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Design procedure for planar slotted waveguide antenna arrays with controllable sidelobe level ratio for high power microwave applications

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This article presents a complete design procedure for planar slotted waveguide antennas (SWA). For a desired sidelobe level ratio (SLR), the proposed method provides a pencil shape pattern with a narrow half power beamwidth, which makes the proposed system suitable for high power microwave applications. The proposed planar SWA is composed of only two layers, and uses longitudinal coupling slots rather than the conventional inclined coupling slots. For a desired SLR, the slots excitation in the radiating and feeder SWAs are calculated based on a specified distribution. Simplified closed-form equations are then used to determine the slots nonuniform displacements, for both the radiating and feeder SWAs, without the need to use optimization algorithms. Using simplified equations, the slots lengths, widths, and their distribution along the length of the radiating and feeder SWAs can be found. The feeder dimensions and slots positions are deduced from the dimensions and total number of the radiating SWAs. An 8 × 8 planar SWA has been designed and tested to show the validity of the proposed method. The obtained measured and simulated results are in accordance with the design objectives.
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Received: 18 April 2020 Revised: 12 June 2020 Accepted: 11 July 2020
DOI: 10.1002/eng2.12255
RESEARCH ARTICLE
Design procedure for planar slotted waveguide antenna
arrays with controllable sidelobe level ratio for high power
microwave applications
Hilal M. El Misilmani1Mohammed Al-Husseini2Karim Y. Kabalan3
1Electrical and Computer Engineering
Department, Beirut Arab University,
Debbieh, Lebanon
2Beirut Research and Innovation Center,
Lebanese Center for Studies and
Research, Beirut, Lebanon
3Electrical and Computer Engineering
Department, American University of
Beirut, Beirut, Lebanon
Correspondence
Hilal M. El Misilmani, Electrical and
Computer Engineering Department,
Beirut Arab University, P.O. Box 11-5020
Beirut, Riad El Solh 1107 2809, Lebanon.
Email: hilal.elmisilmani@ieee.org
Funding information
American University of Beirut; Beirut
Arab University; Beirut Research and
Innovation Center
Summary
This article presents a complete design procedure for planar slotted waveguide
antennas (SWA). For a desired sidelobe level ratio (SLR), the proposed method
provides a pencil shape pattern with a narrow half power beamwidth, which
makes the proposed system suitable for high power microwave applications.
The proposed planar SWA is composed of only two layers, and uses longitudi-
nal coupling slots rather than the conventional inclined coupling slots. For a
desired SLR, the slots excitation in the radiating and feeder SWAs are calculated
based on a specified distribution. Simplified closed-form equations are then used
to determine the slots nonuniform displacements, for both the radiating and
feeder SWAs, without the need to use optimization algorithms. Using simplified
equations, the slots lengths, widths, and their distribution along the length of
the radiating and feeder SWAs can be found. The feeder dimensions and slots
positions are deduced from the dimensions and total number of the radiating
SWAs. An 8 ×8 planar SWA has been designed and tested to show the validity
of the proposed method. The obtained measured and simulated results are in
accordance with the design objectives.
KEYWORDS
antenna arrays, high power microwave applications, slotted waveguide antennas, sidelobe level ratio
1INTRODUCTION
High power microwave (HPM) technology is well known in both military and commercial applications.1An efficient
antenna to be used as the radiating system for these applications is required to have a well directive pattern, large side-
lobe level ratio (SLR), and high gain. It should also have high power handling capability required to extract the HPMs
from their source. Slotted waveguide antennas (SWA)2are taking a major interest in this field, with their major ability of
beam pointing and HPM handling capability.3SWAs can be also directly connected to Reltron HPM sources, without the
need for additional mode converter, which makes them suitable for HPM applications. SWAs are also used in wireless
technologies, maritime, and space applications.
SWAs are made of rectangular waveguides, having slots cuts used to radiate the energy.4The conventional cuts have
a rectangular shape. The slots can be made either on the broadwall or the narrow wall of the waveguide, with the most
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the
original work is properly cited.
© 2020 The Authors. Engineering Reports published by John Wiley & Sons Ltd.
Engineering Reports. 2020;2:e12255. wileyonlinelibrary.com/journal/eng2 1of15
https://doi.org/10.1002/eng2.12255
2of15 EL MISILMANI  .
widely used slots are: the longitudinal broadwall slots, inclined edge or sidewall slots, and crossslots. Two types of SWAs
are found, resonant and nonresonant antennas, also known as standing wave and traveling wave antennas. The resonant
SWAs are preferred to their counterparts due to the short circuit termination that increases their efficiency, with no
power loss and normal main beam independent of the resonance frequency, but with a narrower frequency range.5,6 The
traveling-wave SWAs have a larger bandwidth, but suffer from lower efficiency due to the matched load used to prevent
the reflections of the waves. In addition, a phase difference is present between the radiating slots, whereas, for resonant
slots their impedance or admittance are real values. In this work, resonant SWAs are designed and investigated.
The design of SWAs was first presented by Stevenson and Elliott.5,7,8 Two main equations, based on Stevenson
equations and Babinet’s principle, should be solved simultaneously to determine the different slots displacements from
the waveguide centerline and the slots length. Solving these equations depends on Stegen’s assumption of the universal-
ity of the resonant slot length,9in addition to Tai´
s formula10 and Oliner’s length adjustment factor.11 This conventional
design method is complicated, and mostly rely on numerically solving several equations to deduce both the displacement
and length of each slot. The excitations of the SWA individual slots, which are translated into slots displacements, control
the resulting SLR of the SWA array.7
Pan et al12 have presented an SWA composed of two identical narrow-wall SWAs for HPM application. Using a tun-
able feeding structure, the proposed antenna can be also used for beam-steering. Pan also presented another SWA with
narrow-wall complementary-split-ring slots for HPM applications.13 Periodic air-filled corrugations have been also pro-
posed to be added to the SWA to improve its overall gain. Sabri et al14 have presented an SWA with dual-beam directional
pattern. Longitudinal slots have been made on both broadwalls of the SWA. Pulido-Mancera et al15 have proposed a tech-
nique to enhance the directivity of SWAs using metamaterial parasitic elements with discrete dipole approximation. A
dual-band SWA, operating at 28 and 38 GHz, suitable for 5G applications, has been presented by Da Costa et al.16 Filgueiras
et al17 have also presented an omnidirectional SWA operating at 26.2 GHz for 5G applications. Circular waveguide was
used for their SWA instead of the rectangular one. An SWA with inclined slots on the narrow-wall has been proposed for
beam-scanning by Tan et al.18 Lomakin et al has presented a three-dimensional (3D) printed SWA for automotive radar
applications. A differential feed structure was used to couple the power to the SWA.
A major research in the SWA design field focuses on obtaining a pencil shape directive pattern, with high gain, large
SLR, and narrow half power beamwidth (HPBW). The single element SWA has a relatively high gain, but suffers from
the wide HPBW in the plane perpendicular to the waveguide axis. To achieve the directive pattern features, planar SWAs
can be formed by stacking a specified number of radiating SWAs, fed by an additional SWA. Inclined coupling slots19,20
are used in the conventional planar SWA systems to couple the power from the feeder SWA to the stacked radiating
SWAs. The rotation angles of these coupling slots from the waveguide centerline are either considered to be uniform or
nonuniform. To control the typical inclined coupling slots, usually complicated equations that relate the inclination angle
to the excitation voltage and distribution are used, which makes designing large arrays a complicated procedure.
Wu et al21 have presented a planar SWA operating at 140 GHz. The feeder SWA, composedof a feeding slot, overmode
cavity, and the coupling slots, was designed to provide the same-magnitude but with alternating phase excitations. This
was done using an integrated power divider and phase shifter. Longitudinal slots of the same lengths and offsets were also
used for coupling. Kumar et al22 have proposed a planar SWA to be used in X-band. Genetic algorithm, combined with
Schelkunoff’s unit circle technique, have been used to synthesize the desired current distribution. The feeder was com-
posed of two layers, the inclined coupling slot layer, and a feed layer containing a power divider. A planar SWA designed
to operate at 40 GHz has been presented by Zhang et al.23 It consisted of five different layers, for which a four-corner-fed
structure with inclined coupling slots was used to suppress the sidelobe levels. The feeder was composed of an input aper-
ture, feeding waveguide, and the coupling slots. Inclined coupling slots have been also used by Coburn et al24 with one
layer of feeding but with four different feeding structures to feed four 8×8 subarrays SWAs to achieve low sidelobe levels
for HPM applications. Kim et al has also presented a planar SWA for HPM applications. The planar was composed of four
layers: radiating slot plate, radiating waveguide, feeding waveguide, and E-plane septum divider.25 It was also divided into
8×4 subarrays, each connected to multistage divider, to control the feeding to the SWA elements. Ripoll-Solano et al26
have used a two-step design process with a least-square optimization approach to improve the excitation coefficients to
match the desired SLR of a planar SWA. Other feeding mechanisms used complicated structures to achieve large SLR.27,28
In a previous work, we have also presented a planar SWA with crossshaped radiating slots to achieve circular polarization.
The feeder SWA was collected at the input terminals of the radiating SWAs.19
In this work, we present a complete and efficient design procedure for planar SWAs. The proposed method uses sim-
plified closed-form equations to determine the slots nonuniform displacements, without the need to use optimization
EL MISILMANI  . 3of15
algorithms.29,30 A major contribution lies in the use of the same proposed simplified equations to design both the radi-
ating and feeder SWAs. Longitudinal coupling slots are proposed for the feeder SWA, displaced from the waveguide feed
centerline according to the desired SLR, rather than the conventional inclined coupling slots. This can provide better val-
ues of SLR. The feeder SWA is collected at the back of the radiating SWAs. Only two layers are used in the proposed planar
SWA, one for the radiating SWAs, and the second for the feeding. This resulted in a simplified design when compared
with the traditional planar SWA systems.
The proposed design procedure in this work is outlined as follows. For a desired resonance frequency, the slots lengths,
widths, and their distribution along the length of the radiating SWAs and feeder SWA can be found. For a desired SLR,
the slots excitation of the broadwall longitudinal slots for both the radiating and the feeder SWAs, are calculated from a
certain distribution. The slots excitations are then used to calculate their displacements. The feeder is then coupled to the
radiating SWAs in an efficient manner to obtain the required SLR. To verify the validity of the proposed design approach,
an 8 ×8 planar SWA is designed, simulated, and then fabricated and tested. As will be shown, the results are in accordance
with the design requirements, and the measured results are in good analogy with the simulated ones.
The rest of the article is organized as follows. Section 2 presents the complete design procedure steps, for both the
radiating and feeder SWAs. An investigation of the mutual coupling effects that might arise in these systems is also pre-
sented in this section. Section 3 illustrates the design of a planar 8 ×8 SWA example. Section 4 presents the fabrication
process of the presented example, along with the simulations and measurements results.
2DESIGN PROCEDURE
The design procedure of the planar SWA starts by determining the desired SLR and operating frequency. With these
design requirements, SWAs to be used for the radiating and feeder SWAs, can be designed. The radiating SWAs are first
designed. The slots shape, positions long the axis of the waveguide, length, and width, are first determined. Then, the pro-
posed method used to find the displacements of these slots from the axis of the waveguide for a desired SLR is outlined.
The feeder SWA is then designed based on the dimensions and guide wavelength of the waveguide used in the radiating
SWAs. Eventually, the radiating SWAs are stacked side by side, and the feeder is coupled to the radiating SWAs. At the
end of this section, the mutual coupling effects that might be found in such systems, along with ways to suppress them,
are presented.
2.1 The design of the radiating SWAs
The design of the each radiating SWA is outlined as follows. In typical situations the desired operating frequency and SLR
are known. Based on the desired frequency, the waveguide inner dimensions, that is, width and height, can be found.
If the desired total number of slots on each SWA is known, then using the guide wavelength of the chosen waveguide
with the total number of slots, the length of the SWA can be then found. This length is calculated taking into account the
spacing between the consecutive slots, in addition to the spacing between the end terminals and the first and end slot. In
different situations, a limited choice of waveguides to be used as radiating SWA is found, which sets some constraints on
the operating frequency, as will be seen in the illustrating example in Section 3.
In the following, the design procedure of the radiating SWAs is outlined. The slots shape and dimensions are first
presented. Their positions along the waveguide broadwall are then defined. Then, the proposed method used to find the
displacements of these slots from the axis of the waveguide for a desired SLR is presented. A typical SWA is sketched in
Figure 1.
2.1.1 Slot shape and dimensions
The conventional rectangular slots used in the traditional SWA design could aggravate electrical breakdown problems
when working at HPMs.31 This is due to the enhancement of the microwave electric field which can lead to self-induced
microwave breakdown of the air in the slot.32 Avoiding sharp corners is preferred in such cases. For this, round-ended
slots9that offer improved high power operation and easier manufacturability than the rectangular ones33 are used in
this work.
4of15 EL MISILMANI  .
FIGURE 1 A typical SWA with eight longitudinal slots. SWA, slotted waveguide antennas
The slots length can be either nonuniform, for which the length of each slot is calculated based on optimization
algorithms, or assumed to be uniform for simplicity purposes. Choosing uniform slots length can also lead to the desired
results.
For optimal radiation characteristics, the length of all slots are taken to be at their resonant length. For rectangular
slots,7this length is typically around 0.49𝜆. For round-ended slots, as the one used in this work, a modification of this
length is recommended. This is done as follows. The slots displacements and positions are fixed, and the length is var-
ied starting with the typical value of 0.49𝜆, while checking the reflection coefficient results, till reaching an acceptable
value at the desired frequency. Throughout the different designs that we have worked on using the proposed design pro-
cedure in this work, the modified round-ended slot length values differed from the typical rectangular slot lengths by
1% to 3% only.
As for the width of the slot, we have started with an initial value calculated as follows: for X-band SWAs, the
width of a rectangular slot the mostly used in the literature is 0.0625in =1.5875 mm, corresponding to a=0.9in =22.86
mm. By proportionality,30 the initial width of the slot can be computed as in (1), with abeing the width of the
available waveguide. Then, this width can be varied while fixing the values of the slots length and displacements,
and checking the reflection coefficient results. Usually, a minor change in the width value is seen to increase the
operating bandwidth.
Slot width =a×0.0625 in
0.9in .(1)
2.1.2 Slots positions
The position of the slots along the length of the SWA plays an important role in ensuring feeding the slots in phase.
The phase shift between consecutive slots is determined by the electrical distance 2𝜋d𝜆g,with𝜆gbeing the guide
EL MISILMANI  . 5of15
wavelength defined as the distance traveled by the electromagnetic wave along the length of the waveguide to undergo
a phase shift of 2𝜋radians. It is calculated as in (2), with 𝜆0being the free-space wavelength and cis the speed
of light.
𝜆g=𝜆0
1𝜆0
𝜆cutoff 2
=c
f×1
1c
2a.f2
.(2)
Using longitudinal slots, the waveguide itself acts as a transmission line. Taking a transverse electric field in each slot,
the TE10 mode scattering is considered to be symmetrical. Using an equivalent transmission line, each slot is modeled
as a shunt element. This assumption has been proved to be valid using the method of moment when the width of the
slots is narrow, their offsets are not too large, and the height of the waveguide is relatively large.34 Since resonant SWAs
are terminated by a short circuit, open circuit impedance is found at a quarter guide wavelength down the length of the
waveguide.
The slots are positioned as follows. The first and last slots are separated by a distance of m𝜆g4 from both terminals,
with mbeing an odd number. In order to have the same input impedance viewed a 𝜆g4 away, the separation between the
slots is taken to be 𝜆g2. In this way, all slots can be viewed as being in parallel. The shunt admittance of these terminations
then vanishes at the last slot, while having the admittance of each slot to have a value of 1/N,withNbeing the total
number of slots. This ensures an impedance matching at the input.
2.1.3 The slots displacements
The distance separating the waveguide broadwall centerline and the center of the slot is specified as slot displacement.
Although the slots could be placed at the same distance from the centerline, it was shown in Reference 30 that such a
configuration results in an SLR of around 13 dB, which is similar to the case of having equal excitations to discrete elements
in an antenna array. For this, nonuniform displacements are used to design the radiating SWAs for larger SLR. Referring
to Figure 1, the slots displacements are indicated by Dn, for which nis the index of each slot. To achieve higher efficiency,
all slots must radiate in phase. For this, the slots are placed in an alternating order on the length of the waveguide.
Figure 2 illustrates the methodology used to calculate the slots displacements for both the radiating and the feeder
SWAs. The slots displacements are calculated as follows. Starting with a desired SLR, the conductances of the slots are
obtained from a certain distribution. Using the obtained slots conductances, the slots displacements can be then deduced.
The slots displacements control the excitation of every slot, and hence they can be used to control the total SLR of the
SWA array.
In the following, the equations of Chebyshev and Taylor distributions are given. Afterward, a gain pattern of an SWA
designed using different SLR values with different distributions is given to show the validity of the proposed close-form
equations.
FIGURE 2 Methodology used in the
calculation of the slots displacements for a
desired sidelobe level ratio
6of15 EL MISILMANI  .
Chebyshev distribution
Beginning with the equation of the array factor of a generalized Chebyshev array35,36 given in (3), the array factor is then
calculated for a uniform spacing and an amplitude symmetrical about the center, as given in (4). The excitation coefficients
can be then obtained using (5).
f(u)= 1
R
p
n=1TNn1(𝛾ncos u
2),(3)
where Txis the Chebyshev polynomial of order x,Rnis the SLR, Nnis the number of elements, nis the index of the nth
basis Chebyshev array, 𝛾n=cosh[cosh1(Rn)∕(Nn1)],andu=2𝜋(d𝜆)(cos 𝜃cos 𝜃0)with dbeing the interelement
spacing and 𝜃0the elevation angle of maximum radiation.
f(u)=
2
N2
m=1
Imcos[(m12)u],for Neven
(N+1)∕2
m=1
𝜖mImcos[(m1)u],for Nodd
,(4)
where 𝜖mequals 1 for m=1 and equals 2 for m1.
Im=
2
NR
N2
q=1
f[u=p]cos[q],for Neven
1
NR
N+1
2
q=1
𝜖qf[u=v]cos[w],for Nodd
,(5)
where: p=2𝜋N(q12),q=2𝜋N(m12)(q12),v=2𝜋N(q1),and w=2𝜋N(m1)(q1)
After calculating the slots excitations coefficients, the slots displacements can be calculated. The normalized conduc-
tance of the nth indicated by gncan be calculated using (6) and (7),30 with Nbeing the number of slots, and cnsare the
distribution coefficients calculated using Chebyshev distribution for a desired SLR.
dn=a
𝜋arcsin
gn
2.09 𝜆g
𝜆0
a
bcos2𝜋𝜆0
2𝜆g(6)
gn=cn
N
n=1cn
.(7)
Taylor (one-parameter) distribution
The excitation coefficients, In(z), for continuous line distribution of length l, are equal to:
In(z)=
J0j𝜋B12z
l2,for l2z+l2,
0,elsewhere
.(8)
EL MISILMANI  . 7of15
FIGURE 3 Prototype SWA: A, Gain pattern comparison, and B, |S11| plots, for the three different distribution cases with nonuniform
displacements (using CST). SWA, slotted waveguide antennas
For the discrete case,37 the current magnitudes of an N-element linear array with symmetric excitation are equal to:
am=
I0𝛽1m0.5
M0.52,for N=2M
I0𝛽1m1
M12,for N=2M1
(9)
with 1 mM,a1is the excitation of the array’s center element(s), and aMis that of the two edge elements.
Using the different distribution coefficients detailed here, we have used the close-form equation to design a proto-
type SWA operating at 3 GHz, using the outlined design procedure, and for the following distributions and SLR values:
Chebyshev distribution with 20 dB SLR, and Taylor (One-Parameter) Distribution with 20 and 30 dB SLR. Figure 3 shows
the obtained gain patterns and reflection coefficients results for the three different cases. It clearly shows that SLR design
specifications in each case has been obtained, with the SWA retaining resonance at 3 GHz, despite the different slots
displacements used with every distribution.
2.2 Design of feeder SWA
2.2.1 Feeder SWA design
The design procedure of the feeder SWA starts by obtaining its required dimensions. Referring to Figure 4, in order to place
the longitudinal coupling slots of the feeder SWA centered at the centerline of every radiating SWA, the separating distance
between two consecutive coupling slots must be equal to the inner width of the radiating SWA (aradiating ), in addition to
twice the dimension of the wall thickness of each radiating SWA (W). Referring to the design procedure presented in
Section 2.1, the distance separating two consecutive slots on the feeder must be equal to 𝜆g2 for highest efficiency. As
such, the guide wavelength of feeder SWA (𝜆g(feed)) should be as close as possible to twice the distance separating two
consecutive coupling slots (abranch +2×W).
After obtaining the waveguide dimensions and 𝜆g(feed), the design steps follow the same design procedure of the radiat-
ing SWAs as outlined in Section 2.1. The slot length is to be calculated based on 𝜆g(feed). The first and last slot are separated
from the end terminals by m𝜆g(feed)4withmbeing an odd number, and the consecutive coupling slots are separated by
𝜆g(feed)2.
Once the feeder SWA is designed, the eight radiating SWAs are stacked side by side, and the feeder SWA is collected
at the bottom of the their broadwall faces. It is observed in this manner that the coupling slots are not properly placed
at an equidistant from the neighboring radiating slots on each radiating SWA. This might affect the radiation pattern of
8of15 EL MISILMANI  .
FIGURE 4 Planar SWA design showing only two radiating SWAs with the feeder SWA. Dradiating refers to the displacement of each
radiating slot from the radiating SWA centerline. Dfeed refers to the displacement of each coupling slot from the feeder SWA centerline. W
refers to the wall thickness of all SWAs. Each radiating SWA is moved by Dfeed as per the displacement of the coupling slot feeding it. SWA,
slotted waveguide antennas
the complete system, through increasing the grating lobes and hence decreasing the SLR of the system. For this, each
radiating SWA is repositioned as per the displacement of its corresponding feeding slot, as shown in Figure 4.
2.3 Mutual coupling suppression
In such systems, two different mutual coupling effects can arise. The first is due to the coupling between the radiating
slots on the broadwall of the radiating SWAs (branchlines). The second is due to the coupling between the coupling slots
and the radiating slots. Both of these effects have been suppressed and hence neglected in the equations as outlined in
the following.
2.3.1 Mutual coupling between the radiating slots
This type of coupling is mainly affected by the separating distance between the shunt slots, and their location on the
waveguide broadwall. Their separating distance has been investigated in several articles, for which it was shown that
the mutual coupling is much smaller when the slots are separated by half-waveguide length. In fact, it was concluded in
Reference 38 that this type of mutual coupling can be neglected if this distance is adopted between the slots. In Reference
39, it was also shown that this type of mutual coupling can be also neglected in the design of shunt slot arrays, unless the
SWA has a short length and few lots.
For SWAs, and as described in Section 2.1, the driving impedance of the radiating slots depends on their excitation,
position, and displacement along the length of the waveguide, with respect to neighboring slots. For this, the procedure
presented in this work mainly focuses on calculating the elements excitations for optimized radiation. These excitations,
in their turn, control the displacement of each slot, and hence the coupling between the elements. The distance separating
any consecutive radiating slots is chosen to have the least mutual coupling in between. The slots are also separated by half
guide wavelength in each branchline SWA and feeder SWA, and placed in an alternating order for maximum efficiency and
to suppress the mutual coupling between neighboring slots. Nevertheless, the mutual coupling between the neighboring
slots in the same radiating SWA is not necessarily negligible in all designs, and this will be investigated in further work.
EL MISILMANI  . 9of15
2.3.2 Mutual coupling between the coupling and radiating slots
The coupling effect between two antennas is commonly modeled as an impedance variation. When mutual coupling is
present in SWAs, it generally results in an increase of 8%in slot conductance.39 The effect of mutual coupling in such
designs can be simplified as follows. The resonant slot length might be affected and could result in a shift of the resonance
frequency to a higher value, the impedance bandwidth (VSWR) is shifted to a higher frequency in the SWA branchlines
(radiating SWAs), whereas in the feeder SWA the voltage standing wave ratio (VSWR) is shifted to a lower frequency. The
combination of these effects could still lead to results as desired.
The effect of the mutual coupling on the radiation pattern and the reflection coefficient results for SWAs have been
presented in several articles, for which some of them have neglected this effect,7,9,24,39-45 which is a valid assumption for
resonant slotted arrays.46 It was shown in Reference 44 that the effect of mutual coupling on the array performance is
minimal. In Reference 34, it was concluded that the effects of higher order internal coupling modes can be ignored for
full- and half-height guide. In Reference 45, it was shown that this type of coupling is only significant for small offsets
or tilts.
In this work, the input to each radiating SWA, that is, each coupling slot, is located at a distance of 𝜆g4fromthe
radiating slots to the left and to the right, as seen in Figure 4. Doing this, the impedance to the left and right of the input
is transformed through quarter-wavelength sections and hence should have the same normalized values. In addition, the
inner dimension, b, of the feeder, is chosen to be relatively large, and hence the internal higher order mode coupling
between adjacent slots can be ignored.34 For the planar SWA, the distance separating the radiating slots between the
nearest SWA branchlines is larger than half wavelength, as such the mutual coupling between the slots in different SWA
branchlines is negligible.24
In addition, some work showed that the analytical results in the case of considering the mutual coupling in the calcu-
lations of the slots excitations are very close to those resulting from CST simulation software.40,47,48 Taking into account
the mutual coupling effects, the radiation characteristics can be slightly enhanced in terms of the SLLs and return loss. In
this work, we were able to achieve the desired SLL at the required resonance frequency, and hence any further enhance-
ment that can result from including the mutual coupling effects in the design equations is not essential for the overall
results. Nevertheless, CST simulation software is used in the simulations of this work which takes into account the effects
of mutual coupling in the computational evaluation. Inspecting the results achieved in this article in later sections, even
with the mutual coupling not taken into account in the calculations, the results turned out to have good analogy with the
design requirements and specifications.
3ILLUSTRATING EXAMPLE
Due to some constraints, a we had some limitations related to the design of the radiating SWAs to be used for fabrication.
Several nonstandard waveguides to be used as radiating SWAs were only found with following dimensions: a=5.6 cm
=2.204 in,b=1.6 cm =0.63 in, with a wall thickness of 2 mm. These dimensions put some limits on the choice of the
operating frequency that can be used for the planar SWA. For this, a frequency of 3.952 GHz is chosen, which is known in
the maritime applications, one of the applications of SWAs. The rest of the design requirements are as follows: a desired
SLR of not less than 20 dB is required, with eight slots on each SWA, and eight radiating SWAs, henceresulting in an 8 ×8
planar SWA.
Starting with the design procedure, knowing the waveguide dimensions to be used for the radiating SWAs, in addition
to the desired operating frequency, 𝜆gis calculated to be 103.36 mm. With this value of 𝜆g, each radiating SWA is designed
to have a total length of 5𝜆g. Using the design procedure presented in Section 2.1, the optimized slots length and width
are found to be 37.1 mm (0.477𝜆)and5mm(0.066𝜆), respectively. The slots are distributed along the waveguide as
discussed in Section 2.1.2. The first and last slot are chosen to be separated by 3𝜆g4 from the end terminals, with the
succeeding slots separated by 𝜆g2. Using Chebyshev distribution, with a desired SLR of 20 dB, the slots displacements
are calculated using the equations provided in Section 2.1.3, and they are listed in Table 1, second column.
As for the feeder SWA, for the illustrating example, the distance separating two consecutive coupling slots is 60 mm
(0.79𝜆). Hence, the closest waveguide having a guide wavelength as close as possible to 120 mm (1.58𝜆) at 3.952 GHz
is the WR-187 waveguide, having a guide wavelength 𝜆g(feed)of 125.78 mm (1.66𝜆), with inner dimensions of: a=4.75
cm =1.872 in,b=2.214 cm =0.872 in. It is worth mentioning here that a nonstandard waveguide could be also fabricated
10 of 15 EL MISILMANI  .
with the needed guide wavelength, but the WR-187, which has close specifications to the required ones, has been chosen
for fabrication due to its availability.
The feeder SWA is designed in the same procedure illustrated in Section 2.1, with eight slots made on its broadwall.
The slot length of the feeder has been also optimized and found to be equal to 38 mm (0.5𝜆). The width of the slot is taken
also to be 5 mm (0.066𝜆). The first and last slot are separated from the end terminals by 3𝜆g(feed)4, and the consecutive
coupling slots are separate by 𝜆g(feed)2. Using Chebyshev distribution, with a desired SLR of 20 dB, the slots displacements
on the feeder SWA, indicated by Dfeed in Figure 4, are calculated using the equations provided in Section 2.1.3, and they
are listed in Table 1, third column.
4SIMULATIONS AND MEASUREMENTS RESULTS
The designed planar SWA has been simulated using CST. The computed SLR, HPBW, and the gain in E- and H-planes
are listed in Table 2, with the 3D gain pattern plot shown in Figure 5. As can be inspected, a pencil shape pattern
has been attained, with an SLR in both planes of not less than 20 dB, with narrow HPBW, suitable for HPM applica-
tions. Lower sidelobe levels can be easily obtained if the desired SLR used to find the slots displacements is made larger
than 20 dB.
The illustrating example has been also fabricated as follows. The Feeder SWA and the eight radiating SWAs are first
fabricated. CNC HAAS VF-6 three axis milling machine with a precision of 0.001 mm has been used to drill the slots
using a 3 mm type carbide. The eight radiating SWAs are then stacked side by side, before moving each one, upward or
downward, according the displacement of the coupling slot. The eight moved radiating SWAs are then collected using a
Displacement (mm)
Slot number SWA branchlines (WR-229) SWA feeder (WR-187)
1 & 8 2.78 1.88
2&7 4.36 2.94
3 & 6 5.71 3.85
4&5 6.48 4.36
Abbreviation: SWA, slotted waveguide antennas.
TABLE 1 Slot displacements in radiating and
feeder SWAs for the 8 ×8 planar SWA example
E-plane H-plane
Antenna SLR HPBW SLR HPBW Gain (dB)
8×8 planar SWA 22.3 dB 9.628.1 dB 11.424.6
Abbreviations: HPBW, half power beamwidth; SLR, sidelobe level ratio; SWA, slotted waveguide antennas.
TABLE 2 Simulated results of the
8×8 planar SWA example
FIGURE 5 Three-dimensional simulated gain
pattern plot of the 8 ×8 planar SWA example. SWA,
slotted waveguide antennas
EL MISILMANI  . 11 of 15
FIGURE 6 Fabricated 8 ×8 planar SWA, (left)
front view, (right) back view. SWA, slotted waveguide
antennas
−80
−60
−40
−20
0
20
−80 −60 −40 −20 0 20 40 60 80
Gain [dBi]
Azimuth Angle [degree]
Simulated
Measured
Cross Pol.
−50
−40
−30
−20
−10
0
10
20
30
−80 −60 −40 −20 0 20 40 60 80
Gain [dBi]
Elevation Angle [degree]
Simulated
Measured
Cross Pol.
FIGURE 7 Gain pattern comparison of the simulated and fabricated 8 ×8 planar SWA. SWA, slotted waveguide antennas
FIGURE 8 |S11| results comparison of the simulated
and fabricated 8 ×8 planar SWA. SWA, slotted waveguide
antennas
12 of 15 EL MISILMANI  .
glue. The feeder SWA is then attached to the radiating SWAs, and welded using L-shaped copper corners on the back of
the radiating SWAs. The fabricated planar SWA is shown in Figure 6.
The simulated gain pattern results are compared with the measured ones in Figure 7. The measured reflection coeffi-
cient results are also compared with those simulated using CST in Figure 8. As can be seen, the obtained measured results
are very close to the simulated ones, and they are also in accordance with the design objectives.
The breakdown capability of this antenna array has been also studied. The maximum value of the voltage has been
calculated on the slot responsible for the maximum radiation. The slots that give the maximum radiation are the slots
found in the middle of the array system: having the maximum fed power input from the SWA feeder, and the maximum
displacements from the SWA branchline centerline where the slots are located. Simulating the design taking a high input
power to the feeder SWA of a 6.25 MW, the maximum voltage on these slots is found to be equal to 5.55×105 V/m. This
maximum voltage is still lower than the onset of air breakdown 3 ×106V/m that can cause the air to begin to break down.
A lower value of this maximum voltage, and hence a higher value of power radiated, can be attained using larger slot
width value, if needed.
5CONCLUSION
This article presented a complete design procedure of planar SWA arrays with controllable large SLR, and a pencil shape
pattern, suitable for HPM applications. Longitudinal slots made on the broadwall of the waveguides are used for coupling
the wave and radiating it. The procedure starts by designing the radiating SWAs taking as input the desired SLR, resonance
frequency, total number of radiating SWAs, and total number of slots made on each radiating SWA. Using the dimensions
of the radiating SWAs, the feeder SWA is designed to operate at the same resonance frequency, and the same value of
SLR of the radiating SWAs. Using simplified closed-form, the distribution of the slots along the length of the radiating
SWAs and feeder SWA are calculated based on the slots excitation from a specified distribution. An 8 ×8planarSWA
illustrating example has been designed and tested to show the validity of the proposed method. The obtained measured
and simulated results are in accordance with the design objectives.
ACKNOWLEDGEMENTS
This work was partially supported by the American University of Beirut, Beirut Arab University, and Beirut Research and
Innovation Center.
PEER REVIEW INFORMATION
Engineering Reports thanks the anonymous reviewers for their contribution to the peer review of this work.
PEER REVIEW
The peer review history for this article is available at https://publons.com/publon/10.1002/eng2.12255/.
AUTHOR CONTRIBUTIONS
Hilal M. El Misilmani contributed to the Conceptualization-Equal, Data curation-Lead, Formal analysis-Equal,
Investigation-Lead, Methodology-Lead, Project administration-Equal, Software-Lead, Supervision-Equal,
Validation-Equal, Visualization-Lead, Writing-original draft-Lead, Writing-review & editing-Lead. Mohammed
Al-Husseini contributed to the Conceptualization-Equal, Data curation-Supporting, Formal analysis-Equal,
Investigation-Equal, Project administration-Equal, Supervision-Equal, Validation-Equal, Writing-original
draft-Supporting, Writing-review & editing-Supporting. Karim Kabalan contributed to the Conceptualization-Equal, For-
mal analysis-Equal, Funding acquisition-Lead, Investigation-Equal, Project administration-Equal, Supervision-Equal,
Validation-Equal, Writing-original draft-Supporting, Writing-review & editing-Supporting.
CONFLICT OF INTEREST
The authors declare no potential conflict of interests.
ORCID
Hilal M. El Misilmani https://orcid.org/0000-0003-1370-8799
Mohammed Al-Husseini https://orcid.org/0000-0001-5849-0872
EL MISILMANI  . 13 of 15
Karim Y. Kabalan https://orcid.org/0000-0002-4494-9395
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AUTHOR BIOGRAPHIES
Hilal M. El Misilmani was born in Beirut, Lebanon in 1987. He received the B.E degree in
communications and electronics engineering from Beirut Arab University, Debbieh, Lebanon,
in 2010 and the M.E and Ph.D. degrees in Electrical and Computer Engineering from the Amer-
ican University of Beirut, Beirut, Lebanon, in 2012 and 2015, respectively. From August 2011
to September 2012, he was a Telecommunications Engineer with Dar Al-Handasah Consultants
(Shair and Partners). From September 2012 to August 2014, he was a Researcher with Beirut
Research and Innovation Center. From September 2014 to May 2015 he was a Lecturer with the
American University of Beirut. From June 2015 to September 2016, he was a Research Associate
with the American University of Beirut. Since September 2015, he has been an Assistant Professor with the Electrical
and Computer Engineering Department, Beirut Arab University, Debbieh, Lebanon. He is the author of more than
20 articles. His research interests include the design of high power microwave antennas, slotted waveguide antennas
and vlasov antennas, antenna arrays, reconfigurable antennas, circularly polarized antennas, antennas for biomedical
applications, and machine learning in antenna design. Dr. El Misilmani was a recipient of Rafic Hariri Foundation
Scholarship from September 2005 to June 2010, the Association of Specialization and Scientific Guidance (SSG) Schol-
arship from February 2006 to June 2010, the Lebanese Association for Scientific Research (LASeR) scholarship from
September 2013 to May 2015, and the National Council for Scientific Research (CNRS) doctoral scholarship award
from 2013 to May 2015.
Mohammed Al-Husseini received his Ph.D. in Electrical and Computer Engineering in 2012
from the American University of Beirut (AUB), Beirut, Lebanon. During his Ph.D. studies, he
was recipient of the Kamal Shair Ph.D. Fellowship. He is currently a lecturer at AUB and a
senior researcher at Beirut Research and Innovation Center (BRIC), Beirut, Lebanon. From 2009
to 2011, he was an exchange research scholar at the University of New Mexico (UNM), Albu-
querque, NM, USA. In 2013, he was also a visiting researcher at UNM. His research interests
include cognitive radio, antennas and sources for high power electromagnetics, and the design
and applications of antenna arrays, reconfigurable antennas, wearable antennas, metamaterials,
RF energy harvesting, and RF circuits. He is currently working on material characterization and on the use of machine
EL MISILMANI  . 15 of 15
learning for the detection of underground targets. He has over 100 publications in international refereed journals and
conference proceedings.
Karim Y. Kabalan was born in Jbeil, Lebanon. He received the B.S. degree in Physics from the
Lebanese University in 1979, and the M.S. and Ph.D. degrees in Electrical and Computer Engi-
neering from Syracuse University, in 1983 and 1985, respectively. During the 1986 fall semester,
he was a visiting assistant professor of Electrical and Computer Engineering at Syracuse Univer-
sity. Currently, he is a Professor of Electrical and Computer Engineering with the Electrical and
Computer Engineering Department, Faculty of Engineering and Architecture, American Uni-
versity of Beirut. He is the author of two copyrighted software, six book chapters, more than 100
journal articles, and more than 124 conference articles. His research interest includes Electro-
magnetic and Radio Frequency, microstrip antenna design by using sophisticated patch element and array theoretical
modeling techniques, cognitive radio antenna, and MIMO antenna systems.
How to cite this article: El Misilmani HM, Al-Husseini M, Kabalan KY. Design procedure for planar slotted
waveguide antenna arrays with controllable sidelobe level ratio for high power microwave applications.
Engineering Reports. 2020;2:e12255. https://doi.org/10.1002/eng2.12255
... The introduced slots are used to radiate the energy from the antenna. Typical SWAs have rectangular-shaped slots but could also have elliptical or corner edge slots that provide enhanced power handling abilities [3], [4]. ...
... Equation (4) guarantees that N n=1 g n = 1. ...
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Book
Techniques based on the method of modal expansions, the Rayleigh-Stevenson expansion in inverse powers of the wavelength, and also the method of moments solution of integral equations are essentially restricted to the analysis of electromagnetic radiating structures which are small in terms of the wavelength. It therefore becomes necessary to employ approximations based on "high-frequency techniques" for performing an efficient analysis of electromagnetic radiating systems that are large in terms of the wavelength. One of the most versatile and useful high-frequency techniques is the geometrical theory of diffraction (GTD), which was developed around 1951 by J. B. Keller [1,2,3]. A class of diffracted rays are introduced systematically in the GTD via a generalization of the concepts of classical geometrical optics (GO). According to the GTD these diffracted rays exist in addition to the usual incident, reflected, and transmitted rays of GO. The diffracted rays in the GTD originate from certain "localized" regions on the surface of a radiating structure, such as at discontinuities in the geometrical and electrical properties of a surface, and at points of grazing incidence on a smooth convex surface as illustrated in Fig. 1. In particular, the diffracted rays can enter into the GO shadow as well as the lit regions. Consequently, the diffracted rays entirely account for the fields in the shadow region where the GO rays cannot exist.