1D Slotted Waveguide Antenna with Controlled
Beamwidth and Sidelobe Level Ratio
Hilal M. El Misilmani
Department of Electrical and Computer Engineering
Beirut Arab University
Beirut Research and Innovation Center
Lebanese Center for Studies and Research
Abstract—Slotted waveguide antennas (SWAs) are widely used
in high power microwave applications. In this paper, the slots
displacements in broadwall SWAs, previously used to control
the SWA sidelobe level ratio (SLR), are further investigated to
also adjust the beamwidth of the SWA. A modiﬁed Taylor array
design method is used to estimate the excitations of the SWA
slots leading to independently controllable SLR and ﬁrst-null
beamwidth (FNBW). The slots displacements are then calculated
from these excitations. An example is presented where the SWA
has 7 slots and the proposed method is employed to ﬁnd the
displacements required for desired SLR and FNBW.
The design of a resonant SWA is generally based on the
procedure described by Stevenson and Elliot , , and
further simpliﬁed by the El Misilmani et al. in , . In
these works, the excitations of the SWA individual slots,
which are translated into slots displacements, control the
resulting SLR of the SWA array. The obtained beamwidth is
a byproduct of the design for the desired SLR. This is due
to the fact that conventional antenna array synthesis methods,
e.g. Dolph-Chebyshev and the Taylor one-parameter , 
permit to control the sidelobe levels without allowing for the
independent control of the beamwidth. To overcome this, a
simple antenna array synthesis method was presented in  by
which the SLR and the FNBW of linear arrays can be adjusted
with relative independence. This method, which can be thought
of as a modiﬁcation to Taylor One-parameter method, was later
extended to rectangular and circular arrays in .
As a continuation of the work done by the authors mainly
in , in this paper, the slots of a SWA are considered as
the elements of a linear array, to which the modiﬁed Taylor
method of , is applied. The goal is to design a SWA with
a FNBW and a SLR that can be independently controlled.
Taking as inputs the number of slots in the SWA, the operation
frequency, and the desired SLR and FNBW, the method in 
computes the slots excitations required for the wanted SLR
and the FNBW. The slots displacements are then deduced from
these excitations by employing the authors’ method in . To
verify the validity of this SWA design method, an example is
taken for which a single desired SLR is speciﬁed along with
three different FNBWs. The radiation pattern plots in addition
to the excitations and the slots displacements are reported for
each of the three case.
II. DESIGN EQ UATIO NS
Based on a modiﬁed Taylor distribution, the equation of
the FNBW used in this paper to derive and deduce the SWA
slots displacements has been derived in . The equation of
the individual antenna elements excitations is ﬁrst given in the
where Nis the total number of elements (taken odd for
simplicity), J0is the Bessel function of the ﬁrst kind zero
order, and nis the index. Bis a constant determined from
the speciﬁed SLR using (2), with R0being the ratio of the
intensity of the main lobe to the highest side lobe.
Then, using the equations of the angles of the ﬁrst two nulls
of the pattern, the FNBW of the linear array can be given by
ΘF N =π−2 arccos "√B2+ 1
A value of dcan be found that results in a prescribed
ΘF N , and it is given in (4) , however, in order not to
change the λ/2separation distance between the slots in the
SWA, the remaining part of this section is used to obtain the
excitations and hence the displacements without affecting the
(N−1) sin ΘF N
Using the array factor of an N-element uniform-spacing linear
array positioned along the z-axis, the array factor can be
2,·· · , a0,·· · , a (N−1)
ejP−Mcos(−π). . . ejP−Mcos(0) . . . ejP−Mcos(π)
..... . . ....
1. . . 1. . . 1
..... . . ....
ejPMcos(−π). . . ejPMcos(0) . . . ejPMcos(π)
2,P−M=−2πM d/λ, PM= 2πMd/λ.
The excitations vector of the SWA can be then given by:
where Hdenotes the complex conjugate.
Eventually, the slots displacements snare deduced from the
slots excitations using (8), with aand bbeing the waveguide
As a summary, in order to design an SWA with a ﬁxed
number of slots and interelement spacing, for a desired SLR
1) obtain the value of Busing (2).
2) compute avfrom (1).
3) calculate dΘfrom (4).
4) compute Pfrom (6), and deduce Pvfrom by replacing
dwith dΘ. The array factor is now equal to av×Pv.
5) compute the excitations vector using (7).
6) deduce the slots displacements using (8).
III. EXA MP LE : 7-SL OTS SWA WITH SLR OF 20 DB
A WR-284 waveguide, with 7 slots, is designed for a
frequency of 3.4045 GHz, SLR of not less than 20 dB, and
three different values of FNBW: 57.5◦,70◦, and 80◦.
Using the method mainly discussed in , the slots dis-
placements related to the individual slots excitations, resulting
from the modiﬁed Taylor method proposed here, are listed in
Table I. Fig. 1 shows a comparison of the gain patterns of
the three different cases each designed for a different FNBW,
while maintaining the desired SLR of not less than 20 dB
and the slots interspacing to be equal to λguide/2. Table II
compares the desired FNBW and the obtained FNBW through
simulations using CST software. As can been, the results
validate the proposed method, for which the obtained FNBW
are in accordance with the desired FNBW in each case, while
maintaining an SLR of not less than 20 dB.
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EXC ITATIO N COE FFIC IEN TS A ND CO RR ESP OND IN G SLO TS
DI SPL ACE MEN TS F OR TH E TH REE D IFF ERE NT C ASE S OF FNBW
FNBW Slot Number Excitation Coefﬁcient Displacement (mm)
1 & 7 0.2007 6.7585
2 & 6 0.5195 11.1494
3 & 5 0.8557 14.7459
4 1 16.1713
1 & 7 0.0636 4.1122
2 & 6 0.3870 10.4461
3 & 5 0.7939 15.6305
4 1 18.0088
1 & 7 0.0084 1.5823
2 & 6 0.2902 9.5312
3 & 5 0.7544 16.2537
4 1 19.4243
-80 -60 -40 -20 0 20 40 60 80
FNBW = 57.5 deg
FNBW = 70.0 deg
FNBW = 80.0 deg
Fig. 1. Gain pattern in the elevation plane for the three different cases of
FNBW: 57.5◦,70◦,and 80◦
COMPARISON BETWEEN THE DESIGN CASE OF DIFFERENT DESIRED
FNBW VALUE S,A ND TH EI R COR RE SPO ND ING S IM ULATE D RE SULT S
Design Case Desgined for FNBW of Obtained Result of FNBW
Case 1 57.5◦58◦
Case 2 70◦70◦
Case 3 80◦82◦
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