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Slotted waveguide arrays consist of a
number of slots cut into the walls of a waveguide forming an array with
the slots acting as individual radiating elements.
The resonant slot array employs near half-wavelength long resonant slots
as individual radiators. The array elements are excited in the standing
wave mode, which is formed by a short circuit end of the waveguide.
The concrete design task here is a 10-element transversal slot array cut
into the upper wide side of a WR-51 standard rectangular waveguide. The
operating frequency is the center of the K band, 18.5 GHz. The
dimensions of the waveguide cross-section are A=0.51 inch=12.95 mm, and
B=0.255 inch=6.477 mm.
Single Slot Simulation
TE10 waveguide mode is excited by a coaxial probe, modeled by a wire
segment λ/4 from the waveguide end, as shown in Fig.1. Slot is cut into
the waveguide at the point where surface currents would otherwise be
longitudinal, at the upper side of the waveguide. Only half of the
waveguide is modeled, due to symmetry. The complete model is shown in
Fig.2.
The real part of the longitudinal component of the Poynting vector
calculated along the axis of the waveguide shows the transfer of power
from the generator to the slot (Fig.3). The first marker is set to the
position of the wire-probe feeder, while the second marker is at the
position of the center of the slot.
The radiation pattern (in dBi) of a single slot is shown in Fig.4. Only
radiation pattern in half-space has been shown here for reasons of
clarity, even though full radiation pattern was calculated.
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Fig.1. Model of one waveguide
slot – one symmetry plane |
Fig.2. Complete model of
waveguide slot |
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Fig.3. Real part of the Poynting
vector longitudinal component along
the axis of the waveguide (one slot) |
Fig.4. Radiation pattern in
half-space of a single slot |
This model requires only 222 unknowns
thanks to higher order MoM applied in WIPL-D Pro 3D EM Solver. The
simulation of a single slot including calculation of radiation pattern
in 32761 directions and near field in 209 points took 8 seconds on an
Intel Core2 E7300 Duo CPU with 2.66 GHz clock.
Waveguide Slot Array Simulation
The 10-element model is built by using the single slot model and
applying a single Copy operation to create the other 9 array elements.
The slots are positioned periodically at the points where surface
currents would otherwise be longitudinal, at the upper side of the
waveguide, one guide-wavelength apart. This distance enables in phase
excitation of all slots.
The real part of the longitudinal component of the Poynting vector
calculated along the axis of the waveguide shows the transfer of power
from the generator to the slots, with a part of power being radiated at
each slot (Fig.6). The markers designate the positions of the generator
and the fifth slot.
The radiation pattern (in dBi) of the slot array is shown in Fig.7. The
gain is 14.8 dBi and the radiation is broadside, with two pronounced
grating lobes, which are expected since distance between array elements
is one guide-wavelength.
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Fig.5. 10-element slot array
model – one symmetry plane |
Fig.6. Real part of the Poynting
vector longitudinal component along
the axis of the waveguide (array) |
Fig.7. Radiation pattern of the array
The model of a 10-element slot array
takes only 1059 unknowns (around 9 MB of RAM) for rigorous MoM
simulation. The complete simulation, with calculation of radiation
pattern in 32761 directions and near field in 470 points is done in 16
seconds on the same Core2 Duo CPU.
Fig.8. Near field in front of slots in case of 10-element array
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