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Design Procedure of Two-Dimensional Circularly
Polarized Slotted Waveguide Antenna Arrays
Hilal M. El Misilmani
Electrical & Computer Eng. Department
Beirut Arab University
Beirut, Lebanon
hilal.elmisilmani@ieee.org
Mohammed Al-Husseini
Beirut Research & Innovation Center
Lebanese Center for Studies & Research
Beirut, Lebanon
husseini@ieee.org
Karim Y. Kabalan
Electrical & Computer Eng. Department
American University of Beirut
Beirut, Lebanon
kabalan@aub.edu.lb
Abstract—This paper presents a procedure for the design of
a 2D Slotted Waveguide Antenna (SWA) array having circular
polarization. The 2D array is formed by a defined number of
1D branchlines broadwall SWAs, which are fed using an extra
broadwall SWA. The SWA branchlines have cross-shaped slots
that radiate with a circular polarization. The dimensions of
these slots are optimized for best performance. The feed SWA
is made with rectangular slots, which are designed to achieve a
low SLL. An example SWA with 10 ×10 slots is designed using
this procedure, and the design results are reported in this paper.
Index Terms—Slotted Waveguide Antennas, SWA, Circular
Polarization
I. INTRODUCTION
Slotted Waveguide Antennas (SWAs) radiate energy through
slots cut in a broad or narrow wall of a rectangular waveguide.
Their advantages include relatively low weight and small
volume, simple design, a high power handling, high efficiency,
and good reflection coefficient [1]. They have been ideal
solutions for many radar, communications, navigation, and
high power microwave applications.
In contrast to the wide interest in the linearly polarized
Slotted Waveguide Antenna arrays, the circularly polarized
SWA arrays have received little interest in the literature. They
were first introduced by Watson in [2] where he described
the possibility of achieving circular polarization with an SWA
from slot pair combinations.
Simmons, following the work of Watson, proposed obtain-
ing circular polarization with a circular hole or a cross-slot
cut in the broadface of the rectangular waveguied at a specific
location [3]. After experimenting with several slot shapes,
Watson concluded that the use of a cross-shaped slot, rotated
by 45◦, can produce the best axial ratio results and reception
of incident energy. Other peoperty of this slot, as illustrated
by Watson in [3], is the ability to radiate in different sense of
circular polarization when excited by different directions of a
traveling wave. Also, when it is used to receive an incident
wave, the wave traveling generated inside the SWA will have
different directions inside the SWA based on the sense of the
incident wave.
Following our design procedure described in [4] and [5]
for the one-dimensional (1D) SWA case, and in [6] for the
two-dimensional (2D) SWA case, this paper adds the circular
polarization feature to the 2D SWA. The SWA array is also
designed for a pattern with low desired Sidelobe Levels
(SLLs) or no undesired grating lobes. The resulting Sidelobe
Level Ratio (SLR) is related to the excitation of each slot
of each branch, which is proportional to the slot conductance,
controlled by the displacement of each slot from the broadface
centerline [7].
The 2D-SWA proposed in this paper consists of multiple
branchline waveguides with broadwall cross-shaped radiating
shunt slots. These slots are responsible for obtaining circular
polarization. The different dimensions of these slots, including
the width, length, rotation angle, and displacement from the
centerline, are presented. Stacking the different branchline
waveguides, a main waveguide is used to feed the branchlines
through a series of coupling slots. The coupling slots are
designed as described by the authors of this work in [4]–[6],
for which the displacement of each slot control the SLR of
the whole system.
To explain the design procedure, a 10 ×10 SWA is taken
as an example. Ten identical SWAs are required for the
branchlines, attached side by side. The proper design of one
of these branchlines ensure radiating with circular polarzation.
To enforce low desired SLL over the whole 3D pattern, special
care should be given to the design of the feed SWA, whose
slots should power the radiating SWAs according to a correct
distribution. This is done by using our procedure described in
[6]. For the taken example, the feed SWA should have 10 slots,
separated consecutively by a distance related to the radiating
SWA aperture width and wall thickness. Since this distance
can be different from a half-guide wavelength, additional steps
are taken to design the feed SWA. The feed SWA also here is
proposed to be collected in a novel way, using the broadwall
for the radiating slots, and not the narrow wall.
II. DESIGN PRO CE DU RE
The complete SWA system consists of 10 branchline SWAs,
each with 10 broadwall radiating cross-shaped shunt slots, and
a 10-slot feed SWA. The feed SWA is designed to have a
minimum SLR value of 20 dB, using the procedure in [4],
[5]. The design is done for the 3.952 GHz frequency.
(a) (b)
(c)
Fig. 1: (a) T-Slot, (b) Offset Compound Slot Pair, (c) Cross-
Shaped Slot
A. Branchline SWAs Design
Ten WR-284 waveguides (a= 2.84 in, b= 1.34 in) are
used for the branchline SWAs. Each -284 waveguide contains
10 slots distributed as follows: the center of the first slot
and the last slot are placed at a distance of quarter guide
wavelength (λg/4), or 3λg/4, from the the waveguide feed
and the waveguide short-circuited side respectively; and the
distance between the centers of two consecutive slots is λg/2.
Concerning the design of the radiating slot, several shapes,
shown in Figure 1 have been proposed for this type of
polarization: T-Slot, Offset Compound Slot Pair (OCSP), and
Cross-Shaped Slot
The 10 slots have cross shape, as shown in Figure 1(c). The
cross shape is used to radiate in a circular polarization. Both
components of the magnetic field on the broadface of the SWA
has two components. These magnetic field components are 90◦
out of phase except for certain locations (or displacement)
from the waveguide centerline. At these specific locations, the
magnetic field components of the dominant (T E01)mode in
rectangular waveguide, given in Equation 1 will be equal in
magnitude and in phase quadrature, and hence resulting in
a circular polarization radiation. The displacements at where
circular polarization can be achieved can be calculated using
Equation 2, suggested in [3]. At this location, d, the magnetic
field, −→
H, is circularly polarized, as well as the vector-current
distribution −→
J.
Fig. 2: Feed Waveguide
Hx=H0s1−λ
2a2
sin πd
a
Hz=−jH0λ
2acos πd
a
(1)
where:
•Hx: the tranverse magnetic field intensity
•Hz: the longitudinal magnetic field intensity
•H0: constant
•λ: the free-space wavelength
•a: the waveguide width
•d: the slot displacement
d=a
πcot−1
±s2a
λ2
−1
(2)
Concerning the arm length, indicated in Figure 1(c), in order
to achieve maximum levels of radiation, it can be designed to
be equal to half the wavelength of the frequency of interest.
This condition however cannot be achieved at some frequency
bands, for which the length of the arm, if taken to be equal
to half the wavelength of the frequency, cannot fit in the
waveguide as a result of the long arm length compared to the
available space of half the waveguide width. For this, in this
work, the arm length has been optimized to reach the desired
radiation without affecting the waveguide structure. The slot
width is taken to be 4mm.
B. Feed SWA Design
The main SWA has to be designed to feed the branchlines
SWAs with a power distribution that results in an SLR not
lower than 20 dB in the azimuth plane if any sidelobes are
TABLE I: Dimensions of the Feed Slot Waveguide
Parameter Value
Waveguide Feed Width a66.26 mm
Waveguide Feed Height b33.13 mm
Slot Length 49.5mm
Slot Width 5mm
TABLE II: Slot Displacements in Feed SWA
Slot Number Displacement (mm)
12.11
23.65
35.17
46.40
57.08
67.08
76.40
85.17
93.65
10 2.11
found. For this, the feed SWA is designed as described in [6],
with 10 rectangular slots made to the broadwall, each displaced
from the waveguide centerline with a specific displacement, as
shown in Figure 2.
A major difference between the proposed feeder and the
conventional SWA is the spacing between the slots. To position
each slot on the feeder SWA facing the center of each
branchline SWA, the distance between neighboring feed slots
on the feeder is equal to a+ 2w, where ais the brancline
width, and wis the branchlines’ wall thickness. This is
different from the conventional λg/2distance assumed in
[4], [5] and [7], and would affect the operating frequency of
the feed SWA if not addressed properly. To overcome this
issue, the waveguide dimensions for the feed SWA should
be selected such that half the guide wavelength of the feed
SWA is as close as possible to a+ 2wof the branches, or
λg(feed)'2×(abranch + 2wbranch). For this example, a
resonance of 3GHz is required, and λg(f eed)must be equal to
152.4mm. Hence, the feed waveguide can have the following
dimensions: afeed = 66.26 mm, bfeed = 33.13 mm.
The feed waveguide and slots’ dimensions are listed in Table
I. The corresponding slots displacements of the feed slots are
calculated from a Chebyshev taper, and are listed in Table II.
C. 2D SWA: The Whole System
The feed SWA is collected to the branchlines SWAs by
having every feed slot of the feed SWA positioned at the
input of every branchline SWA. The combined SWA system
is shown in Fig. 3.
III. SIMULATIONS AND RES ULTS
Simulating the design with an initial value of cross-shaped
slot displacement in the branchlines SWA of 17 mm, resulted
in circular polarization at an angle of 44◦in the φ= 90◦
plane. However, it was noticed through inspecting the radi-
ation pattern and axial ratio results the possible presence of
another circular polarization radiation in the second maximum
direction. For this, a parametric study was performed, for
(a)
(b)
Fig. 3: (a) Design of the 2D SWA, (b) Side view with cross
cut in the feed SWA
TABLE III: Dimensions of the cross-shaped radiating slot
Parameter Value
Waveguide Width a72.136 mm
Waveguide Height b34.036 mm
Cross-Slot Displacement 11 mm
Arm Length 49 mm
Arm Width 4mm
Rotation Angle 46◦
which the arm length, arm width, rotation angle and the
displacement of the cross-shaped slot, have been varied and
studied independently and along mutual variations. The final
result of the reflection coefficient, the 3D gain pattern, and the
2D gain pattern and axial ratio results in the φ= 90◦plane
(YZ-plane), are shown in Figure 4. The optimized parameters
are listed in III.
The whole system is resonating at 3GHz as required. The
-25
-20
-15
-10
-5
0
2.6 2.8 3 3.2 3.4
[dB]
Frequency [GHz]
S11
(a)
(b)
0
5
10
15
20
0 20 40 60 80 100 120 140 160 180
[dB]
Theta [Degrees]
Gain Pattern
Axial Ratio
(c)
Fig. 4: (a) S11 results, (b) 3D pattern , (c) Gain pattern and
axial ratio results in YZ-plane
two maximum radiation points are at: 44◦and 132◦, with a
gain of 18.16 and 18.11 dB respectively. As can be inspected,
circular polarization has been achieved at both angles, with
RHCP in the entire 3dB HPBW between 31◦−63◦and 122◦−
143◦.
IV. CONCLUSION
This paper presented a procedure for the design of 2D
slotted waveguide antenna arrays with circular polarization.
Multiple SWA branches are used as radiating antennas, with
a main SWA used in a novel way as the feed. The procedure
was explained through the example design of a 10 ×10
SWA. Circular polarization has been obtained at two different
angles of maximum radiation, and throughout the entire 3dB
beamwidth of each angle of maximum radiation
REFERENCES
[1] R. J. Mailloux, Phased Array Antenna Handbook. Artech House, 2005.
[2] W. H. Watson, “The Physical Principles of Wave Guide Transmission and
Antenna Systems,” The Clarendon Press, Oxford, Eng., p. 103, 1947.
[3] A. Simmons, “Circularly polarized slot radiators,” IRE Transactions on
Antennas and Propagation, vol. 5, no. 1, pp. 31–36, January 1957.
[4] H. M. El Misilmani, M. Al-Husseini, and K. Y. Kabalan, “Design
of Slotted Waveguide Antennas with Low Sidelobes for High Power
Microwave Applications,” Progress In Electromagnetics Research C,
vol. 56, pp. 15–28, 2015.
[5] H. M. El Misilmani, M. Al-Husseini, K. Y. Kabalan, and A. El-Hajj, “A
Design Procedure for Slotted Waveguide Antennas with Specified Side-
lobe Levels,” International Conference on High Performance Computing
& Simulation, pp. 828–832, 2014.
[6] H. M. El Misilmani, M. Al-Husseini, and K. Y. Kabalan, “Design
Procedure for 2D Slotted Waveguide Antenna with Controllable Sidelobe
Level,” IEEE International Symposium on Antennas and Propagation
(APS), Canada, July 2015.
[7] R. S. Elliott and W. R. O’Loughlin, “The Design of Slot Arrays Including
Internal Mutual Coupling,” IEEE Trans. Antennas Propagat., vol. 34,
pp. 1149–1154, September 1986.
