antenna design & prototyping overview · antenna surrounded by air (vacuum), copper replaced by...
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Antenna design & prototyping overviewFrom model design to prototype measurement
Maxime SPIRLET 29/05/2019
ULiege,Department of Electrical Engineering and Computer Science,
Montefiore Institute, Applied and Computational Electromagnetics (ACE)
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Introduction
What is an antenna?
An antenna is an electromagneticenergy converter betweenconducted and radiatedelectromagnetic energy.
Designing an antenna mainly consists inmaximizing the energy conversion ratio.
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Antenna Modeling and SimulationIntroduction
Focus on microstrip antennas(cheap, compact, versatile, ...).
Antenna design complementary toEMC rules:
How to make a PCB track(NOT) radiate?
Design a patch antenna to use @2.45 GHz.
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Antenna Modeling and SimulationMicrostrip ”patch”antenna
h� λ and L ≈ λ,
Radiation from the fringingfields,
Cavity model with ~E fieldalong z and vanishing ~Ht atedges,
Solution of Maxwell equations and boundary conditionsHy (x) = 0 at x = ±L/2 (lowest resonant mode L ≥W ):
Ez(x) = −E0 sin(πx
L
)(1)
Hy (x) = −H0 cos(πx
L
), (2)
for −L/2 ≤ x ≤ L/2 and −W /2 ≤ y ≤W /2,
H0 = −E0/Z , Z = Z0/√εr .
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Antenna Modeling and SimulationResonant frequency
Identifying k to πL (standing waves: A sin (kx ± ωt) in 1-D),
ω =πc
L, (3)
The resonant frequency is
f = 0.5c
L= 0.5
c0L√εr, (4)
The length of the patch should be
L = 0.5λ√εr, (5)
where εr is the relative permittivity of the dielectric (typ. 4.5@ 2.5 GHz for epoxy FR4).
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Antenna Modeling and SimulationMagnetic currents
Fringing fields extended over alength a around patch edges,
Due to h� λ, Fringing fieldsreplaced by ~Ea, tangential tosubstrate surface,
Eliminate ground plane usingimage theory: ~Jms = −2n× ~Ea,
Sides 1 and 3:∮ABCD
~E · ~dl = ∓E0 ± Eaa = 0⇒ ~Ea = xhE0
a⇒ ~Jms = −y 2hE0
a,
(6)Sides 2 and 4:
~Ea = ±y hEz(x)
a= ∓y hE0
asin(πx
L
)⇒ ~Jms = ±x 2hE0
asin(πx
L
).
(7)
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Antenna Modeling and SimulationRadiation vectors
Radiated electric field:
~E = ke−kr
4πrr × ~Fm, (8)
Magnetic radiation vector:
~Fm(θ, φ) =
∫A
~Jms(x , y)ekxx+kyy dS , (9)
~Fm,1,3 = −y 2hE0
a
∫ W /2
−W /2
(e−kxL/2 + ekxL/2
)ekyy a dy ,
(10)
~Fm,2,4 = x2hE0
a
∫ L/2
−L/2
(e−kyW /2 + ekyW /2
)sin(πx
L
)ekxx a dx ,
(11)
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Antenna Modeling and SimulationRadiation vectors
~Fm,1,3 = −y4E0hW cos (πνx)sin (πνy )
πνy, (12)
~Fm,2,4 = x4E0hL4νx cos (πνx)
π (1− 4ν2x )sin (πνy ) , (13)
with the normalized wavenumbers
νx =kxL
2π=
L
λsin θ cosφ, (14)
νy =kyW
2π=
W
λsin θ sinφ. (15)
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Antenna Modeling and SimulationRadiation pattern
From sides 1 and 3:
~E (θ, φ) = −k e−kr
4πr4E0hW
(φ cos θ sinφ− θ cosφ
)F (θ, φ) ,
(16)with
F (θ, φ) = cos (πνx)sin (πνy )
πνy, (17)
From side 2 and 4:
~E (θ, φ) = ke−kr
4πr4E0hL
(φ cos θ cosφ+ θ sinφ
)f (θ, φ) ,
(18)with
f (θ, φ) =4νx cos (πνx)
π (1− 4ν2x )sin (πνy ) . (19)
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Antenna Modeling and SimulationRadiation pattern
Normalized gain for sides 1 and 3 (left):
g (θ, φ) =
∣∣∣~E (θ, φ)∣∣∣2∣∣∣~Emax
∣∣∣2 =(cos2 θ sin2 φ+ cos2 φ
) ∣∣∣~F (θ, φ)∣∣∣2 ,(20)
Normalized gain for sides 2 and 4 (right):
g (θ, φ) =(cos2 θ cos2 φ+ sin2 φ
) ∣∣∣~f (θ, φ)∣∣∣2 . (21)
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Antenna Modeling and SimulationRadiation pattern
E-plane gain obtained by setting φ = 0 (left):
gE (θ, φ) =|Eθ|2
|Eθ|2max
= |cos (πνx)|2 , νx =L
λsin θ, (22)
H-plane gain obtained by setting φ = 90 (right):
gH (θ, φ) =|Eφ|2
|Eφ|2max
=
∣∣∣∣cos (θ)sin (πνy )
πνy
∣∣∣∣2 , νy =W
λsin θ.
(23)
−90 −60 −30 0 30 60 90
−4
−2
0
θ
−90 −60 −30 0 30 60 90−40
−30
−20
−10
0
θ
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Antenna Modeling and SimulationNumerical modeling of the patch antenna
Modeling with the freeFEM solver ONELAB(http://onelab.info),
Fullwave 3D model,
Antenna surrounded by air(vacuum),
Copper replaced by aPerfect Electric Conductor(σ =∞),
Free-space modeled withPML’s or ABC’s to avoidspurious reflections (i.e.numeric model of infinity),
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Antenna Modeling and SimulationNumerical modeling of the patch antenna
3D Radiation pattern canbe computed,
Input impedance and otherparameters can also beobtained.
Mesh size is the criticalparameter,
Computation time vsaccuracy.
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Antenna Modeling and SimulationNumerical modeling of the patch antenna
Frequency sweep toget reflectionscoefficient wrtfrequency,
Parameter sweep tooptimize antennadimensions,
Finite size groundplane taken intoaccount,
Housing can be takeninto account,
...
2.4 2.42 2.44 2.46 2.48 2.5
·109
−7
−6
−5
−4
−3
−2
Frequency (Hz)
R(d
B)
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Antenna Measurement
2D radiation pattern,
3D radiation pattern,
Reflection coefficient,
VSWR and matchingcircuit,
Antenna efficiency.
Te
st &
Mea
sure
men
t
Prod
uct B
roch
ure
| 11.
00
R&S®ZVAVector Network AnalyzerHigh performance up to 110 GHz with up to four test ports
ZVA_bro_en_5213-5680-12_v1100.indd 1 30.07.2014 13:17:26
Important: measure the antenna as it will beused in practice.
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Antenna Measurement
New ULiege’s FAC
External dimensions: 4 m × 4 m × 7.5 m,
Test frequency range: 700 MHz - 18 GHz (validated),
Test device/antenna: max. 10 kg - 30 cm × 30 cm × 30 cm.
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Q/A
Questions?
Contact:
Veronique Beauvois ([email protected]),
Maxime Spirlet ([email protected]).
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