Progress In Electromagnetics Research Symposium Proceedings, Suzhou, China, Sept. 12–16, 2011
207
A Fan-beam Millimeter-wave Antenna Based on Modified Luneberg
Cylindrical Lens
Changzhou Hua1, 2 , Xidong Wu1 , Nan Yang1 , Huixian Wu1 , Bo Li1, 2 , and Wen Wu2
1
Department of Information Science and Electronic Engineering, Zhejiang University
Hangzhou 310027, China
2
Ministerial Key Laboratory of JGMT, Nanjing University of Science and Technology
Nanjing 210094, China
Abstract— A new design of lens antenna at millimeter-wave frequencies is introduced with
special focus on ease of manufacturing and reliability. The system is composed of a modified
Luneberg cylindrical lens and a feed antenna. The modified Luneberg cylindrical lens consists
of two parallel plates with the space between plates only filled with air, thus free of dielectric
loss. A planar linear tapered slot antenna (LTSA) is inserted into the air region between the
parallel plates at the edge of the lens as a feed antenna. A combined ray-optics method and
CST-MWS are used to analyze and design this cylindrical lens antenna at 30 GHz. Due to its
spherical symmetry, the proposed lens can be used to launch multiple beams by implementing
an arc array of planar LTSA elements at the periphery of the lens. The proposed antenna can
be easily extended for higher mm-wave frequencies, and is well suitable for scanning fan-beam
applications, such as aircraft landing systems.
1. INTRODUCTION
In recent years, wide-angle scanning antennas are required in many mm-wave applications such
as modern wireless communications, automotive radars, and imaging systems. And there has
been an increased research interest in spherical lens antennas to launch pencil beams [1–3]. For
some applications, such as aircraft landing system [4], it is more desirable to launch fan-beam
scanning in one plane. In [5], a two-dimensional Luneberg lens based on partially-filled parallel
plate technique was designed to launch scanning fan beams. In this paper, an air-filled modified
Luneberg cylindrical lens is proposed for mm-wave multiple fan beam applications.
2. STRUCTURE OF THE MODIFIED LUNEBERG CYLINDRICAL LENS ANTENNA
The proposed modified Luneberg cylindrical lens is designed by using the technique of parallel
plates propagating the TE 10 mode. It is well-known that the TE 10 mode’s wave number k for a
parallel-plate waveguide can be written as,
s
µ ¶2
λ0
k = k0 1 −
,
(1)
2h
and the effective index of refraction is given by,
n = k/k0 ,
(2)
where λ0 is wavelength in free space, k0 is the free space wave number and h is the plate spacing.
Figure 1 shows the structure of the proposed lens antenna. As shown, it consists of two parallel
plates filled with air. The plate spacing h(r) is varied with the normalized radius r in order to
achieve the general Luneberg’s variation of the effective index of refraction,
p
n = N0 2 − δr2 ,
(3)
where N0 and δ are two adjustable parameters. When N0 and δ are chosen to be equal to 1, it will
reduce to the Luneberg’s Law. Then, we can determine the h(r) by using (1)–(3). The modified
Luneberg lens antenna is fed with a LTSA, which excites TE 10 mode (horizontal polarization)
between the two parallel plates when the height h is chosen to be λ0 /2 < h < λ0 . In order to
achieve the best illumination, the phase-center of the LTSA should coincide with the focal position
of the lens.
PIERS Proceedings, Suzhou, China, September 12–16, 2011
208
L
LTSA
TE10
h(r)
h
ε0
S
RM
Air-filled
DS
θM
cylindrical
Parallel conductor
W
lens
WS
plate
WM
ε0
LTSA
S
R
g
2.0 mm
R1
0.5 mm
Figure 1: Structure of the proposed lens antenna.
0.2 mm
Figure 2: Structure of the feed LTSA.
In Fig. 2, the feed LTSA with a microstrip/slotline transition is integrated on a dielectric
substrate Duroid 5870 with a thickness of 0.254 mm and a relative permittivity of 2.33. The
main structural parameters as defined in Fig. 1 and Fig. 2 are given as follow: R = 50 mm,
R1 = 62 mm, h = 6.6 mm, L = 6.1 mm, W = 3.5 mm, S = 2.3 mm, WS = 0.25 mm, WM = 0.76 mm,
DS = 1.5 mm, RM = 1.4 mm and θM = 80◦ . Simulations and designs are carried out using the
commercial software CST-MWS. The length of the tapered slot line (L) is much shorter than that
of conventional LTSA to generate a wide H-plane pattern, ensuring a smooth transition to TE 10
mode excitation. The opening of the LTSA (W ) is adjusted to generate the required illumination
beamwidth in E-plane. The periodic arrangement of slits along the LTSA edges is used to minimize
the back radiation. The proper selection of the parameters of the microstrip/slotline transition is
crucial to the wideband performance of the LTSA. Finally, the simulated LTSA patterns in free
space exhibit a 10-dB beamwidth of 98◦ in the E-plane and 122◦ in the H-plane at 30 GHz.
3. THEORETICAL ANALYSIS AND DISCUSSION
The ray-tracing technique is used to analyze the focusing property of the modified Luneberg cylindrical lens [3]. In this way, the optimum focal position d/R of the cylindrical lens can be easily
determined. Fig. 3 shows the ray tracing from a point source at a distance d from the edge of the
proposed cylindrical lens. The main difference here is that the index of refraction n is a function
of the distance r from the origin. The angle θ can be obtained from the integral equation [6],
Z r
dr
√
θ = θ0 ± e
,
(4)
2
2
2
r0 r n r − e
with
e = nr sin φ,
where ϕ denotes the angle from the positive direction along the ray to the direction of increasing
r, and e is constant for a particular ray. The constant e and the ambiguous sign are determined
by the direction of the ray at the initial point (r0 , θ0 ). In order to achieve a diffraction-limited
pattern, which means a maximum directivity, whose limit is given by the size of the aperture, the
exit angle θe should be as small as possible for all input angles θs . As shown in Fig. 4, the optimum
focal position is obtained for d/R ≈ 0.14 (N0 = 0.685, δ = 1.17). Then, the focusing properties
of the designed cylindrical lens and their dependence on the phase-center of the LTSA are studied
by adjusting the insertion depth of the feeding LTSA. With the aid of CST-MWS, we find that
diffraction-limited patterns occur at the position of g = 10.5 mm, indicating that the phase-center
of the LTSA is about 6.1 − (10.5 − 0.14 × 50) = 2.6 mm away from its opening tip.
To calculate the far-field pattern of the proposed cylindrical lens, a combined ray-tracing/diffraction method is used follows the technique described in [5]. Fig. 5 shows the calculated and simulated
Progress In Electromagnetics Research Symposium Proceedings, Suzhou, China, Sept. 12–16, 2011
209
y
Parallel conductor plate
θe
M
Q
x
θ
R
P
θs
Air-filled cylindrical
-R-d
lens
S
Figure 3: Ray-tracing of the proposed lens antenna.
0
20
Magnitude (dB)
d/R = 0.30
10
θ e (deg)
0.20
0.14
0
0.10
10
20
30
40
Ray-tracing
CST-MWS
-20
-30
-10
0
-10
50
-40
-90
θs (deg)
-60
-30
0
30
60
90
θ (deg)
Figure 4: Exit angle θe as a function of the input
angle θs for different d/R.
Figure 5: Calculated and simulated radiation patterns of the proposed lens antenna at 30 GHz.
radiation patterns of the proposed lens antenna at the design frequency of 30 GHz. As shown, the
theoretical calculations in both E- and H-planes agree well with the CST-MWS simulations. The
calculated 3-dB E- and H-plane beamwidths are about 8.9◦ and 67.8◦ , respectively, which agrees
very well with the beamwidths of 9.0◦ and 68.0◦ simulated by CST-MWS. The simulated first
sidelobe level in E-plane is −19.8 dB, whereas the theoretical level is −17.6 dB. The disagreement
between theoretical calculations and simulations for higher order sidelobes is due to the approximate
feed pattern. Meanwhile, no reflections from the lens-air interface have been taken into account in
ray-tracing analysis.
The aperture efficiency of the lens antenna is given by,
η = D0 /Dmax ,
with
Dmax
(5)
· µ
¶¸
2Rh
8
,
= 2 4π
π
λ20
where D0 is the directivity of the designed lens antenna, and Dmax is the maximum directivity
which the TE 10 mode distribution aperture can achieve. The simulated directivity is 15.7 dB, and
the corresponding aperture efficiency is about 55%.
Due to its spherical symmetry, the proposed modified Luneberg cylindrical lens can be used to
launch multiple beams by implementing an arc array of planar LTSA elements at the periphery
PIERS Proceedings, Suzhou, China, September 12–16, 2011
210
Air-filled
Parallel conductor plate
cylindrical
0
Magnitude (dB)
lens
LTSA array
θ'
R
-10
-20
R1
-30
-90
-60
-30
0
30
60
90
θ (deg)
Figure 6: Top view of the proposed multiple-beam
lens antenna.
Figure 7: Simulated E-plane patterns at 30 GHz of
the 15 beam array with a crossover of −3 dB.
of the lens. Beam scanning can be achieved by switching among the feed antenna elements. A
top view of the proposed multiple-beam lens antenna is shown in Fig. 6. In our design, the LTSA
elements are placed on the d = 7.0 mm arc with a center-to-center spacing of 9.4 mm. This results
in a beam scan of 9◦ between any two adjacent antenna elements, and the pattern crossover occurs
at the 3 dB level. A total of 15 LTSA elements are required to cover total 135◦ scan angle, and the
simulated patterns are shown in Fig. 7. As shown, the designed 15-element array results in virtually
no directivity loss over the entire 135◦ scan angle, which proves to be a wide scan-angle antenna at
millimeter-wave frequencies.
4. CONCLUSIONS
A modified Luneberg cylindrical lens at mm-wave frequencies which utilizes the technique of parallel
plates propagating the TE 10 mode has been designed. The effective index of refraction of the mode
TE 10 can be easily obtained by controlling the spacing between the parallel plates. A combined
ray-tracing/diffraction method is used to analyze the modified Luneberg cylindrical lens antenna
system. Then, a modified Luneberg cylindrical lens at 30 GHz was designed. For this prototype, a
directivity of 15.7 dB with 3-dB E- and H-plane beamwidths of 9.0◦ and 68.0◦ is achieved at the
design frequency of 30 GHz, and the sidelobe level in the E-plane is −19.8 dB. Due to its spherical
symmetry, the proposed modified Luneberg cylindrical lens can be used to launch multiple beams
by implementing an arc array of planar LTSA elements at the periphery of the lens. In conclusion,
the proposed lens antenna system is suits for wide-angle scanning fan-beam applications due to its
low weight and high performance.
ACKNOWLEDGMENT
This work is supported by Ministry of Science and Technology of China under Project 863 Grant
2009AA01Z226 and by NSFC under grant # 60871010.
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