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{{Note|EM.Picasso is the frequency-domain, full-wave '''[[Planar Module]]''' of '''[[EM.Cube]]''', a comprehensive, integrated, modular electromagnetic modeling environment. EM.Picasso shares the visual interface, 3D parametric CAD modeler, data visualization tools, and many more utilities and features collectively known as '''[[CubeCAD]]''' with all of [[EM.Cube]]'s other computational modules.}}

=== An Overview of Planar Method of Moments ===

In a planar MoM simulation, the unknown electric and magnetic currents are discretized as a collection of elementary currents with small finite spatial extents. As a result, the governing integral equations reduce to a system of linear algebraic equations, whose solution determines the amplitudes of all the elementary currents defined over the planar structure's mesh. Once the total currents are known, you can calculate the fields everywhere in the structure.

== Building a Planar Structure ==

# '''Embedded Dielectric Sets:''' These are prismatic dielectric objects inserted inside a substrate layer. You can define a finite permittivity and conductivity for such objects, but their height is always the same as the height of their host layer. The embedded dielectric objects are modeled as vertical volume polarization currents.

=== Defining the Layer Stack-Up ===

After creating a substrate layer, you can always edit its properties in the Layer Stack-up Settings dialog. Click on any layer's row in the table to select and highlight it and then click the '''Edit''' button. The substrate layer dialog opens up, where you can change the layer's label and assigned color. In the material properties section of the dialog, you can change the name of the material and its properties: permittivity (e_r), permeability (µ_r), electric conductivity (s) and magnetic conductivity (s_m). To define electrical losses, you can either assign a value for electric conductivity (s), or alternatively, define a loss tangent for the material. In the latter case, check the box labeled "'''Specify Loss Tangent'''" and enter a value for it. In this case, the electric conductivity field becomes greyed out and reflects the corresponding s value at the center frequency of the project. You can also set the thickness of any substrate layer in the project units except for the top and bottom half-spaces.

For better visualization of your planar structure, EM.Picasso displays a virtual domain in a default orange color to represent part of the infinite background structure. The size of this virtual domain is a quarter wavelength offset from the largest bounding box that encompasses all the finite objects in the project workspace. You can change the size of the virtual domain or its display color from the Domain Settings dialog, which you can access either by clicking the '''Computational Domain''' [[File:domain_icon.png]] button of the '''Simulate Toolbar''', or by selecting '''Simulate > Computational Domain > Domain Settings...''' from the Simulate Menu or by right clicking the '''Virtual Domain''' item of the Navigation Tree and selecting '''Domain Settings...''' from the contextual menu, or using the keyboard shortcut '''Ctrl+A'''. Keep in mind that the virtual domain is only for visualization purpose and does not affect the MoM simulation. The virtual domain also shows the substrate layers in translucent colors. If you assign different colors to your substrate layers, you have get a better visualization of multilayer virtual domain box surrounding your project structure.

For antennas and planar circuits, where you typically define one or more ports, you usually use lumped sources. A lumped source is indeed a gap discontinuity that is placed on the path of an electric or magnetic current flow, where a voltage or current source is connected to inject a signal. Gap sources are placed across metal or slot traces. Probe sources are placed across vertical PEC vias. A de-embedded source is a special type of gap source that is placed near the open end of an elongated metal or slot trace to create a standing wave pattern, from which the scattering [[parameters]] can be calculated accurately. To calculate the scattering characteristics of a planar structure, e.g. its radar cross section (RCS), you excite it with a plane wave source. Short dipole sources are used to explore propagation of points sources along a layered structure. Huygens sources are virtual equivalent sources that capture the radiated electric and magnetic fields from another structure possibly in another [[EM.Cube]] computational module and bring them as a new source to excite your planar structure.

[[Image:PMOM64.png|thumb|600px|EM.Picasso's Lumped Element dialog.]]

'''You can define any number of ports equal to or less than the total number of sources in your project.''' The Port List of the dialog shows a list of all the ports in ascending order, with their associated sources and the port's characteristic impedance, which is 50S by default. You can delete any port by selecting it from the Port List and clicking the '''Delete''' button of the dialog. Keep in mind that after deleting a port, you will have a source in your project without any port assignment and make sure that is what you intend. You can change the characteristic impedance of a port by selecting it from the Port List and clicking the '''Edit''' button of the dialog. This opens up the Edit Port dialog, where you can enter a new value in the box labeled '''Impedance'''.

=== Modeling Coupled Ports ===

In particular, it may be useful to plot the S_ii [[parameters]] on a Smith chart. To change the format of a data plot, select it in the Data Manager and click its '''Edit''' button. In the Edit File Dialog, choose one of the options provided in the dropdown list labeled '''Graph Type'''.

=== Visualizing Current Distributions ===

At the end of a planar MoM simulation, the current distribution nodes in the Navigation Tree become populated by the magnitude and phase plots of the three vectorial components of the electric ('''J''') and magnetic ('''M''') currents as well as the total electric and magnetic currents.

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Note that unlike [[EM.Cube]]'s other computational modules, near field calculations in the [[Planar Module]] usually takes substantial time. This is due to the fact that at the end of a planar MoM simulation, the fields are not available anywhere (as opposed to the [[FDTD Module]]), and their computation requires integration of complex dyadic Green's functions (as opposed to [[MoM3D Module]]'s free space Green's functions).

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Once a planar MoM simulation is finished, three far field items are added under the Far Field item in the Navigation Tree. These are the far field component in &theta; direction, the far field component in &phi; direction and the &quot;Total&quot; far field. The 2D radiation pattern graphs can be plotted from [[EM.Cube]]'s '''Data Manager'''. A total of eight 2D radiation pattern graphs are available: 4 polar and 4 Cartesian graphs for the XY, YZ, ZX and user defined plane cuts.

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* At the end of a planar MoM simulation, besides calculating the RCS data over the entire (spherical) 3D space, a number of 2D RCS graphs are also generated. These are RCS cuts at certain planes, which include the three principal XY, YZ and ZX planes plus one additional constant f-cut. This fourth plane cut is at &phi; = 45° by default. You can assign another &phi; angle in degrees in the box labeled '''Non-Principal Phi Plane'''.

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