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# High-gain S-band slotted waveguide antenna arrays with elliptical slots and low sidelobe levels

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• Beirut Research & Innovation Center and American University of Beirut
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# High-gain S-band slotted waveguide antenna arrays with elliptical slots and low sidelobe levels

## Abstract and Figures

Slotted waveguide antenna arrays offer clear advantages in terms of their design, weight, volume, power handling, directivity and efficiency. Slots with rounded corners are more robust for high power applications. This paper presents a slotted waveguide antenna with elliptical slots made to one broadwall of an S-band rectangular waveguide. The antenna is designed for operation at 3 GHz. The slots length and width are optimized for this frequency, and their displacements are determined for a 20 dB sidelobe level ratio. Two rectangular metal sheets are then symmetrically added as reflectors to focus the azimuth plane beam and increase the gain.
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Progress In Electromagnetics Research Symposium Proceedings, Stockholm, Sweden, Aug. 12-15, 2013 1821
High-gain S-band Slotted Waveguide Antenna Arrays with Elliptical
Slots and Low Sidelobe Levels
M. Al-Husseini1,A. El-Hajj2,and K. Y. Kabalan2
1Lebanese Center for Studies and Research, Beirut 2030 8303, Lebanon
2American University of Beirut, Beirut 1107 2020, Lebanon
AbstractSlotted waveguide antenna arrays oﬀer clear advantages in terms of their design,
weight, volume, power handling, directivity and eﬃciency. Slots with rounded corners are more
robust for high power applications. This paper presents a slotted waveguide antenna with ellip-
tical slots made to one broadwall of an S-band rectangular waveguide. The antenna is designed
for operation at 3 GHz. The slots length and width are optimized for this frequency, and their
displacements are determined for a 20 dB sidelobe level ratio. Two rectangular metal sheets are
then symmetrically added as reﬂectors to focus the azimuth plane beam and increase the gain.
1. INTRODUCTION
Slotted waveguide antennas (SWAs) [1] radiate energy through slots cut in a broad or narrow wall
of a rectangular waveguide. They are attractive due to their design simplicity, since the radiating
elements are an integral part of the feed system, that is the waveguide itself. This removes the need
for baluns or matching networks. They also oﬀer signiﬁcant advantages in terms of weight, volume,
high power handling, high eﬃciency and good reﬂection coeﬃcient [2]. Thus, they have been ideal
solutions for many radar, communications, navigation, and high power microwave applications [3].
SWAs can be realized as resonant or non-resonant according to the wave propagation inside
the waveguide (respectively standing or traveling wave) [4, 5]. The design of a resonant SWA is
generally based on the procedure described by Elliot [4, 6, 7], by which the waveguide end is short-
circuited at a distance of a quarter-guide wavelength from the center of the last slot, and the
inter-slot distance is one-half the guide wavelength. For rectangular slots, the slot length should
be about half the free-space wavelength. Slot shapes that avoid sharp corners are more suitable for
high power applications, since sharp corners aggravate the electrical breakdown problems. Elliptical
slots are an excellent candidate for such applications [8].
As with all antenna arrays, the resulting sidelobe level is related to the excitations of the
individual elements. In SWAs, the excitation of each slot is proportional to its conductance. For
the case of longitudinal slots in the broadwall of a waveguide, a slot conductance is controlled by its
displacement from the broadface centerline [9]. Thus, for a desired sidelobe level, the corresponding
set of slots displacements should be determined.
In this paper, an SWA designed for operation at 3 GHz is presented, where ten elliptical slots
are made to one broadface of an S-band rectangular waveguide. The slot displacements from the
centerline are determined to obtain a sidelobe level ratio of 20 dB. Later, two metals sheets are
attached to the SWA edges to focus its azimuth plane beam. The reﬂection coeﬃcient, pattern
plots and gain results of the antenna are reported.
2. ANTENNA CONFIGURATION
The target frequency is 3 GHz, so a WR-284 waveguide having a= 2.8400 and b= 1.3700 is used
to construct the SWA. The waveguide is shorted at one end and fed at the other. Ten elliptical
slots are cut into one of its broadsides. The slots are spaced at half the guide wavelength, center to
center, where in this case the guide wavelength λg= 138.5 mm. The slots are positioned such that
the center of the ﬁrst one, Slot1, is at a distance of λg/4 from the waveguide feed, and the center
of the last slot, Slot10, is at λg/4 from the waveguide’s short-circuited side. The total length of
the waveguide is thus 5λg.
The width of each slot, which is 2 times the minor radius of the ellipse, is ﬁxed at 5mm. This
is calculated as follows: for X-band SWAs, which the literature if full of, the adopted width of a
rectangular slot is 0.062500, corresponding to a= 0.900. By proportionality, the width of the elliptical
slot for this S-band SWA is computed from 2.8400 ×0.0625/0.9, which is 0.19700 or 5 mm. Because
of their elliptical shape, the length of the slots (double the major radius) is expected to be larger
than half the free space wavelength. Simulations using ANSYS HFSS are done to optimize the slot
1822 PIERS Proceedings, Stockholm, Sweden, Aug. 12–15, 2013
length for resonance at 3 GHz. For these simulations, it is assumed that all slots are at the same
spacing from the broadside centerline, in an alternating fashion. The resonant slot length is found
to be 54.25 mm.
For a desired sidelobe level ratio (SLR) of 20 dB, a heuristic method is used to obtain the
required set of slots displacements. The slots near the two waveguide edges are closest to the
broadface centerline, whereas those toward the waveguide center have the largest displacement.
The detailed displacements values are given in Section 3.
Two metal sheets are then attached symmetrically, as shown in Fig. 1, at an angle of 60with
respect to the XZ plane. These 2 sheets act as reﬂectors, thus leading to beam focusing in the
azimuth plane and as a result to a gain increase. The width of each metal sheet, L, is 300.
Figure 1: Slotted waveguide with 10 elliptical slots with two re ectors added.
3. RESULTS
The uniform slots displacement that leads to a good reﬂection coeﬃcient at 3 GHz is calculated
using
du=a
πsarcsin ·1
N×G¸,(1)
where
G= 2.09 ×a
b×λ0
λg×[cos(0.464π×λ0g)cos(0.464π)]2.(2)
In (1), Nis the number of slots, which is equal to 10, and in (2), λ0is the free-space wavelength.
At 3 GHz, λ0= 100 mm. For this SWA, du= 7.7mm. This displacement value is used in the
HFSS simulations to obtain the resonant elliptical slot length, which is found to be 54.25 mm. For
this slot length and this uniform displacement of all ten slots, the resulting SLR is around 13 dB,
which is as expected. The reﬂection coeﬃcient S11 and the Y Z-plane gain pattern in this case are
given in Fig. 2. A peak gain of about 17 dB and an SLR of 13.2 dB are recorded. The half-power
beamwidth (HPBW) in this plane is 7.2 degrees. These values are obtained using CST Microwave
Studio, but are also veriﬁed with HFSS.
Since better SLRs are desirable, the slots displacements are changed, to non-uniform, using a
heuristic method, which will not be detailed in this paper. For an example SLR of 20 dB, the
displacement values are given in Table 1. The alternating pattern about the centerline is respected.
The length of all slots is kept at 54.25 mm, as in the uniform case. Simulations have proven that the
resonating length of these elliptical slots is not very sensitive to the distance from the centerline.
For these values, the antenna still resonates at 3 GHz, the SLR is 20 dB, the peak gain is 16.8 dB,
and the Y Z-plane HPBW increases to 8.4 degrees. The broadening of the main beam is expected
when the sidelobes are forced to go lower.
When the two reﬂectors are added, a gain increase of about 3 dB is obtained due to a focus of
the azimuth plane beam. The antenna retains its resonance at 3 GHz, and the SLR remains around
Progress In Electromagnetics Research Symposium Proceedings, Stockholm, Sweden, Aug. 12-15, 2013 1823
(a) S for uniform slots displacement (b) Pattern in the YZ plane
11
Figure 2: Antenna’s reﬂection coeﬃcient and Y Z-plane pattern for the case of uniform slot displacement
and before attaching the two reﬂectors.
Table 1: Displacement of slot centers for an SLR of 20 dB.
Slot number 1 2 3 4 5 6 7 8 9 10
Displacement (mm) 3.74 5.42 7.11 8.4 9.11 9.11 8.4 7.11 5.42 3.74
Figure 3: Reﬂection coeﬃcient without and with the reﬂectors.
(a) Patterns in the azimuth plane (b) Patterns in the YZ plane (c) Patterns in the XZ plane
Figure 4: Antenna’s gain patterns in the three principal planes (red line: no reﬂectors, blue line: with
reﬂectors).
1824 PIERS Proceedings, Stockholm, Sweden, Aug. 12–15, 2013
20 dB. The back lobe level stays about the same, so the main-to-back lobe level ratio also increases
by about 3 dB. The S11 and pattern results of the two cases, with and without the reﬂectors,
are shown in Fig. 3 and Fig. 4, respectively. All results generated in HFSS were veriﬁed in CST
Microwave Studio, where a good match is observed.
4. CONCLUSION
A 3 GHz slotted waveguide antenna was presented. It has 10 elliptical slots, with optimized dimen-
sions, made to one broadwall and displaced around its centerline so as to obtain a 20 dB sidelobe
level ratio. The antenna has a very broad azimuth plane beam and a peak gain of about 17 dB.
Upon adding two reﬂectors to the antenna’s edges, the beam is focused and the gain is increased
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tems,” IEEE Trans. Ind. Applicat., Vol. 16, No. 6, 809–813, 1980.
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503, Aug. 2005.
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Vol. 19, 24–38, 1948.
... The slots were separated by a distance of one wavelength and placed on both sides of the centreline so that they radiate in phase. The distance between the end and the centre of the last slot is a quarter wavelength so that the end acts as a short [32]. ...
... AL-Husseini used a heuristic approach to obtain the required set of slot displacements, the slots closest to the two waveguide ends have least displacement and those towards the waveguide center have the largest displacement from the centreline. The uniform slot displacement was used to formulate the uniform slot array displacement distribution [32]. ...
... Slotted waveguide with two reflectors added[32]. ...
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... SWAs are commonly made of rectangular waveguides. In SWA, slots are cut on the broad wall or narrow wall of the waveguide to radiate the electromagnetic energy in the targeted direction [9]. The most common slot types include longitudinal broad wall slots, inclined edge or sidewall slots, and cross-slot configuration [6,10]. ...
... The width of the slot in the round-edged configuration in our design is taken to be equal to λ 0 /10 due to design limitations related to available fabrication limitations. The thickness of the upper slotted plate is 3 mm, according to which specific slot thickness is considered to obtain a good impedance match at the desired frequency band [5,9,[27][28][29]. ...
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... It is well-known that reflector structures properly positioned in the vicinity of an antenna can improve its gain by reflecting the electromagnetic wave towards a specific point in the far-field region under constructive interference with the transmission wave [37]. This concept has been numerically applied and evaluated to SWAAs, by symmetrically attaching inclined metal sheets to their structures at the microwave range [38], [39]. Regardless, these microwave designs leak from experimental results while our design meets the mmwave frequency range operation and has been experimentally validated with superior impedance bandwidth. ...
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... One antenna that is easy to create is an antenna waveguide slot. This antenna has advantages in simple design, wideband and high gain [6][7][8]. So that this type of antenna can be applied to 2.3 GHz LTE-TDD technology. ...
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... As the elliptical slots can handle more power than the rectangular counterparts, the elliptical slots are used [22]. ...
... We have used the elliptical slots for realising the linear array. The elliptical slots can handle more power than the rectangular counterparts [21,22]. The length of the elliptical slots is expected to be larger than λ/2 due to the round shape at the slot corners. ...
... However, since sharp corners aggravate the electrical breakdown problems, slot shapes that avoid sharp corners are more suitable, especially for high power microwave applications. Elliptical slots are thus an excellent candidate for such applications [10,11]. ...
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... Slot shapes that avoid sharp corners are more suitable for high power applications, since sharp corners aggravate the electrical breakdown problems. Elliptical slots are then an excellent candidate for such applications [8], [9]. ...
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A basic theory of slots in rectangular wave‐guides is given. The analogy with a transmission line is developed and established, and detailed formulae for the reflection and transmission coefficients and for the voltage amplitude'' in the slot generated by a given incident wave are given. While the complete expressions for these quantities are quite complicated and involve the summation of infinite series, certain parts of the expressions are comparatively simple. In particular, the resistance'' or conductance'' of slots which are equivalent to series or shunt elements in a transmission line are given by fairly simple closed expressions. Guide‐to‐guide coupling by slots and slot arrays are also considered. A more detailed summary of the main results of the paper is given in Section 1.
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A method of microwave power application is described for large industrial heating systems in which a preselected temperature distribution may be specified for typical work loads. This goal is approached through the use of a discrete number of fieldradiating slots cut in the broad side of an S-band waveguide. Uniform or graded distributions of microwave power are obtainable through design data that were experimentally determined and empirically recorded. Individual slot power is determined by the waveguide input power, the number of slots, and the location of the slots on the surface of the waveguide. In a system using 30 slots, work-load temperatures at 60-kW input levels were noted to meet a five-percent variation around a 100Â°C requirement.
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Improved array performance (lower sidelobe levels, a better input match) requires elimination of approximations in earlier design procedures. One important change is to include internal higher order mode coupling. That is done here and is found to cause a simple but significant change in existing design formulas.
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An earlier design procedure, valid for arrays of longitudinal slots fed by air-filled rectangular waveguide, is generalized to apply to the increasingly used practical case that the waveguide is dielectric-filled. This requires abandonment of the model of an equivalent array of loaded dipoles, which results in a surprisingly simpler and more direct derivation of the design equations. The new generalized procedure retains an important feature of the earlier approach in that it includes the effect of external mutual coupling.
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An existing design procedure, applicable to standing-wave-fed longitudinal shunt slot arrays, and which accounts for the variability of mutual coupling, is extended to situations in which a traveling-wave feed is employed, i.e., the slots are not λg/2 on centers. The extension permits the design of slot arrays to give an input match and a sum pattern for which the main beam is not at broadside. The technique is also amenable to difference pattern applications. Copyright © 1979 by The Institute of Electrical and Electronics Engineers, Inc.
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The differences in mutual coupling for a central slot and a peripheral slot cannot be ignored in small arrays if good patterns and impedance are to be obtained. A theory has been developed whereby the length and offset of every slot in the array can be determined, in the presence of mutual coupling, for a specified aperture distribution and impedance match. The theory enlarges on Stevenson's method, and uses a modified form of Booker's relation based on Babinet's principle to treat nonresonant longitudinal shunt slots in the broad wall of a rectangular waveguide. A general relation between slot voltage and mode voltage is developed, and then formulas are derived for the active, self-, and mutual admittances among slots. These formulas result in a design procedure. Analogous treatments of inclined series slots in rectangular guide and of strip-line-fed slots are possible. Comparison between various experiments and the theory is presented. Tests of the theory include the resonant length of a zero offset slot, resonant conductance versus offset and resonant conductance versus frequency for a single slot, and self- and mutual admittances for two staggered slots. The design and performance of a two-by-four longitudinal shunt slot array is also described.
Antenna Engineering Handbook , 4th Edition
• R A Gilbert
Gilbert, R. A., "Waveguide slot antenna arrays," Antenna Engineering Handbook, 4th Edition, J. L. Volakis, Ed., McGraw-Hill, 2007.