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Design of slotted waveguide antennas with low sidelobes for high power microwave applications

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Slotted waveguide antenna (SWA) arrays offer clear advantages in terms of their design, weight, volume, power handling, directivity, and efficiency. For broadwall SWAs, the slot displacements from the wall centerline determine the antenna’s sidelobe level (SLL). This paper presents a simple inventive procedure for the design of broadwall SWAs with desired SLLs. For a specified number of identical longitudinal slots and given the required SLL and operating frequency, this procedure finds the slots length, width, locations along the length of the waveguide, and displacements from the centerline. Compared to existing methods, this procedure is much simpler as it uses a uniform length for all the slots and employs closed-form equations for the calculation of the displacements. A computer program has been developed to perform the design calculations and generate the needed slots data. 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. A prototype SWA has been fabricated and tested, and the results are in accordance with the design Objectives
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Progress In Electromagnetics Research C, Vol. 56, 15–28, 2015
Design of Slotted Waveguide Antennas with Low Sidelobes for High
Power Microwave Applications
Hilal M. El Misilmani1, *, Mohammed Al-Husseini2, and Karim Y. Kabalan1
Abstract—Slotted waveguide antenna (SWA) arrays offer clear advantages in terms of their design,
weight, volume, power handling, directivity, and efficiency. For broadwall SWAs, the slot displacements
from the wall centerline determine the antenna’s sidelobe level (SLL). This paper presents a simple
inventive procedure for the design of broadwall SWAs with desired SLLs. For a specified number of
identical longitudinal slots and given the required SLL and operating frequency, this procedure finds the
slots length, width, locations along the length of the waveguide, and displacements from the centerline.
Compared to existing methods, this procedure is much simpler as it uses a uniform length for all the
slots and employs closed-form equations for the calculation of the displacements. A computer program
has been developed to perform the design calculations and generate the needed slots data. 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.
A prototype SWA has been fabricated and tested, and the results are in accordance with the design
objectives.
1. INTRODUCTION
Rectangular Slotted Waveguide Antennas (SWAs) [1] radiate energy through slots cut in a broad or
narrow wall of a rectangular waveguide. This means the radiating elements are an integral part of the
feed system, which is the waveguide itself, leading to a simple design not requiring baluns or matching
networks. The other main advantages of SWAs include relatively low weight and small volume, their
high power handling, high efficiency, and good reflection coefficient [2]. For this, they have been ideal
solutions for many radar, communications, navigation, and high power microwave applications [3].
SWAs can be resonant or non-resonant depending on the way the wave propagates inside the
waveguide, which is a standing wave in the former case and a traveling-wave in the latter [4, 5]. The
traveling-wave SWA has a larger bandwidth, but it requires a matched terminating load to absorb the
wave and prevent it from being reflected, which reduces its efficiency. It also has the shortcoming of the
dependency of the main beam direction on the operating frequency. Resonant SWAs, on the other hand,
have the end of the waveguide terminated with a short circuit, which results in a higher efficiency due to
no power loss at the waveguide end. In addition, the main beam is normal to the array independently
of the frequency, but these advantages come at the cost of a narrower operation band.
The design of a resonant SWA is generally based on the procedure described by Stevenson and
Elliot [4, 6–9], 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. However, since
sharp corners aggravate the electrical breakdown problems, slot shapes that avoid sharp corners are
Received 19 December 2014, Accepted 22 January 2015, Scheduled 30 January 2015
* Corresponding author: Hilal M. El Misilmani (hilal.elmisilmani@ieee.org).
1ECE Department, American University of Beirut, Beirut, Lebanon. 2Beirut Research and Innovation Center, Lebanese Center for
Studies and Research, P. O. Box 11-0236, Beirut 1107 2020, Lebanon.
16 El Misilmani, Al-Husseini, and Kabalan
more suitable, especially for high power microwave applications. Elliptical slots are thus an excellent
candidate for such applications [10, 11].
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 waveguide, the slot conductance varies with its displacement
from the broadface centerline [6]. Hence, for each desired SLL, a suitable set of slots displacements
should be determined.
In his well-known procedure, Elliott has proposed two main equations that should be solved
simultaneously to determine the values of the displacement and length for each slot. These two equations
are based on Stevenson equations and Babinet’s principle, and also rely on Tai’s formula [12] and Oliner’s
length adjustment factor [13], in addition to Stegen’s assumption of the universality of the resonant slot
length [14]. In brief, the existing resonant SWA design procedures are complex, and mostly rely on
numerically solving several equations to deduce both the displacement and length of each slot. This
paper presents a simplified procedure by which all the slots have the same uniform length, and closed-
form equations are used to determine the slots non-uniform displacements, for a desired SLL. The other
parameters such as the slots inter-spacing along the length of the waveguide, and their distances from
both the feed port and the shorted end, are obtained from the guidelines set by Elliott and Stevenson.
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. 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. A computer program written in Python has been developed to perform
the design calculations and output the resulting slots dimensions and coordinates. 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. A prototype SWA with 7 elliptical slots, operating at a frequency of
3.4045 GHz, has been designed, fabricated, and measured, and the results show good analogy with the
simulated ones.
2. CONFIGURATION AND GENERAL GUIDELINES
For the illustrative examples, an S-band WR-284 waveguide with dimensions a=2.84 and b=1.37 is
used. 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.
2.1. Slots Longitudinal Positions
There are general rules for the longitudinal positions of the slots on the broadwall:
The center of the first slot, Slot 1, is placed at a distance of quarter guide wavelength (λg/4), or
3λg/4, from the the waveguide feed,
The center of the last slot, Slot 10, is placed at λg/4, or 3λg/4, from the waveguide short-circuited
side,
The distance between the centers of two consecutive slots is λg/2.
The 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 equation:
λg=λ0
1λ0
λcutoff
=c
f×1
1c
2a·f
(1)
where λ0is the free-space wavelength calculated at 3 GHz, and cis the speed of light. In this case,
λg= 138.5 mm.
Based on the above guidelines, the total length of the SWA is 5λg, as shown in Fig. 1.
Progress In Electromagnetics Research C, Vol. 56, 2015 17
Figure 1. Slotted waveguide with 10 elliptical slots.
2.2. The Slot Width
The width of each elliptical slot, which is 2 times the minor radius of the ellipse, is fixed at 5 mm.
This is calculated as follows: for X-band SWAs, the width of a rectangular slot the mostly used in the
literature is 0.0625 , corresponding to a=0.9 . By proportionality, the width of the elliptical slot for
this S-band SWA is computed as follows:
SlotWidth =a×0.0625
0.9=2.84 ×0.0625
0.9=0.197 =5mm
2.3. The Slot Displacement
A slot displacement refers to the distance between the center of a slot and the centerline of the waveguide
broadface, as illustrated in Fig. 2.
Figure 2. Slotted waveguide with 10 elliptical slots.
With uniform slot displacements, 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 slots displacements. In both
the uniform and non-uniform displacement cases, the slots should be placed around the centerline in
18 El Misilmani, Al-Husseini, and Kabalan
an alternating order. This is done to ensure that all slots radiate in phase and hence result in higher
efficiency of the antenna.
The value of the uniform slot displacement that leads to a good reflection coefficient is given
by [15, 16]:
du=a
πarcsin 1
N×G(2)
where:
G=2.09 ×a
b×λg
λ0
×cos 0.464π×λ0
λgcos(0.464π)2
(3)
In Equation (2), Nis the number of slots, which is equal to 10. In Equation (3), λ0= 100 mm at
3 GHz. Combining Equations (2) and (3), duis found to be 7.7 mm.
2.4. The Slot Length
For rectangular slots, the length is usually 0.98 ×λ0/2λ0/2. 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, having 10 slots, is modeled assuming a uniform
displacement (du=7.7 mm); this 10-slot SWA is used to obtain the optimized slot length which takes
into account the effect of mutual coupling on the slot resonant length. An initial length of 0.98 ×λ0/2
per slot; the length is increased while inspecting 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 16.6 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, and then verified with ANSYS HFSS.
-40
-30
-20
-10
0
10
20
0 20 40 60 80 100 120 140 160 180
Gain [dB]
Theta [Degree]
CST
HFSS
-35
-30
-25
-20
-15
-10
-5
0
2.6 2.8 3 3.2 3.4
Reflection Coefficient [dB]
Frequency [GHz]
CST
HFSS
(a) (b)
Figure 3. Antenna’s reflection coefficient and YZ-plane pattern for the case of uniform slot
displacement. (a) S11 for uniform slots displacement. (b) Pattern in the YZ plane.
3. NON-UNIFORM DISPLACEMENT CALCULATION PROCEDURES
The simulations performed in this paper have proven that the resonating length of the elliptical slots is
not very sensitive to the slots displacements calculated using the method proposed in this paper. This
Progress In Electromagnetics Research C, Vol. 56, 2015 19
will be addressed again in later sections. 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 [15, 17–19]:
dn=a
πarcsin
gn
2.09λg
λ0
a
bcos2πλ0
2λg(4)
gn=cn
N
n=1
cn
.(5)
In Equation (5), Nis the number of slots, and cnsare the distribution coefficients that should be
determined to achieve the desired SLL. Equation (5) guarantees that
N
n=1
gn=1.
Several distributions (tapers) well-known in discrete antenna arrays can be used to generate the
cns(e.g., Taylor and Chebyshev). 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.
3.1. Example 1: 20 dB SLR with Chebyshev Distribution
In this example, the target is an SLR of 20 dB, where the cnsare selected according to a Chebyshev
distribution.
3.1.1. Coefficients and Slots Displacements
The coefficients cnsfor a Chebyshev distribution are calculated from equations in [20, 21], as given in
the following. The array factor of a generalized Chebyshev array can be written as:
f(u)=
p
n=1 1
Rn
TNn1γncos u
2=1
R
p
n=1 TNn1γncos u
2 (6)
where:
Txdenotes a Chebyshev polynomial of order x,
γn=cosh[cosh
1(Rn)/(Nn1)],
u=2π(d/λ)(cos θcos θ0)withdbeing the inter-element spacing and θ0the elevation angle of
maximum radiation,
Rnis the sidelobe level ratio of the nth basis Chebyshev array,
and Nnis the number of elements of the nth basis array.
For a uniform spacing and an amplitude symmetrical about the center, the array factor can be
written as:
f(u)=
2
N/2
m=1
Imcos[(m1/2)u],for Neven
(N+1)/2
m=1
mImcos[(m1)u],for Nodd
(7)
20 El Misilmani, Al-Husseini, and Kabalan
where mequals 1 for m= 1 and equals 2 for m= 1. Finally, the excitation coefficients are found using:
Im=
2
NR
N/2
q=1
f[u=p]cos[q],for Neven
1
NR
N+1
2
q=1
qf[u=v]cos[w],for Nodd
(8)
where:
p=2π/N(q1/2),
q=2π/N(m1/2)(q1/2),
v=2π/N(q1),
and w=2π/N(m1)(q1)
Equation (8) uses Chebyshev polynomials and the computed excitation currents result in a
normalized array factor.
For a 35 dB Chebyshev taper, the cnsand their corresponding slots displacements, calculated
from Equation (8), are given in Table 1. The 35 dB Chebyshev taper has been selected after some
simulation iterations, as it provides the desired 20 dB SLL for the SWA. A 20 dB Chebyshev taper
leads to SWA sidelobes higher than the 20 dB goal.
Tabl e 1. 35 dB Chebyshev taper coefficients and corresponding slots displacements leading to an
SWA SLL of 20 dB.
Slot Number Chebyshev Coefficient Displacement (mm)
1 1 3.74
22.086 5.42
33.552 7.11
44.896 8.4
55.707 9.11
65.707 9.11
74.896 8.4
83.552 7.11
92.086 5.42
10 13.74
It is clear from Table 1 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.
3.1.2. 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 p eak 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.
3.2. Example 2: 20 dB SLR with Taylor (One-parameter) Distribution
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 [22].
Progress In Electromagnetics Research C, Vol. 56, 2015 21
-40
-30
-20
-10
0
10
20
0 20 40 60 80 100 120 140 160 180
Gain [dB]
Theta [Degree]
CST
HFSS
Figure 4. Antenna’s YZ-plane pattern for the case of non-uniform slots displacements with Chebychev
distribution. A 20 dB SLR is obtained.
3.2.1. Coefficients and Slots Displacements
The cnsfor a Taylor one-parameter distribution can be computed using the equations in [23] or [24],
as given in the following. The excitation coefficients, In(z), for continuous line distribution of length l,
are equal to:
In(z)=
J0
jπB12z
l2
,for l/2z+l/2,
0,elsewhere
(9)
For the discrete case [24], the current magnitudes of an N-element linear array with symmetric
excitation are equal to:
am=
I0
β1m0.5
M0.52
,for N=2M
I0
β1m1
M12
,for N=2M1
(10)
where:
1mM,
a1is the excitation of the array’s center element(s),
and aMis that of the two edge elements.
For a 20 dB SLL for the SWA, a 30 dB Taylor (one-parameter) taper is required. The resulting
coefficients, and the corresponding slots displacements are listed in Table 2.
3.2.2. Results
For the slots displacements in Table 2, 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 20 dB, the determined Chebyshev and Taylor (one-parameter)
coefficients have led to almost identical radiation patterns, HPBW and gain parameters.
22 El Misilmani, Al-Husseini, and Kabalan
Tabl e 2. 30 dB Taylor (one-parameter) coefficients and corresponding slots displacements leading to
an SWA SLL of 20 dB.
Slot Number Taylor-based Coefficient Displacement (mm)
1 1 3.493
22.467 5.518
34.137 7.194
45.597 8.419
56.449 9.070
66.449 9.070
75.597 8.419
84.137 7.194
92.467 5.518
10 13.493
-40
-30
-20
-10
0
10
20
0 20 40 60 80 100 120 140 160 180
Gain [dB]
Theta [Degree]
CST
HFSS
Figure 5. Antenna’s YZ-plane pattern for the case of non-uniform slot displacement with Taylor
(one-parameter) distribution for an SLR of 20 dB.
3.3. Example 3: 30 dB SLR with Taylor (One-Parameter) Distribution
In this example, a Taylor (one-parameter) distribution is used to obtain an SWA SLR of 30 dB. For
this, the taper coefficients for a 40 dB Taylor (one-parameter) distribution are required, and these
are listed in Table 3 alongside 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.
3.4. 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 cnsfrom a Binomial distribution and observe the resulting SWA SLL. The binomial coefficients
are obtained from the binomial expansion:
(1 + x)m1=1+(m1)x+(m1)(m2)
2! x2(m1)(m2)(m3)
3! x3+... (11)
Progress In Electromagnetics Research C, Vol. 56, 2015 23
Tabl e 3. 40 dB Taylor (one-parameter) coefficients and corresponding slots displacements leading to
an SWA SLL of 30 dB.
Slot Number Taylor-based Coefficient Displacement (mm)
1 1 1.631
26.611 4.215
316.828 6.785
428.573 8.937
536.519 10.181
636.519 10.181
728.573 8.937
816.828 6.785
96.611 4.215
10 11.631
-40
-30
-20
-10
0
10
20
0 20 40 60 80 100 120 140 160 180
Gain [dB]
Theta [Degree]
CST
HFSS
Figure 6. Antenna’s YZ-plane pattern for the case of non-uniform slots displacements with Taylor
Line-Source distribution for an SLR of 30 dB.
Tabl e 4. Binomial coefficients and corresponding slots displacements.
Slot Number Binomial Coefficient Displacement (mm)
1 1 0.964
2 9 2.900
336 5.847
484 9.069
5126 11.268
6126 11.268
784 9.069
836 5.847
9 9 2.900
10 10.964
24 El Misilmani, Al-Husseini, and Kabalan
For the case of 10 slots, the binomial coefficients and the resulting slots displacements are listed in
Table 4. For these displacements values, the obtained SLR is 33.5 dB, and the peak gain is 15 dB. The
YZ-plane HPBW increases to 11.1 degrees, as shown in Fig. 7.
-40
-30
-20
-10
0
10
20
0 20 40 60 80 100 120 140 160 180
Gain [dB]
Theta [Degree]
CST
HFSS
Figure 7. Antenna’s YZ-plane pattern for the case of non-uniform slots displacements with binomial
distribution.
3.5. Reflection Coefficients
The S11 plots for the four examples are shown in Fig. 8. For all the studied examples where all the
slots have a fixed length of 54.25 mm, the SWAs retain resonance at 3 GHz, despite the different slots
displacements used. This is evident by comparing the S11 plot for the case of uniform displacements in
Fig. 3(a) to those of the four SWA examples in Fig. 8, where the resonating length of the elliptical slots
proved insensitive to the slots displacements.
-30
-25
-20
-15
-10
-5
0
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
Binomial
Figure 8. Reflection coefficient plots for the four illustrated examples in case of non-uniform
displacements (using CST).
Progress In Electromagnetics Research C, Vol. 56, 2015 25
4. COMPUTER PROGRAM
A computer program written in Python has been written to generate the slots displacements for a desired
SLL. The program takes as input the design frequency, waveguide dimensions aand b,thenumberof
slots, and the highest allowable SLL. It computes and outputs λ0,λg, the total needed waveguide
length, the resonant length of a rectangular slot (which serves as a starting point in optimizing the
length of any used slot shape), the width of the slot (which is kept the same for any slot type), the taper
coefficients (Chebyshev or Taylor), and the corresponding slots displacements. The units are indicated
on the program graphical user interface (GUI). A screenshot of the program output is given in Fig. 9.
This program was used for the examples in Section 3, and for the design in Section 5. Improvements to
the program interface are still being done.
Figure 9. A screenshot of the python program output.
5. FABRICATION AND MEASUREMENTS
In order to validate the procedure illustrated in this paper, a prototype SWA array has been fabricated
and tested. The waveguide in hand has a length of 50cm. This length is not enough to fit 10 slots
respecting the different slot distance and length guidelines, so the design has been made with 7 slots,
of elliptical shape. To avoid the two edge slots intersecting the waveguide flanges, the distance between
each of these two slots and the nearby waveguide edge has been increased from λg/4to3λg/4, leading
to a total SWA length of 4.5λg. This change was accounted for in the Python computer program, which
was used for this design. To keep the waveguide length of 50 cm, the SWA is designed for a frequency of
3.4045 GHz. At this frequency, λg= 111.11 mm, and 4.5λg= 50 cm. After initially designing the SWA
with the correct uniform distribution displacement, the elliptical slot length has been optimized to get
to this resonance frequency. It is found equal to 48 mm. With this optimized length, and for a slot
width of 5 mm, the SWA has later been designed to radiate with a sidelobe level of less than 20 dB.
A Chebyshev distribution of 35 dB has been used to calculate the excitation coefficients in this case.
These coefficients and the corresponding slots displacements are listed in Table 5.
26 El Misilmani, Al-Husseini, and Kabalan
Tabl e 5. Normalized Chebyshev taper coefficients and corresponding slots displacements.
Slot Number Chebyshev Coefficient Displacement (mm)
1 1 6.759
22.588 11.149
34.262 14.746
44.981 16.171
54.262 14.746
62.588 11.149
7 1 6.759
The design of the fabricated antennas and a photo of the fabricated prototype are shown in Fig. 10.
The reflection coefficient plot in Fig. 11 shows a comparison between the results simulated computed
using both CST and HFSS software, and two measured results. During Measurement 1, the antenna
had some protrusions on the corners of the elliptical slots, which were filed for Measurement 2, resulting
in a perfect elliptical shape of the slot. The gain patterns computed in both HFSS and CST compared
to the measured results are also shown in Fig. 12. Inspecting the S11 and pattern figures, credible
analogy has been revealed despite the slight difference, which is due to the other inaccuracies in the
fabrication. An SLL of less than 20 dB has been achieved, with a gain of around 14.5 dB, validating
the design procedure illustrated in this paper.
(a) (b)
Figure 10. SWA: (a) designed (dimensions in mm), (b) fabricated.
Progress In Electromagnetics Research C, Vol. 56, 2015 27
-30
-25
-20
-15
-10
-5
0
2.8 3 3.2 3.4 3.6
Reflection Coefficient [dB]
Fre
q
uenc
y
[GHz]
Measured 1
Measured 2
Simulated (CST)
Simulated (HFSS)
Figure 11. The compared measured and simulated reflection coefficient results.
0
2
4
6
8
10
12
14
16
0 20 40 60 80 100 120 140 160 180
Gain [dB]
Phi [Degree]
CST
HFSS
Measured
-40
-30
-20
-10
0
10
20
0 20 40 60 80 100 120 140 160 180
Gain [dB]
Theta [Degree]
CST
HFSS
Measured
(a) (b)
Figure 12. The compared measured and simulated gain pattern results using HFSS and CST: (a) XY -
plane, (b) YZ-plane.
6. CONCLUSION
This paper presented a simple procedure for designing SWAs with specified SLLs. General guidelines for
the slots width, length and longitudinal positions were first given. The offsets of the slots positions with
respect to the waveguide centerline, which determine the SLL, were then obtained from well-known
distributions. An intuitive rule regarding the used distribution was deduced, which was to select a
distribution with an SLL 15 dB lower than the desired SWA SLL. This procedure was implemented
using a Python computer program. Illustrative examples showing the distribution coefficients, slots
displacements, resulting patterns and S11 plots were given. A prototype antenna was fabricated and
tested, and the results were presented.
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28 El Misilmani, Al-Husseini, and Kabalan
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... This dissertation has been submitted to the Turnitin module and I confirm that my supervisor has seen my report and any concerns revealed by such have been resolved with my supervisor. 5. 8 A sketch of the Paardefontein Antenna Test Range Setup . . . . . 100 5.9 The antenna radiation pattern at 2.4 1.1 Background to the Project Waveguide slot antennas (WSAs) are used in radar, communications, navigation and several other high frequency applications. WSAs have various significant advantages over other antennas, making them stand out as antennas of choice for many applications [1]. ...
... * Reasonable size < 2 m 1. 3 Objectives of Study 1. 3 ...
... The main aim of the research is to investigate the waveguide slot antenna and come up with an optimum design that meets all the requirements stated above. 1. 4 ...
Thesis
Full-text available
In Surveillance Radars, waveguide slot antennas (WSAs) are mainly used due to their various advantages over other antennas such as high power handling capability and high structural rigidity. The purpose of this dissertation is to investigate and design an S-band WSA for surveillance radar application. The desired specification of the antenna include a centre frequency of 2.4 GHz and an azimuth 3dB beamwidth of less than 10°. The antenna is required to handle minimum power of 1 kW over a 120 MHz bandwidth (2.34 GHz - 2.46 GHz). Vertical polarisation with high cross-polarisation isolation is desired from the antenna. After investigating and analysing past research work on WSAs, a novel method that seeks to improve the radiation efficiency while achieving the above specifications was designed. The antenna design implements triple slots on a wide waveguide. CST was used in the design process to simulate the antenna and FEKO was used for validating the design. The antenna prototype was fabricated using aluminium sheets. The fabricated antenna was initially tested in an anechoic chamber at Alaris Antennas and then in an open field at the Paardefontein National Antenna Test Range. The antenna prototype achieved HPBW of 6.9°, SLL of -11.95 dB and a gain of 19.05 dB. The measured sidelobe levels were higher than expected due to fabrication errors. The overall measured results corresponds well with the simulated results, showing that the prototype meets the antenna design requirements.
... The proposed method uses simplified closed-form equations to determine the slots nonuniform displacements, without the need to use optimization algorithms. 29,30 A major contribution lies in the use of the same proposed simplified equations to design both the radiating 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. ...
... 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 a being 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. ...
... where: p = 2 ∕N(q − 1∕2), q = 2 ∕N(m − 1∕2)(q − 1∕2), v = 2 ∕N(q − 1), and w = 2 ∕N(m − 1)(q − 1) After calculating the slots excitations coefficients, the slots displacements can be calculated. The normalized conductance of the nth indicated by g n can be calculated using (6) and (7), 30 with N being the number of slots, and c n s are the distribution coefficients calculated using Chebyshev distribution for a desired SLR. ...
Article
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.
... The proposed method uses simplified closed-form equations to determine the slots nonuniform displacements, without the need to use optimization algorithms. 29,30 A major contribution lies in the use of the same proposed simplified equations to design both the radiating 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. ...
... 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 a being 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. ...
... where: p = 2 ∕N(q − 1∕2), q = 2 ∕N(m − 1∕2)(q − 1∕2), v = 2 ∕N(q − 1), and w = 2 ∕N(m − 1)(q − 1) After calculating the slots excitations coefficients, the slots displacements can be calculated. The normalized conductance of the nth indicated by g n can be calculated using (6) and (7), 30 with N being the number of slots, and c n s are the distribution coefficients calculated using Chebyshev distribution for a desired SLR. ...
... 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]. ...
... Taylor and Chebyshev distributions. The air-filled SWA can be designed as detailed by El Misilmani et al. in [3], and summarized as follows: ...
Article
Full-text available
This paper presents the use of machine learning (ML) to facilitate the design of dielectric-filled Slotted Waveguide Antennas (SWAs) with specified sidelobe levels. Conventional design methods for air-filled SWAs require the simultaneous solving of complex equations to deduce the antenna’s design parameters, which typically requires further manual simulation-based optimization to reach the desired resonance frequency and sidelobe level ratio (SLR). The few works that investigated the design of filled SWAs, did not optimize the design for a specified SLR. For an accelerated design process in the case of specified SLRs, we formulate the design of dielectric-filled SWAs as a regression problem where based on input specifications of the antenna’s SLR, reflection coefficient, frequency of operation, and relative permittivity of the dielectric material, the developed ML model predicts the filled SWA’s design parameters fast and with very low error. These parameters include the unified slots length and the non-uniform slots displacements required to achieve the desired performance. We experiment with several regressive ML algorithms and provide a comparative study of their results. Our numerical evaluations and validation experiments with the best performing ML models demonstrate the high efficiency of the proposed ML approach in estimating the dielectric-filled SWA’s design parameters in only a few milliseconds. A comparison to the design obtained through conventional optimization using the Genetic Algorithm also indicate superiority in computation time and resulting antenna performance.
... Due to their planar and rigid construction with low loss, high power handling capability, and high efficiency, SWAAs are more attractive candidates for application in microwave systems such as wireless communications, radars, and SPS systems [16][17][18][19][20][21]. The general principles and components of microwave power transmission systems and their space applications are outlined in [16], while several SWA arrays were designed in [17] with different tapered distributions for high power microwave applications. ...
... Due to their planar and rigid construction with low loss, high power handling capability, and high efficiency, SWAAs are more attractive candidates for application in microwave systems such as wireless communications, radars, and SPS systems [16][17][18][19][20][21]. The general principles and components of microwave power transmission systems and their space applications are outlined in [16], while several SWA arrays were designed in [17] with different tapered distributions for high power microwave applications. A slotted waveguide linear antenna array with 16 elements was designed at 9.4GHz for radar applications and simulated using HFSS in [18]. ...
Article
Full-text available
This study attempts to identify, design, and evaluate transmitting antennas for Solar Power Satellite (SPS) systems. The design approach aimed at meeting the SPS operational requirements at ISM bands, namely 2.4-2.5GHz for the NASA and 5.725-5.875GHz for the JAXA models. The primary attributes of SPS antennas for transmitting Beamed High-Power Microwaves (BHPMs) are high power handling capability, efficiency, and directivity with narrow beamwidth and lower sidelobe levels. Using a planar end-fed 20×20 SWA module, the whole planar Slotted Waveguide Antenna Arrays (SWAAs) were designed for both the NASA and JAXA reference models having 1km diameter antenna aperture, peak power level over 1GW, directivity over 80dBi, Side Lobe Level (SLL) less than 20dB, and pencil beam with HPBW less than 0.01°. The proposed slotted waveguide transmitting antenna arrays fulfilled the operational requirements for both the NASA and JAXA SPS reference models. Due to the higher operating frequency, the results showed that the proposed planar SWA array performs better on the JAXA than on the NASA SPS model.
... These structures radiate the incident power to the free space through slots in the rectangular or circular waveguide wall. According to the shape of the wave propagating inside the waveguide, slotted waveguide antennas can be divided into two main categories, standing wave slotted antennas and travelling wave slotted antennas [7,8]. A standing wave slotted antenna is characterised by a short wall at its end. ...
Article
Full-text available
Abstract In this article, three novel slotted substrate integrated waveguide (SIW) antenna elements are demonstrated with different radiator configurations, namely, two arms Archimedean antenna, single‐arm spiral antenna (monofilar), and four concentric circular loops antenna. Additionally, their near, as well as far‐field characteristics, have been investigated. The two arms Archimedean spiral antenna has a superior radiation characteristic of 18% return loss bandwidth (RLBW), 12% boresight axial ratio bandwidth (ARBW), and five dBi directivity. Furthermore, a 1 × 10 slotted SIW travelling wave antenna array has been designed, fabricated, and measured. The performance of the proposed antenna array versus the last reported antenna was evaluated and the proposed antenna array performance is superior to that of the others. Moreover, the measurements of the proposed array have a good agreement with the simulation results in which, 35%, 13% RLBW, and ARBW, respectively, have been achieved. The directivity of the proposed antenna array is 14 dBi.
... The development and modernization of radars that meet the demands of current surveillance systems [1][2][3][4] or the various applications in the civil field [5][6][7] such as meteorological control [8], requires the design and replacement of some of the Radar stages [1,9]. This need acquires a distinctive connotation in a country like Cuba, which has a large number of radars in service, and the call from institutions to substitute imports is extended. ...
Article
Full-text available
Current radars must meet the technological demands of today's world, which is why the modernization, replacement, or design of any of its parts is a strategic step. The antenna unit does not escape this reality. In it, it is usual to find several blocks among which are the power dividers, especially in radars that use antenna arrays and in particular air exploration radars such as the P18 and P12 use an unequal Wilkinson power divider with output to the two rows that are part of its antenna array. This paper proposes the design and simulation of an unequal Wilkinson power divider at the center frequency of 160 MHz of the Very High Frequency (VHF) band with a power ratio at the output ports of 60%-40%. The calculation of the components is carried out in Mathcad and the lumped circuit is simulated in AWR Microwave Office. From the results, Return Loss (RL) of-45.18 dB, isolation between the output ports of-49 dB, and power ratio at the output of S31 =-2.21 dB and S21=-3.98 dB in ports 3 and 2 respectively.
Article
Full-text available
In marine and coastal radar applications it is usual to find antennas consisting of a slotted waveguide antenna and a horn antenna. To increase the effectiveness of the cuban coastal surveillance system, it is proposed to modify the AU11-07N slotted waveguide antenna of the Navy-Radar 4000 based on the design of an optimal pyramidal horn antenna, causing the half power beamwidth to be reduced by half in the vertical plane. To achieve the objective, the original antenna is measured and modeled to then simulate it in the Ansoft HFSS software and compare it with the data from the radar manual. Then, the original antenna is modified based on the design of an optimal pyramidal horn, simulated and adjusted to the final dimensions based on the variation in the length of its plates. With the proposed modification, the half power beamwidth is achieved for the vertical plane of 11,30o and for the horizontal plane of 0.71o, a secondary lobe level of -35 dB for the azimuth plane and a final gain of 34 dB, greater than that of the original antenna.
Article
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.
Article
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.
Book
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.
Article
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.
Article
Essential principles, methods, and data for solving a wide range of problems in antenna design and application are presented. The basic concepts and fundamentals of antennas are reviewed, followed by a discussion of arrays of discrete elements. Then all primary types of antennas currently in use are considered, providing concise descriptions of operating principles, design methods, and performance data. Small antennas, microstrip antennas, frequency-scan antennas, conformal and low-profile arrays, adaptive antennas, and phased arrays are covered. The major applications of antennas and the design methods peculiar to those applications are discussed in detail. The employment of antennas to meet the requirements of today's complex electronic systems is emphasized, including earth station antennas, satellite antennas, seeker antennas, microwave-relay antennas, tracking antennas, radiometer antennas, and ECM and ESM antennas. Finally, significant topics related to antenna engineering, such as transmission lines and waveguides, radomes, microwave propagation, and impedance matching and broadbanding, are addressed.
Article
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.
Article
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.
Article
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.