{{projectinfo|TutorialApplication| Designing A Slot-Coupled Patch Antenna Array With A Corporate Feed Network Using EM.Picasso|PMOM372ART PATCH Fig title.png|In this project, we will build and analyze a 16-element slot-based coupled patch antenna array with a microstrip corporate feed network.|*[[Building Geometrical Constructions in CubeCAD| CubeCAD]]*[[EM.Picasso]]
*PEC Traces
*SlotTracesSlot Traces
*Mesh Density
*Scattering Wave Port
*Lumped ElementStrip Gap Circuit
*Radiation Pattern
|All versions|None }}
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[[Image:Picasso L9 Fig14.png|thumb|left|550px480px|The geometry of the Wilkinson power divider with the lumped resistor.]]
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== Constructing a Four-Element Patch Sub-Array ==
A binary H-tree structure is used to construct a 1:4 Wilkinson power divider network as shown in the figures below. In this case, the network involves three ring-type Wilkinson power dividers.
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The 4-element slot-coupled patch sub-array is simulated using [[EM.Picasso]]'s [[Planar Method of Moments|planar method of moments]] (MoM) solver. An adaptive frequency sweep is performed to compute the frequency response of the structure over the frequency range [2.2GHz - 2.6GHz]. The figures below show the variation of the sub-array's return loss with frequency and its 3D far-field radiation pattern computed at 2.4GHz.
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==Building the Array Structure== The corporate feed network on the microstrip trace plane (PEC_1) consists entirely of rectangle and circle strip objects. For the Wilkinson power dividers, circle strips with unequal outer and inner radii and incomplete start and end angles are used just as you saw in Tutorial Lesson 7. A 50Ω microstrip line on the lower thin substrate has Constructing a width of 2.4mm. Small circle strips of (outer) radius 2.4mm are used to provide a round bend junctions between two perpendicular microstrip line segments. Rather than a quarter-circle, a 3/4-circle shape is used to have some good overlap area over the conjoining line objects. This helps with a smoother and more consistent mesh in such junction areas. Draw the following 9 circle strip objects, all on PEC_2 trace plane, with the given coordinates and dimensions: {| border="0"|-| valign="top"|| valign="bottom"|{| class="wikitable" style="text-align: center;"|-! scope="col"| Label! scope="col"| Host Trace! scope="col"| Object Type! scope="col"| Function! scope="col"| LCS Origin! scope="col"| LCS Rotation Angles! scope="col"| Outer Radius! scope="col"| Inner Radius! scope="col"| Start Angle! scope="col"| End Angle|-! scope="row"| Circle_Strip_1| PEC_2| Circle Strip| Wilkinson Power Divider 1| (-17mm, 0, 0)| (0°, 0°, 0°)| 9.65mm| 8.25mm| 20°| 340°|-! scope="row"| Circle_Strip_2| PEC_2| Circle Strip| Wilkinson Power Divider 2| (10mm, 62.5mm, 0)| (0°, 0°, 0°)| 9.65mm| 8.25mm| 20°| 340°|-! scope="row"| Circle_Strip_3| PEC_2| Circle Strip| Wilkinson Power Divider 3| (10mm, -62.5mm, 0)| (0°, 0°, 0°)| 9.65mm| 8.25mm| 20°| 340°|-! scope="row"| Circle_Strip_4| PEC_2| Circle Strip| Round Bend Junction| (-6.75mm, 61.3mm, 0)| (0°, 0°, 0°)| 2.4mm| 0mm| 0°| 270°|-! scope="row"| Circle_Strip_5| PEC_2| Circle Strip| Round Bend Junction| (-6.75mm, -61.3mm, 0)| (0°, 0°, 0°)| 2.4mm| 0mm| 90°| 360°|-! scope="row"| Circle_Strip_6| PEC_2| Circle Strip| Round Bend Junction| (20.25mm, 92.55mm, 0)| (0°, 0°, 0°)| 2.4mm| 0mm| 0°| 270°|-! scope="row"| Circle_Strip_7| PEC_2| Circle Strip| Round Bend Junction| (20.25mm, -92.55mm, 0)| (0°, 0°, 0°)| 2.4mm| 0mm| 90°| 360°|-! scope="row"| Circle_Strip_8| PEC_2| Circle Strip| Round Bend Junction| (20.25mm, 32.45mm, 0)| (0°, 0°, 0°)| 2.4mm| 0mm| 90°| 360°|-! scope="row"| Circle_Strip_9| PEC_2| Circle Strip| Round Bend Junction| (20.25mm, -32.45mm, 0)| (0°, 0°, 0°)| 2.4mm| 0mm| 0°| 270°|-|} Rectangle strip objects are used for microstrip line segments. Draw the following 16 rectangle strip objects, all on PEC_2 trace plane, with the given coordinates and dimensions: {| border="0"|-| valign="top"|| valign="bottom"|{| class="wikitable" style="text-align: center;"|-! scope="col"| Label! scope="col"| Host Trace! scope="col"| Object Type! scope="col"| Function! scope="col"| LCS Origin! scope="col"| LCS Rotation Angles! scope="col"| X Dimension! scope="col"| Y Dimension|-! scope="row"| Rect_Strip_1| PEC_2| Rectangle Strip| 50Ω Input Microstrip Feed Line| (-38mm, 0, 0)| (0°, 0°, 0°)| 8mm| 2.4mm|-! scope="row"| Rect_Strip_2| PEC_2| Rectangle Strip| 50Ω Input Line for Wilkinson Power Divider 1| (-30mm, 0, 0)| (0°, 0°, 0°)| 8mm| 2.4mm|-! scope="row"| Rect_Strip_3| PEC_2| Rectangle Strip| 50Ω Output Line for Wilkinson Power Divider 1| (-7.95mm, 32.06mm, 0)| (0°, 0°, 0°)| 2.4mm| 58.48mm|-! scope="row"| Rect_Strip_4| PEC_2| Rectangle Strip| 50Ω Output Line for Wilkinson Power Divider 1| (-7.95mm, -32.06mm, 0)| (0°, 0°, 0°)| 2.4mm| 58.48mm|-! scope="row"| Rect_Strip_5| PEC_2| Rectangle Strip| 50Ω Input Line for Wilkinson Power Divider 2| (-2.75mm, 62.5mm, 0)| (0°, 0°, 0°)| 8mm| 2.4mm|-! scope="row"| Rect_Strip_6| PEC_2| Rectangle Strip| 50Ω Input Line for Wilkinson Power Divider 3| (-2.75mm, -62.5mm, 0)| (0°, 0°, 0°)| 8mm| 2.4mm|-! scope="row"| Rect_Strip_7| PEC_2| Rectangle Strip| 50Ω Output Line for Wilkinson Power Divider 2| (19.05mm, 78.935mm, 0)| (0°, 0°, 0°)| 2.4mm| 27.23mm|-! scope="row"| Rect_Strip_8| PEC_2| Rectangle Strip| 50Ω Output Line for Wilkinson Power Divider 3| (19.05mm, -78.935mm, 0)| (0°, 0°, 0°)| 2.4mm| 27.23mm|-! scope="row"| Rect_Strip_9| PEC_2| Rectangle Strip| 50Ω Output Line for Wilkinson Power Divider 2| (19.05mm, 46.065mm, 0)| (0°, 0°, 0°)| 2.4mm| 27.23mm|-! scope="row"| Rect_Strip_10| PEC_2| Rectangle Strip| 50Ω Output Line for Wilkinson Power Divider 3| (19.05mm, -46.065mm, 0)| (0°, 0°, 0°)| 2.4mm| 27.23mm|-! scope="row"| Rect_Strip_11| PEC_2| Rectangle Strip| 50Ω Slot Feed Line| (30.125mm, 93.75mm, 0)| (0°, 0°, 0°)| 19.75mm| 2.4mm|-! scope="row"| Rect_Strip_12| PEC_2| Rectangle Strip| 50Ω Slot Feed Line| (30.125mm, -93.75mm, 0)| (0°, 0°, 0°)| 19.75mm| 2.4mm|-! scope="row"| Rect_Strip_13| PEC_2| Rectangle Strip| 50Ω Slot Feed Line| (30.125mm, 31.25mm, 0)| (0°, 0°, 0°)| 19.75mm| 2.4mm|-! scope="row"| Rect_Strip_14| PEC_2| Rectangle Strip| 50Ω Slot Feed Line| (30.125mm, -31.25mm, 0)| (0°, 0°, 0°)| 19.75mm| 2.4mm|-! scope="row"| Rect_Strip_15| PEC_2| Rectangle Strip| Resistor Line for Wilkinson Power Divider 1| (-7.95mm, 0, 0)| (0°, 0°, 90°)| 5.64mm| 1mm|-! scope="row"| Rect_Strip_16| PEC_2| Rectangle Strip| Resistor Line for Wilkinson Power Divider 2| (19.05mm, 62.5mm, 0)| (0°, 0°, 90°)| 5.64mm| 1mm|-! scope="row"| Rect_Strip_17| PEC_2| Rectangle Strip| Resistor Line for Wilkinson Power Divider 3| (19.05mm, -62.5mm, 0)| (0°, 0°, 90°)| 5.64mm| 1mm|-|} You will use array objects to represent the repetitive pattern of slot-coupled patch radiators. Specifically, you will build three array objects for the patch element on the top PEC_1 trace plane, the coupling slot on the middle ground plane PMC_1, and the microstrip open stub underneath the slot on the bottom trace plane PEC_2. The table below shows the coordinate and dimensions of the primitive or "parent" objects for each of these arrays. First, you have to draw these objects on the respective planes: {| border="0"|-| valign="top"|| valign="bottom"|{| class="wikitable" style="text-align: center;"|-! scope="col"| Label! scope="col"| Host Trace! scope="col"| Object Type! scope="col"| Function! scope="col"| LCS Origin! scope="col"| LCS Rotation Angles! scope="col"| X Dimension! scope="col"| Y Dimension|-! scope="row"| Rect_Strip_18| PEC_2| Rectangle Strip| Microstrip Open Stub| (51.5mm, -93.75mm, 0)| (0°, 0°, 0°)| 23mm| 2.4mm|-! scope="row"| Rect_Strip_19| PMC_1| Rectangle Strip| Coupling Slot| (45mm, -93.75mm, 0.787mm)| (0°, 0°, 0°)| 1.5mm| 12mm|-! scope="row"| Rect_Strip_20| PEC_1| Rectangle Strip| Radiating Element Patch| (45mm, -93.75mm, 2.787mm)| (0°, 0°, 0°)| 31.6mm| 31.6mm|-|} Now, select each of the above primitive objects and use [[EM.Cube]]'s Array Tool to create a 1×4 Y-directed linear array of that object on the proper plane. Make sure that right trace group on the Navigation Tree is activated before creation of each array object. Use the table below for element count and spacing along the three principal directions. {{Note|Once you create an array object, the array's local coordinate system (LCS) takes over the parent object's LCS. The array's LCS rotation angles are independent of the parent object's rotation angles.}} {| border="0"|-| valign="top"|| valign="bottom"|{| class="wikitable" style="text-align: center;"|-! scope="col"| Label! scope="col"| Host Trace! scope="col"| Primitive Object! scope="col"| Array LCS Origin! scope="col"| Array LCS Rotation Angles! scope="col"| X Count! scope="col"| Y Count! scope="col"| Z Count! scope="col"| X Spacing! scope="col"| Y Spacing! scope="col"| Z Spacing|-! scope="row"| Rect_Strip_18| PEC_2| Rect_Strip_18| (51.5mm, -93.75mm, 0)| (0°, 0°, 0°)| 1| 4| 1| 0| 62.5mm| 0|-! scope="row"| Rect_Strip_19| PMC_1| Rect_Strip_19| (45mm, -93.75mm, 0)| (0°, 0°, 0°)| 1| 4| 1| 0| 62.5mm| 0|-! scope="row"| Rect_Strip_20| PEC_1| Rect_Strip_20| (45mm, -93.75mm, 0)| (0°, 0°, 0°)| 1| 4| 1| 0| 62.5mm| 0|-|}
The binary H-tree structure described earlier is expanded to construct a 1:16 Wilkinson power divider network as shown in the figures below. In this case, the network involves 15 ring-type Wilkinson power dividers.
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[[Image:PMOM370ART PATCH Fig10.png|thumb|left|640px|The geometry of the 416-element slot-coupled patch antenna array with a corporate feed network.]]
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Next, define three lumped elements of "Resistor" type with a 100Ω value and place them in the middle of the line segments Rect_Strip_15, Rect_Strip_16 and Rect_Strip_17. Also define a default +X-directed de-embedded source on the line object Rect_Strip_1 and assign a default Port Definition observable to it. Define three Current Distribution observables for the PEC_1, PEC_2 and PMC_1 traces. Define a Far Fields Radiation Pattern observable with a 3° Angle Increment for both Theta and Phi, and check its Front-to-Back Ratio (FBR) checkbox. Your antenna array is complete at this point.
[[Image:PMOM371.png|thumb|380px|The Planar MoM Mesh Settings dialog.]]
==Examining the Mesh of the Planar Array==
Similar to Tutorial Lessons 7 and 8, set the mesh density to 40 cells per effective wavelength. Open the Mesh Settings dialog and increase the minimum angle of defective triangular cells to 20°. Also, check the checkbox labeled " Refine Mesh at Gap Locations". This is due to the presence of three lumped elements on very narrow line objects. In [[EM.Cube]]'s [[Planar Module]], lumped elements behave very similar to gap sources.
Generate and view the planar MoM mesh of your array structure on all three PEC_1, PMC_1 and PEC_2 planes. The mesh of the corporate feed network is the most complicated one and requires special attention. In particular, closely inspect the mesh at the junctions of microstrip line segments with the Wilkinson circular rings and the around the round corner bend junctions. Also examine the connections to the open stub array. Connections to array objects might sometime be tricky in complicated configurations.
{{Note|If your planar structure involves a large number of interconnected objects, individual objects with curved shapes, many overlap regions and several gap sources or lumped elements, [[EM.Cube]]'s mesh generator may fail with low mesh density values. You may be asked to increase the mesh density.}}
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[[Image:PMOM372ART PATCH Fig11.png|thumb|800pxleft|640px|The Planar MoM mesh geometry of the 416-element slot-coupled patch antenna array with a corporate feed networkthe patches in the freeze state.]]
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Using the same mesh densities as before, the planar mesh shown in the figure below is generated for the 16-element patch array.
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[[Image:PMOM373ART PATCH Fig12.png|thumb|350pxleft|Details of the 640px|The hybrid planar mesh around the Wilkinson power divider.]]</td><td>[[Image:PMOM374.png|thumb|500px|Details of the planar mesh around the round corner bend junctions16-element slot-coupled patch array with a corporate feed network.]]
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==Running a Planar The matrix size for this planar MoM Analysis simulation is N = 10,771. [[EM.Picasso]]'s LU solver was used to solver the linear system. The total computation time including the LU decomposition, back-substitution and computation of the Antenna Array==full 3D far-field radiation pattern at an angular resolution of 1° along both the azimuth and elevation directions was 150 seconds. At the end of the planar MoM simulation, the following port characteristics are reported:
Run a quick planar MoM analysis of your slot-couple patch array structureS11: 0. The size of the linear system in this case is N = 3,546447781 + 0. At the end of the simulation, the following port characteristic values are reported in the Output Message Window: 118984j
S11(dB): -06.197431 - 0.916521j682387
S11(dB)Z11: -0123.560162053609 + 37.286922j
Z11: 2.660904 - 40.306972j Y11: 0.001631 + 007443 - 0.024702j Note that input match of the array has been seriously degraded compared to that of the single slot-coupled patch antenna you built in Tutorial Lesson 8. Visualize all three current distributions on the PEC_1, PEC_2 and PMC_1 trace planes. You may have to change the limits of the current plot for the feed network due to the presence of a few very hot spots around the line discontinuities. 002255j
The figures below show the 3D far-field radiation pattern as well as 2D Cartesian radiation pattern cuts in the principal YZ and ZX planes computed at 2.4GHz. A directivity of D<sub>0</sub> = 17.3dB is predicted for this array.
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[[Image:PMOM375ART PATCH Fig13.png|thumb|750pxleft|The surface electric current distribution on the microstrip feed network 640px|3D far-field radiation pattern of the 16-element patch array after limiting the plot values to 99% confidence intervalcomputed at 2.4GHz.]]
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[[Image:PMOM376ART PATCH Fig14.png|thumb|450pxleft|480px|The surface electric current distribution on the top patches 2D Cartesian radiation pattern of the 16-element patch array.]]</td><td>[[Image:PMOM377.png|thumb|450px|The surface magnetic current distribution on in the coupling slots of the arrayYZ principal plane.]]
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Also visualize the 3D radiation pattern of your patch antenna array and plot the 2D Cartesian and polar graphs in EM.Grid. Note the portion of the radiation pattern in the lower half-space (90° ≤ θ ≤ 180°). This is due to the radiation from the feed network. Open the Data Manager and view the contents of the data file "FBR.DAT". You will see a value of 2.304221e-002 for the front-to-back ratio of the slot-coupled patch array. But it important to note that the computed FBR value is ratio of the total far field value at θ = 180° to the total far field value at θ = 0°. A close inspection of the patterns in the lower half-space reveals that the back lobes peak at θ = 130°, not at θ = 180°. The directivity of the antenna array is found to be 11.15 (or 10.47dB).
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[[Image:PMOM378ART PATCH Fig15.png|thumb|640pxleft|480px|The 3D 2D Cartesian radiation pattern of the slot16-coupled element patch antenna array with a corporate feed networkin the ZX principal plane.]]
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The figures below show the surface electric current distribution maps on the patch and feed planes, as well as the surface magnetic current distribution map on the middle ground plane, all computed at 2.4GHz.
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[[Image:PMOM379ART PATCH Fig16.png|thumb|400pxleft|640px|The 2D Cartesian graph of surface electric current distribution map on the YZ-feed network plane radiation pattern of the slot-coupled patch antenna arrayat 2.]]</td><td>[[Image:PMOM380.png|thumb|400px|The 2D Cartesian graph of the ZX-plane radiation pattern of the slot-coupled patch antenna array4GHz.]]
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[[Image:PMOM381ART PATCH Fig17.png|thumb|400pxleft|640px|The 2D polar graph of surface electric current distribution map on the YZ-plane radiation pattern of the slot-coupled patch antenna arrayradiators at 2.]]</td><td>[[Image:PMOM382.png|thumb|400px|The 2D polar graph of the ZX-plane radiation pattern of the slot-coupled patch antenna array4GHz.]]
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[[Image:PMOM383.png|thumb|450px|The 3D radiation pattern of a single stand-alone slot-coupled patch antenna multiplied by a 4×1 array factor.]]
==Comparison with Array Factor Method==
In Tutorial Lesson 8, you could have defined a linear array factor in the Radiation Pattern dialog of the slot-couple patch antenna. Had you done that, the computed radiation pattern would have corresponded to an array of slot-coupled patch antennas rather than the single stand-alone radiator appearing your project workspace. However, the array pattern computed in this manner does not account for the inter-element coupling effects. The figures below have been obtained by multiplying the radiation pattern of the single slot-coupled patch antenna by a 1×4 Y-directed array factor with an element spacing of 62.5mm. The directivity of the array is calculated to be 12.15 (or 10.89dB), which is fairly close to the directivity of the array with the corporate feed network. Comparing the two sets of radiation pattern plots, you can see that even the side lobe and nulls are very similar in both cases. The main difference, however, is in the back lobe characteristics.
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[[Image:PMOM384ART PATCH Fig18.png|thumb|400pxleft|The 2D Cartesian graph of the YZ-plane radiation pattern of a single stand-alone slot-coupled patch antenna multiplied by a 4×1 array factor.]]</td><td>[[Image:PMOM385.png|thumb|400px640px|The 2D Cartesian graph of surface magnetic current distribution map on the ZX-plane radiation pattern of a single stand-alone slot-coupled patch antenna multiplied by a 4×1 array factorcoupling slots at 2.]]</td></tr><tr><td>[[Image:PMOM386.png|thumb|400px|The 2D polar graph of the YZ-plane radiation pattern of a single stand-alone slot-coupled patch antenna multiplied by a 4×1 array factor.]]</td><td>[[Image:PMOM387.png|thumb|400px|The 2D polar graph of the ZX-plane radiation pattern of a single stand-alone slot-coupled patch antenna multiplied by a 4×1 array factor4GHz.]]
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