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1
Abstract—A general and accurate design method based on the
Method of Least Squares is developed to resonant planar SIW
arrays fed by slot couplers. In this approach, which uses Elliott’s
design formulas by the concept of the equivalent waveguide, a
multi-term error function for achieving the input impedance
matching and the desired pattern synthesis is formulated and
minimized by an efficient hybrid optimization method. For
accuracy verification purpose, a SIW slot array with 3
6
elements is considered. The results of the proposed method
without further optimization by the full-wave simulations are
compared with the results of the simulation softwares (Ansoft
HFSS and CST) and it shows a good agreement.
Index Terms— Pattern synthesis, planar slot array, SIW, and
Standing-wave feeding.
I. I
NTRODUCTION
Substrate integrated waveguide (SIW) technology have been
introduced as a promising candidate for microwave and
millimeter-wave wireless systems due to the advantages
namely low cost, compact size, low losses, good power
handling, and full integration capability (passive and active
components)[1]-[3].
Different kinds of antennas have been proposed based on SIW
architecture using printed circuit board (PCB) or low
temperature co-fired ceramic (LTCC) technology [4]–[6].
Those include standing-wave and travelling-wave slotted
waveguides, leaky-wave antennas, cavity-backed slot, and
patch antennas that are reviewed in [1], [7]. Resonant slotted
SIW array antennas have attracted increasing attention because
of having high gain, high efficiency, low side lobe levels, and
low cross polarization [8]-[10].
For a linear slot array, the radiation pattern tends to have a very
wide beamwidth in the E-plane (nearly omnidirectional) and a
relatively small beamwidth in the H-plane because the physical
dimensions along the E-plane is much shorter than that along
the H-plane. Therefore, a pencil beam can be obtained by a
planar slot array. In the previous works, the results of Elliott’s
formulas served as the initial design for the further accurate
optimization by the full-wave simulations of planar slotted SIW
array antennas [11]. Therefore, an accurate design approach for
achieving the input impedance matching and the desired
radiation pattern simultaneously without full-wave
optimizations is an almost untouched topic in this class of
antenna.
In this letter, following the previous efforts made on the design
of travelling-wave and standing-wave slotted SIW linear slot
arrays [5], [12], [13], the Method of Least Squares (MLS) is
used to develop a general design procedure for standing-wave
slotted SIW planar array antennas with a compact feed
structure.
The multi-term error function consisting of three
terms is minimized with respect to the design parameters (slot
lengths, offsets, and excitations) by using a combination of a
global optimization method and a local optimization method.
Briefly, Section II explains the design theory, Section III
describes the design procedure, Section IV verifies the
accuracy of the proposed method by presenting an example,
and finally, conclusion section finishes the paper.
II. T
HEORY
Using the equivalent waveguide for SIW, many design
concepts of conventional metallic waveguide can be transferred
to this new platform with special considerations, such as the
antenna and coupler that these are presented in Section A and B.
A. Planar Slot Array
A planar array consisting of M waveguides and N longitudinal
slots on each one is considered. It should be noted that SIWs
have considerably lower height than conventional rectangular
waveguides. Therefore, the internal mutual coupling of higher
order modes is significant and it is necessary to use the design
formulas which account for incident field, external, and internal
coupling [14]
nm
s
nm
nm
a
nm
V
V
fK
G
Y
1
0
=
(1)
nm
nm
a
nm
Q
f
G
Y
2
0
2
=
(2)
in which
nm
nmnm
nm
nm
MC
lx
G
Y
f
Q +=
),(
2
0
2
(3)
where nm indicates n'th slot in the m'th waveguide. Y
nm
a
/G
0
is
the normalized active admittance, V
nm
is the mode voltage, V
nm
s
is the maximum voltage at the center of the slot and Y/G
0
is the
normalized admittance of isolated slot which the procedure
presented in [13] is followed for its calculation. K
1
, f
nm
and
MC
nm
(the mutual coupling term including external and internal
mutual coupling) are defined in [14].
Accurate Design of Planar Slotted SIW Array
Antennas
S. E. Hosseininejad, N. Komjani, and A. Mohammadi
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