Conference PaperPDF Available

A design procedure for slotted waveguide antennas with specified sidelobe levels


Abstract and Figures

Slotted waveguide antenna (SWA) arrays offer clear advantages in terms of their design, weight, volume, power handling, directivity, and efficiency. For broad-wall SWAs, the slot displacements from the wall centerline determine the antenna's sidelobe level (SLL). This paper presents an inventive procedure for the design of broadwall SWAs with desired SLLs. For a specified number of identical longitudinal slots, this procedure finds the slots length, width, locations along the length of the waveguide, and displacements from the centerline. Illustrative examples, based on Taylor, Chebyshev and the binomial distributions are given. In these examples, elliptical slots are considered, since their rounded corners are more robust for high power applications.
Content may be subject to copyright.
A Design Procedure for Slotted Waveguide
Antennas with Specified Sidelobe Levels
H. M. El Misilmani1,2, M. Al-Husseini2, K. Y. Kabalan1, and A. El-Hajj1
1ECE Department, American University of Beirut, Beirut, Lebanon
2Beirut Research and Innovation Center, Lebanese Center for Studies and Research, Beirut, Lebanon,,,
Abstract—Slotted waveguide antenna (SWA) arrays offer clear
advantages in terms of their design, weight, volume, power han-
dling, directivity, and efficiency. For broad-wall SWAs, the slot
displacements from the wall centerline determine the antenna’s
sidelobe level (SLL). This paper presents an inventive procedure
for the design of broadwall SWAs with desired SLLs. For a
specified number of identical longitudinal slots, this procedure
finds the slots length, width, locations along the length of the
waveguide, and displacements from the centerline. Illustrative
examples, based on Taylor, Chebyshev and the binomial distribu-
tions are given. In these examples, elliptical slots are considered,
since their rounded corners are more robust for high power
Keywords—Slotted waveguide antenna arrays, high power
microwaves, binomial, Chebychev, Taylor (one-parameter)
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 design simplicity
removes the need for baluns or matching networks. SWAs
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 prob-
lems. Elliptical slots are then an excellent candidate for such
applications [8], [9].
The resulting sidelobe level (SLL) for antenna arrays 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 waveg-
uide, a slot conductance is controlled by its displacement from
the broadface centerline [10]. Thus, for a desired SLL, the
corresponding set of slots displacements should be determined.
This paper outlines the procedural steps for designing
resonant SWAs with longitudinal slots cut in the broadwall.
There are general guidelines for determining the width of the
slots, their inter-spacing along the length of the waveguide, and
their distances from both the feed port and the shorted end.
For rectangular slots, the slot length is about half the free-
space wavelength. However, for elliptical slots, as the ones
used in this work, the exact length is to be optimized. The
main focus of the presented procedure is to determine the slot
displacements that result in a specified SLL, which is done
as follows: for a desired SLL, the conductances of the slots
are obtained from a certain distribution, Chebyshev, Taylor, or
Binomial; then an equation that relates these conductances to
the displacements from the centerline is used to deduce these
displacements. Optimized parameters of the used distribution
should be found to lead to the desired SLL. Several examples
are given in this paper to illustrate the presented procedure. An
S-band SWA with 10 elliptical slots is used for these examples.
For each example, results for the obtained displacements,
reflection coefficients and radiation patterns are presented.
The S-band WR-284 waveguide used in our illustrative
examples has dimensions a= 2.8400 and b= 1.3700. The
design is done for the 3 GHz frequency. Ten elliptical slots
are made to one broadwall. The waveguide is shorted at one
end and fed at the other.
A. Slots Longitudinal Positions
The are general rules for the longitudinal positions of the
slots on the broadwall:
The center of the first slot, Slot1, is placed at a distance
of quarter guide wavelength, or λg/4, from the the
waveguide feed,
The center of the last slot, Slot10, is placed at λg/4from
the waveguide short-circuited side,
The distance between the centers of two consecutive slots
is λg/2.
A guide wavelength is defined as the distance between
two equal phase planes along the waveguide. It is a function
of the operating wavelength (or frequency) and the lower
cutoff wavelength, and is calculated according to the following
where λ0is the free-space wavelength calculated at 3 GHz,
and cis the speed of light. In this case, λg= 138.5mm.
Based on the above guidelines, the total length of the SWA
is 5λg, as shown in Fig. 1.
Figure 1. Slotted waveguide with 10 elliptical slots
B. The Slot Width
The width of each elliptical slot, which is 2times the minor
radius of the ellipse, is fixed at 5mm. This is calculated as
follows: for X-band SWAs, the width of a rectangular slot
the mostly used in the literature is 0.062500, corresponding to
a= 0.900. By proportionality, the width of the elliptical slot
for this S-band SWA is computed as follows:
Sl otW idth =a×0.0625
0.9= 2.84×0.0625
0.9= 0.19700 = 5mm
C. The Slot Displacement
By slot displacement, we refer to the distance between the
center of a slot and the centerline of the waveguide broadface,
as illustrated in Fig. 2.
With uniform slot displacement, all slots are at the same
distance from the centerline. This is similar to the case of
antenna arrays with discrete elements having equal excitation,
which results in an SLL around -13 dB. Lower SLLs are
obtained upon using non-uniform slot displacements. In both
the uniform and non-uniform displacement cases, the slots
should be placed around the centerline in an alternating order.
This is done to ensure the high efficiency of the antenna.
Figure 2. Slotted waveguide with 10 elliptical slots
The value of the uniform slot displacement that leads to a
good reflection coefficient is given by [11], [12]:
πsarcsin 1
G= 2.09 ×a
In Equation 2, Nis the number of slots, which is equal to
10. In 3, λ0= 100 mm at 3 GHz. Combining 2 and 3, duis
found to be 7.7mm.
D. The Slot Length
For rectangular slots, the length is usually 0.98 ×λ0/2'
λ0/2. Because of the narrower ends of elliptical slots, their
length (double the major radius) is expected to be slightly
larger than λ0/2. The optimized elliptical slot length is
determined as follows: the SWA is modeled assuming a
uniform displacement (du= 7.7mm) and an initial length
of 0.98 ×λ0/2; the length is increased while watching the
computed reflection coefficient S11 until the antenna resonates
at 3 GHz with a low S11 value. In our case, the elliptical slot
length is found to be 54.25 mm.
For these uniform displacement and slot length, the resulting
sidelobe level ration (SLR) is around 13 dB, which is as
expected. The reflection coefficient S11 and the YZ-plane
gain pattern in this case are given in Figs. 3(a) and 3(b),
respectively. A peak gain of 16.6dB and an SLR of 13.2
dB are recorded. The half-power beamwidth (HPBW) in this
plane is 7.2degrees. These values are obtained using CST
Microwave Studio, and then verified with ANSYS HFSS.
(a) S11 for uniform slots displacement
(b) Pattern in the YZ plane
Figure 3. Antenna’s reflection coefficient and YZ-plane pattern for the case
of uniform slot displacement
Our simulations have proven that the resonating length of
the elliptical slots is not very sensitive to the slots displacement
from the center line. For this, in the next calculations the length
of all slots is fixed at 54.25 mm. The displacement of the nth
slot is related to its normalized conductance gnby [11], [13]–
πarcsin v
In 5, Nis the number of slots, and cnsare the distribution
coefficients that we should determine to end up with the
desired SLL. Equation 5 guarantees that
gn= 1.
Several distributions (tapers) well-known in discrete antenna
arrays can be used to generate the cns(e.g. Taylor, Cheby-
shev). However, the resulting SLL of the SWA is always higher
than the SLL used for the discrete array distribution. To reach
the desired SWA SLL, a few iterations of the simulation setup
are required, where in each the SLL of the discrete array used
to generate the taper values is decreased. Illustrative examples
are shown below to further highlight this design procedure.
A. Example 1: 20 dB SLR with Chebyshev Distribution
In this example, our target is an SLR of 20 dB, where the
cnsare selected according to a Chebyshev distribution.
1) Coefficients and Slots Displacements: The coefficients
cnsfor a Chebyshev distribution are calculated from equations
in [16], [17]. For a 35dB Chebyshev taper, the cnsand their
corresponding slots displacements, calculated from Equation
4, are given in Table I. The 35dB Chebyshev taper has been
selected after some simulation iterations, as it provides the
desired 20dB SLL for the SWA. A 20dB Chebyshev taper
leads to SWA sidelobes higher than the 20dB goal.
-20 DB
Slot number Chebyshev coefficient Displacement (mm)
1 1 3.74
2 2.086 5.42
3 3.552 7.11
4 4.896 8.4
5 5.707 9.11
6 5.707 9.11
7 4.896 8.4
8 3.552 7.11
9 2.086 5.42
10 1 3.74
It is clear from Table I that the slots near the two waveguide
ends are closest to the broadface center line, whereas those
toward the waveguide center have the largest displacement.
This property applies to all the examples.
2) Results: For the previously determined slot parameters
(length, width, and coordinates), the SWA computed results
show a resonance at 3 GHz, an SLR of 20 dB, and a peak
gain of 16.1dB. The YZ-plane HPBW has increased to 8.4
degrees, compared to the uniform displacement case, as shown
in Fig. 4. The broadening of the main beam is expected since
the sidelobes have been forced to go lower.
Figure 4. Antenna’s YZ-plane pattern for the case of non-uniform slot
displacement with Chebychev distribution. A 20dB SLR is obtained.
Figure 5. Antenna’s YZ-plane pattern for the case of non-uniform slot
displacement with Taylor (one-parameter) distribution for an SLR of 20dB
B. Example 2: 20 dB SLR with Taylor (One-Parameter) Dis-
In this example, the SWA is designed to have an SLR of
20 dB, where the cnswill be obtained from a Taylor one-
parameter distribution [18].
1) Coefficients and Slots Displacements: The cnsfor a
Taylor one-parameter distribution can be computed using the
equations in [19] or [20]. For a 20dB SLL for the SWA, a
30dB Taylor (one-parameter) taper is required. The resulting
coefficients, and the corresponding slots displacements are
listed in Table II.
-20 DB
Slot number Taylor-based coefficient Displacement (mm)
1 1 3.493
2 2.467 5.518
3 4.137 7.194
4 5.597 8.419
5 6.449 9.070
6 6.449 9.070
7 5.597 8.419
8 4.137 7.194
9 2.467 5.518
10 1 3.493
2) Results: For the slots displacements in Table II, the
antenna keeps its resonance at 3GHz, shows an SLR of about
20 dB, and has a peak gain of 16 dB. The YZ-plane HPBW is
8.5 degrees, as shown in Fig. 5. It is to note that for the same
SLL of 20dB, the determined Chebyshev and Taylor (one-
parameter) coefficients have led to almost identical radiation
patterns, HPBW and gain parameters.
C. Example 3: 30 dB SLR with Taylor (One-Parameter) Dis-
In this example, we use a Taylor (one-parameter) distri-
bution to obtain an SWA SLR of 30dB. For this, the taper
coefficients for a 40dB Taylor (one-parameter) distribution
are required, and these are listed in Table III alongside
Figure 6. Antenna’s YZ-plane pattern for the case of non-uniform slot
displacement with Taylor Taylor Line-Source distribution for an SLR of 30dB
their corresponding slots displacements. The results show an
antenna resonance at 3 GHz, and a peak gain of 15.3dB. The
30dB SLL has been attained, and the YZ-plane HPBW has
increased to 10 degrees. The YZ-plane gain pattern is shown
in Fig. 6.
-30 DB
Slot number Taylor-based coefficient Displacement (mm)
1 1 1.631
2 6.611 4.215
3 16.828 6.785
4 28.573 8.937
5 36.519 10.181
6 36.519 10.181
7 28.573 8.937
8 16.828 6.785
9 6.611 4.215
10 1 1.631
D. Example 4: Binomial Excitation
Although it is not directly possible to use a binomial
distribution to control the SLL, it is interesting to use the cns
from a binomial distribution and observe the resulting SWA
SLL. The binomial coefficients are obtained from the binomial
(1 + x)m1= 1 + (m1)x+(m1)(m2)
2! x2
3! x3+... (6)
For the case of 10 slots, the binomial coefficients and the
resulting slots displacements are listed in Table IV. For these
displacements values, the obtained SLR is 38.6dB, and the
peak gain is 15 dB. The YZ-plane HPBW increases to 11.1
degrees, as shown in Fig. 7.
Slot number Binomial coefficient Displacement (mm)
1 1 0.964
2 9 2.900
3 36 5.847
4 84 9.069
5 126 11.268
6 126 11.268
7 84 9.069
8 36 5.847
9 9 2.900
10 1 0.964
Figure 7. Antenna’s YZ-plane pattern for the case of non-uniform slot
displacement with binomial distribution
E. Reflection Coefficients
For all the above examples, the SWAs retain their resonance
at 3GHz. The S11 plots for the four examples are shown in
Fig. 8.
2.6 2.8 3 3.2 3.4
Reflection Coefficient [dB]
Frequency [GHz]
Chebyshev with -35 dB
Taylor with -30 dB
Taylor with -40 dB
Figure 8. Reflection coefficient plots for the four illustrated examples
This paper presented a simple procedure for designing
SWAs with specified SLLs. General guidelines for the slots
width, length and longitudinal positions are first given. The
offsets of the slots positions with respect to the waveguide
centerline, which determine the SLL, are then obtained from
well-known distributions. An intuitive rule regarding the used
distribution can be deduced, which is to select a distribution
with an SLL 15 dB lower than the desired SWA SLL. Il-
lustrative examples showing the distribution coefficients, slots
displacements, resulting patterns and S11 plots were given.
[1] R. A. Gilbert, Antenna Engineering Handbook, ch. Waveguide Slot
Antenna Arrays. McGraw-Hill, 2007.
[2] R. J. Mailloux, Phased Array Antenna Handbook. Artech House, 2005.
[3] W. Rueggeberg, “A Multislotted Waveguide Antenna for High-Powered
Microwave Heating Systems,IEEE Trans. Ind. Applicat., vol. IA-16,
no. 6, pp. 809–813, 1980.
[4] R. S. Elliott and L. A. Kurtz, “The Design of Small Slot Arrays,” IEEE
Trans. Antennas Propagat., vol. 26, pp. 214–219, March 1978.
[5] R. S. Elliott, “The Design of Traveling Wave Fed Longitudinal Shunt
Slot Arrays,” IEEE Trans. Antennas Propagat., vol. 27, no. 5, pp. 717–
720, September 1979.
[6] R. S. Elliott, “An Improved Design Procedure for Small Arrays of Shunt
Slots,” IEEE Trans. Antennas Propagat., vol. 31, pp. 48–53, January
[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.
[8] C. E. Baum, “Sidewall Waveguide Slot Antenna for High Power,Sensor
and Simulation Note 503, August 2005.
[9] M. Al-Husseini, A. El-Hajj, and K. Y. Kabalan, “High-gain S-band Slot-
ted Waveguide Antenna Arrays with Elliptical Slots and Low Sidelobe
Levels,PIERS Proceedings, Stockholm, Sweden, August 12-15, 2013.
[10] A. F. Stevenson, “Theory of Slots in Rectangular Waveguides,Journal
of Applied Physics, vol. 19, pp. 24–38, 1948.
[11] R. J. Stevenson, “Theory of Slots in Rectangular Waveguide,J. App.
Phy., vol. 19, pp. 4–20, 1948.
[12] W. H. Watson, “Resonant Slots,” Journal of the Institution of Electrical
Engineers - Part IIIA: Radiolocation, vol. 93, pp. 747–777, 1946.
[13] W. Coburn, M. Litz, J. Miletta, N. Tesny, L. Dilks, C. Brown, and
B. King, “A Slotted-Waveguide Array for High-Power Microwave
Transmission,Army Research Laboratory, January 2001.
[14] A. L. Cullen, “Laterally Displaced Slot in Rectangular Waveguide,
Wireless Eng., pp. 3–10, January 1949.
[15] K. L. Hung and H. T. Chou, “A Design of Slotted Waveguide Antenna
Array Operated at X-band,” 2010 IEEE international Conference on
Wireless Information Technology and System, pp. 1–4, 2010.
[16] A. Safaai-Jazi, “A New Formulation for the Design of Chebyshev
Arrays,” IEEE Trans. Antennas Propag., vol. 42, pp. 439–443, 1980.
[17] A. El-Hajj, K. Y. Kabalan, and M. Al-Husseini, “Generalized Chebyshev
Arrays,” Radio Science, vol. 40, RS3010, June 2005.
[18] T. T. Taylor, “One Parameter Family of Line-Sources Producing Modi-
fied Sin(πu)/ πu Patterns,” Hughes Aircraft Co. Tech., Mem. 324, Culver
City, Calif., Contract AF 19(604)-262-F-14, September 4, 1953.
[19] C. A. Balanis, Antenna Theory Analysis and Design. Wiley, 2005.
[20] K. Y. Kabalan, A. El-Hajj, and M. Al-Husseini, “The Bessel Planar
Arrays,” Radio Science, vol. 39, no. 1, RS1005, Jan. 2004.
Full-text available
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.
Conference Paper
Full-text available
This paper presents an inventive and simple procedure for the design of a 2D slotted waveguide antenna (SWA) having a desired sidelobe level (SLL) and a pencil shape pattern. The 2D array is formed by a defined number of 1D broadwall SWAs, which are fed using an extra broadwall SWA. For specified number of identical longitudinal slots in both dimensions, the desired SLL and the required operating frequency, this procedure finds the slots length, width, locations along the length of the waveguide, and offsets from its centerline. This is done for the radiating SWAs as well as the feed SWA. An example SWA with 8×8 elliptical slots is designed using this procedure for an SLL lower than −20 dB, where the design results are also reported in this paper.
Full-text available
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.
Full-text available
Directive antennas are required for the development of high-power microwave (HPM) transmission system concepts. The type of system considered includes a single HPM source with waveguide output, the antenna, and the control/support equipment integrated onto a ground-mobile platform. A parabolic reflector with a custom-designed horn feed has been demonstrated as one antenna option that allows direct connection to the HPM source waveguide output. An alternative approach to reflector antennas is desired, so a slotted-waveguide array was selected to meet the operational requirements. The array design is modular (with four symmetric modules) to ease fabrication and to maximize transportability and repairability. A rectangular waveguide corporate-feed network is used to minimize the antenna subsystem volume (i.e., depth) and allow the HPM source to be integrated into the feed structure. An S-band array and feed structure were fabricated and assembled for laboratory evaluation. The array was fabricated from WR-284 copper waveguide with brass end caps to a +5-mil tolerance. The array design, fabrication, assembly, and testing are discussed. Preliminary test data for a single module of the four-module full array are presented. As expected, the array as fabricated requires "fine-tuning" to optimize performance. Empirical results will be used to evaluate design alternatives appropriate for particular HPM applications.
Conference Paper
Full-text available
This paper presents a design of X-band slotted waveguide antenna array that has a linear polarization and exhibits high directivity for a long-distance communication. Especially we present a procedure that is very useful in a realistic implementation. The design is validated by numerical simulation using HFSS, and measurement results will be presented in the conference presentation.
The discipline of antenna theory has experienced vast technological changes. In response, Constantine Balanis has updated his classic text, Antenna Theory, offering the most recent look at all the necessary topics. New material includes smart antennas and fractal antennas, along with the latest applications in wireless communications. Multimedia material on an accompanying CD presents PowerPoint viewgraphs of lecture notes, interactive review questions, Java animations and applets, and MATLAB features. Like the previous editions, Antenna Theory, Third Edition meets the needs of electrical engineering and physics students at the senior undergraduate and beginning graduate levels, and those of practicing engineers as well. It is a benchmark text for mastering the latest theory in the subject, and for better understanding the technological applications. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.
This paper discusses a concept for high-power microwave antennas based on an array of slots in the sidewall where the electric fields are lower. This gives a polarization which is perpendicular to a plane containing the waveguide axis. By combining two such waveguides one can also suppress grating lobes.
This paper describes how the coupling of a resonant half-wave slot to a rectangular wave guide in the wall of which the slot is cut, came to be studied in order to solve the problem of linear microwave radiators fed from wave guides. The methods of experimental investigation are described and the results are presented in terms of a method of representing the loading of the dominant wave in the guide. The important conception is the transformation of the circle-diagram variable (w) representing the dominant wave-system in the guide. It is shown that wave guides may be coupled by resonant slots. If such a slot is cut in the wall of a wave guide and lies opposite a registering slot in a second guide in contact with the first, the wave guides are coupled if the slot can be excited by the dominant wave in both guides. The type of coupling depends on the aspect of the slot in each guide. The laws of guide coupling are explained in terms of the manner in which impedance is transferred from the position of the slot centre guide 2 into guide 1 at the same position. The coupling of variable reactances to the guide by resonant slots to produce a T-section load is described, with experimental confirmation of the transformation of impedance and phase by the load. The method of radiation coefficients is applied to deduce the law of guide-coupling in the general case; it may be applied to treat loading and coupling of two waves in the same guide. Finally, directive aerial coupling by a pair of slots is discussed. Finally, the elements of the design problem for a linear microwave array and the theory of the wave-guide feed are discussed. Both transverse and longitudinal polarization are considered, together with the effects of mutual interaction between the inclined slots cut in the narrow face of the guide in the longitudinally-polarized array. The bandwidth of arrays is treated and a broad-band array of inclined-displaced slots in the broad face is described with measurements of - its performance. The principle of the microwave Yagi aerial is briefly presented.
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.
In this paper, we introduce a new class of planar arrays that we call the Bessel planar arrays. A formula for the current distribution in the elements of these arrays is presented, which is related to Bessel functions. For the Bessel planar arrays, the maximal sidelobe level is controllable, the directivity is very high, and the half-power beam width is slightly larger compared to the optimal Chebyshev planar arrays. Methods to set the maximal sidelobe level and compute the directivity and the half-power beam width are described, and numerical examples are given to illustrate the features of the proposed arrays.