications).
• Its directivity (2.15 dBi) is reasonable – larger than short dipoles• The input impedance is not sensitive to the radius and is about 73 Ω, which is
well matched with a standard transmission line of characteristic impedance 75 or 50 Ω (with VSWR< 2). This is probably the most important and unique reason.
• dBd – decibels above /2 dipole, 0 dBd = 2.15 dBi
The dipole
15
, , 60cos 2 cos
sin
15 sin 15 2
1 cos≅ 2.435
22 ⋅ 15 ⋅ 2,435 ≅ 73Ω
Radiation resistance obtained from integration of the far‐field power density
Note: To obtain input reactance X too, we must integrate complex power‐flow in near fieldof an antenna (at antenna surface!). Then it could be shown that:
30 ∗∗
′sin
/
/
′/
/
30 ∗∗
′cos
/
/
′/
/
.
/2 dipole input impedance of infinitely thin dipole!
The dipole is not resonant ( ) and should be shortened a little, depending on radius
I sin I cos kz
Note – radiation resistance
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I sin 2
Radiation resistance is referred to the maximum current. For some lengths (0.5 ) this maximum does not occur at the input terminals (which we assume to be at the center) of the antenna and where we are measuring the .
2 2
0 I sin 2
sin 2
Peak value
sin 2
Thin center-fed dipole input impedance
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3GHz, 0.1m, l 0.05m, a 0.2mm, Ω 2 ln 12.4
/2, 73 42.5Ω
≅ 0.48 , ≅ 72 0Ω
≅ %
% shortening to produce resonance req.
32
Resonance0
Antiresonance0
Thin center-fed dipole input impedance
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3GHz, 0.2m, l 0.1m, a 0.2mm, Ω 2 ln 12.4
/
Thin center-fed dipole input impedance
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/ % shortening required
Resonant lengthΩ 2 ln
Dipole Thickness Class
10000 2 0.49λ 18.4 Very thin
1000 5 0.475λ 13.8 Thin
20 9 0.455λ 6 Thick
Natural resonances of a dipole
Thin center-fed dipole
20
sin 2
sin 2
Frequency bandwidth
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Frequency bandwidth of antenna is connected to its input impedance function of frequency
Relative frequency bandwidth:
≅1
2
≅ 2 ≅ 2.34 1.29 ln
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 13
4
5
6
7
8
9
10
11
12
13
100*a/
Q
QXselfQX (FEKO)
/2 dipole
The folded dipole
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The folded dipole
23
For ≪ , the current distributions are identical
The two currents of closely spaced arms are equal to the one current of the ordinary dipole
2
Also the input power of the two dipoles are identical
12
12
4 ≅ 4 ⋅ 73 ≅ 300Ω
May be generalized for N arms
For /2 dipoles
≅
The folded dipole
24
100 ≅ /2s 3
0.46
Symmetrization - balun
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Balun properly connects a balanced transmission line to an unbalanced transm. line.
Equal and opposite currents – balanced mode. Closely spaced equal and opposite currents don’t radiate.
Symmetrization - balun
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“Balun transforms the balanced input impedance of the dipole to the unbalanced impedance of the coaxial line such that there is no net current on the outer conductor of the coax.”
Sleeve (bazooka) balun
/4 parallel line – very large impedance:• Suppression of the currents on the outer shield• No interference with the antenna input impedance
Symmetrization - balun
27
4 to 1 balun
75Ω300Ω
Monopole antennas – vertical current above PEC ground
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• Method of images
Monopole antenna – infinite ground
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12 36.5 21.25Ω
For infinite ground plane
This “ /4 “ antenna can be tuned by shortening the radiator.Using arms instead of real ground, could be made close to 50Ω and thus matched to coaxial cable.
It radiates only into the space above the ground plane (half the space of a dipole antenna), a monopole antenna will have a gain of twice (3 dBi over) the gain of a similar dipole antenna, and a radiation resistance half that of a dipole
Monopole antennas – low-gain base-station/mobile antennas
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Discone antenna VSWR<3 for frequency 1 to 10.
Monopole above ground
31W. Weiner, Monopole Antennas, Marcel Dekker, 2003
Monopole above ground - resistance
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.
W. Weiner, Monopole Antennas, Marcel Dekker, 2003
Monopole above ground - reactance
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..
W. Weiner, Monopole Antennas, Marcel Dekker, 2003
Monopole top-loading, T-antenna
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Monopole top-loading
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Transmitting antennas
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Vertical monopole
Transmitting antennas
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Horizontal dipole
Transmitting antennas
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Horizontal dipole above ground plane
Transmitting antennas - Liblice
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• Highest construction in CR (355m)• Pin = 1.5 MW @ 639 kHz, 470
Transmitting antennas - Liblice
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Transmitting antennas - Liblice
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Curtain antenna arrays – short wave
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Curtain antenna arrays
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Curtain antenna arrays
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Literature
• C. A. Balanis, Antenna Theory and Design, Wiley, 2005• J. D. Kraus, Antennas, McGraw‐Hill, 1997• W. Weiner, Monopole Antennas, Marcel Dekker, 2003
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Supplementary material
• Numerical solution of current on thin linear antennas
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Linear (wire) antennas - current
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, /
/
4 1 2 3 /
/
Pocklington integral equation′
Thin‐wire approximation (reduced integral kernel)
voltagecurrent
Impedance operator EFIE
Method of Moments solution:
, R
≅
Basis (expansion) function: dirac pulses, rectangular/triangular/sin pulse,..
Unknown expansion coefficients
Result of the MoM is complex impedance matrix, which depends on frequency and topology only
Current on linear antenna (dipole)
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