The Method of Moments (MoM) is a rigorous, full-wave numerical technique for solving open boundary electromagnetic problems. Using this technique, you can analyze electromagnetic radiation, scattering and wave propagation problems with relatively short computation times and modest computing resources. The method of moments is an integral equation technique; it solves the integral form of Maxwellâs equations as opposed to their differential forms that are used in the finite element or finite difference time domain methods.
[[Image:PMOM11.png|thumb|250px|EM.Picasso's Navigation Tree.]]
[[Image:PMOM8(1).png|thumb|600px|EM.Picasso's Layer Stack-up Settings dialog.]]
In EM.Picasso, the background structure is usually a layered planar structure that consists of one or more laterally infinite material layers always stacked along the Z-axis. In other words, the dimensions of the layers are infinite along the X and Y axes. Metallic traces are placed at the boundaries between the substrate or superstrate layers. These are modeled by perfect electric conductor (PEC) traces or conductive sheet traces of finite thickness and finite conductivity. Some layers might be separated by infinite perfectly conducting ground planes. The two sides of a ground plane can be electromagnetically coupled through one or more slots (apertures). Such slots are modeled by magnetic surface currents. Furthermore, the metallic traces can be interconnected or connected to ground planes using embedded objects. Such objects can be used to model circuit vias, plated-through holes or dielectric inserts. These are modeled as volume polarization currents.
== Building a Planar Structure ==
[[Image:PMOM11.png|thumb|250px|EM.Picasso's Navigation Tree.]]EM.Picasso is intended for constructing and modeling planar layered structures. By a planar structure we mean one that contains a background substrate of laterally infinite extents, made up of one or more material layers all stacked up vertically along === Understanding the Z-axis. Objects of finite size are then interspersed among these substrate layers. The background structure in EM.Picasso is called the "'''Layer Stack-up'''".Background Structure ===
EM.Picasso is intended for constructing and modeling planar layered structures. By a planar structure we mean one that contains a background substrate of laterally infinite extents, made up of one or more material layers all stacked up vertically along the Z-axis. Objects of finite size are then interspersed among these substrate layers. The background structure in EM.Picasso is called the "'''Layer Stack-up'''". The layer stack-up is always terminated from the top and bottom by two infinite half-spaces. The terminating half-spaces might be the free space, or a perfect conductor (PEC ground), or any material medium. Most planar structures used in RF and microwave applications such as microstrip-based components have a PEC ground at their bottom. Some structures like stripline components require two bounding grounds (PEC half-spaces) at both at their top and bottom.
[[Planar Module|Planar module]] does not allow construction of 3D CAD objects. Instead, you draw the cross section of prismatic objects as planar [[Surface Objects|surface objects]] parallel to the XY plane. [[EM.Cube]] then automatically extrudes these cross sections and constructs and displays 3D prisms over them. The prisms extend all the way across the thickness of the host substrate layer. === Defining the Layer Stack-Up ===
When you start a new project in EM.Picasso, there is always a default background structure that consists of a finite vacuum layer sandwiched between a vacuum top half-space and a PEC bottom half-space. Every time you enter the open EM.Picasso or switched to it from [[Planar Module|Planar moduleEM.Cube]]'s other modules, the '''Stack-up Settings Dialog''' opens up. This is where you define the entire background structure. Once you close this dialog, you can open it again by right clicking the '''Layer Stack-up''' item in the '''Computational Domain''' section of the Navigation Tree navigation tree and selecting '''Layer Stack-up Settings...''' from the contextual menu. Or alternatively, you can select the menu item '''Simulate > Computational Domain > Layer Stack-up Settings...'''
The Stack-up Settings dialog has two tabs: '''Layer Hierarchy''' and '''Embedded Sets'''. The Layer Hierarchy tab has a table that shows all the background layers in hierarchical order from the top half-space to the bottom half-space. It also lists the material label of each layer, Z-coordinate of the bottom of each layer, its thickness (in project units) and material properties: permittivity (e<sub>r</sub>), permeability (µ<sub>r</sub>), electric conductivity (s) and magnetic conductivity (s<sub>m</sub>). There is also a column that lists the names of embedded object sets inside each substrate layer, if any.
You can delete a layer by selecting its row in the table and clicking the '''Delete''' button. To move a layer up and down, click on its row to select and highlight it. Then click either the '''Move Up''' or '''Move Down''' buttons consecutively to move the selected layer to the desired location in the stack-up. Note that you cannot delete or move the top or bottom half-spaces.
[[Image:PMOM8(1).png|thumb|500px|EM.Picasso's Layer Stack-up Settings dialog.]]
=== Editing Substrate Layers ===
# The current version of the Planar MoM simulation engine is based on a 2.5-D MoM formulation. Only vertical volume currents and no circumferential components are allowed on embedded objects. The 2.5-D assumption holds very well in two cases: (a) when embedded objects are very thin with a very small cross section (with lateral dimensions less than 2-5% of the material wavelength) or (b) when embedded objects are very short and sandwiched between two closely spaced PEC traces or grounds from the top and bottom.
# The current release of [[EM.Cube]] allows any number of PEC via sets collocated in the same substrate layer. However, you can define only one embedded dielectric object set per substrate layer, and no vias sets collocated in the same layer. Note that the single set can host an arbitrary number of embedded dielectric objects of the same material properties.
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[[Planar Module|Planar module]] does not allow construction of 3D CAD objects. Instead, you draw the cross section of prismatic objects as planar [[Surface Objects|surface objects]] parallel to the XY plane. [[EM.Cube]] then automatically extrudes these cross sections and constructs and displays 3D prisms over them. The prisms extend all the way across the thickness of the host substrate layer.
=== Managing Objects, Traces & Sets ===
You couple two or more sources using the '''Port Definition Dialog'''. To do so, you need to change the default port assignments. First, delete all the ports that are to be coupled from the Port List of the dialog. Then, define a new port by clicking the '''Add''' button of the dialog. This opens up the Add Port dialog, which consists of two tables: '''Available''' sources on the left and '''Associated''' sources on the right. A right arrow ('''-->''') button and a left arrow ('''<--''') button let you move the sources freely between these two tables. You will see in the "Available" table a list of all the sources that you deleted earlier. You may even see more available sources. Select all the sources that you want to couple and move them to the "Associated" table on the right. You can make multiple selections using the keyboard's '''Shift''' and '''Ctrl''' keys. Closing the Add Port dialog returns you to the Port Definition dialog, where you will now see the names of all the coupled sources next to the name of the newly added port.
{{Note|It is your responsibility to set up coupled ports and coupled [[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|[[Transmission Lines|transmission lines]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]] properly. For example, to excite the desirable odd mode of a coplanar waveguide (CPW), you need to create two rectangular slots parallel to and aligned with each other and place two gap sources on them with the same offsets and opposite polarities. To excite the even mode of the CPW, you use the same polarity for the two collocated gap sources. Whether you define a coupled port for the CPW or not, the right definition of sources will excite the proper mode. The couple ports are needed only for correct calculation of the port characteristics.}}
[[File:PMOM51(2).png|800px]]