Once a mesh is generated, it stays in the memory until the structure is changed or the mesh density or other settings are modified. Every time you view mesh, the one in the memory is displayed. You can force [[EM.Cube]] to create a new mesh from the ground up by selecting '''Menu > Simulate > Discretization > Regenerate Mesh''' or by right clicking on the '''Planar Mesh''' item in the '''Discretization''' section of the Navigation Tree and selecting '''Regenerate''' from the contextual menu.
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=== Planar Mesh Density ===
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[[EM.Cube]]'s [[Planar Module]], by default, generates a hybrid mesh of your planar structure with a mesh density of 20 cells per effective wavelength. It is important to understand the concept of mesh density (either hybrid or triangular) as used by [[Planar Module]]. It gives a measure of the number of cells per effective wavelength that are placed in various regions of your planar structure. The higher the mesh density, the more cells are created on the geometrical objects. Keep in mind that only the finite-sized objects of your structure are discretized. No mesh is generated for the substrate layers of your background structure. The free-space wavelength is defined as <math>\lambda_0 = \tfrac{2\pi f}{c}</math>, where f is the center frequency of your project and c is the speed of light in the free space. The effective wavelength is defined as <math>\lambda_{eff} = \tfrac{\lambda_0}{\sqrt{\varepsilon_{eff}}}</math>, where e<sub>eff</sub> is the effective permittivity.
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The effective permittivity is defined differently for different types of traces and embedded object sets. For metal and conductive sheet traces, the effective permittivity is defined as the larger of the permittivity of the two substrate layers just above and below the metallic trace. For slot traces, the effective permittivity is defined as the mean (average) of the permittivity of the two substrate layers just above and below the metallic trace. These definitions of effective permittivity are consistent with the effective propagation constant of [[Transmission Lines|transmission lines]] realized on such trace types. For embedded object sets, the effective permittivity is defined as the largest of the permittivities of all the substrate layers and embedded dielectric sets. In all cases, for the purpose of calculating the effective wavelength, only the real part of the permittivities are considered. The reason for using an effective wavelength so defined for determination of mesh resolution is to make sure that enough cells are placed in areas that might feature higher field concentration.
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Due to the different definitions of effective wavelength in different parts of your planar structure, you will see different mesh resolutions. For example, if you structure has several substrate layers with different permittivities, the mesh of metal traces on layers with a higher permittivity value will feature more cells than the mesh of metal traces on layers with a lower permittivity value even though the mesh density value is the same for the whole structure.
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[[File:PMOM30.png|800px]]
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Mesh of two rectangular patches at two different planes. The lower substrate layer has a higher permittivity.
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=== Customizing A Planar Mesh ===
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You can change the settings of the planar mesh including the mesh type and density from the planar Mesh Settings Dialog. You can also change these settings while in the mesh view mode, and you can update the changes to view the new mesh. To open the mesh settings dialog, either click the '''Mesh Settings''' [[File:mesh_settings.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Discretization > Mesh Settings...''', or by right click on the '''Planar Mesh''' item in the '''Discretization''' section of the Navigation Tree and select '''Mesh Settings...''' from the contextual menu, or use the keyboard shortcut '''Ctrl+G'''. You can change the mesh algorithm from the dropdown list labeled '''Mesh Type''', which offers two options: '''Hybrid''' and '''Triangular'''. You can also enter a different value for '''Mesh Density''' in cells per effective wavelength (λ<sub>eff</sub>). For each value of mesh density, the dialog also shows the average "Cell Edge Length" in the free space. To get an idea of the size of mesh cells on the traces and embedded object sets, divide this edge length by the square root of the effective permittivity a particular trace or set. Click the '''Apply''' button to make the changes effective.
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[[File:PMOM31.png]]
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The Planar Mesh Settings dialog.
=== Mesh Of Connected Trace Objects ===
Mesh of a vertical PEC via connecting two horizontal metallic strips. The shorter via has one prismatic cell along the Z direction, while the longer via is discretized into several stacked cells.
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=== Planar Mesh Density ===
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[[EM.Cube]]'s [[Planar Module]], by default, generates a hybrid mesh of your planar structure with a mesh density of 20 cells per effective wavelength. It is important to understand the concept of mesh density (either hybrid or triangular) as used by [[Planar Module]]. It gives a measure of the number of cells per effective wavelength that are placed in various regions of your planar structure. The higher the mesh density, the more cells are created on the geometrical objects. Keep in mind that only the finite-sized objects of your structure are discretized. No mesh is generated for the substrate layers of your background structure. The free-space wavelength is defined as <math>\lambda_0 = \tfrac{2\pi f}{c}</math>, where f is the center frequency of your project and c is the speed of light in the free space. The effective wavelength is defined as <math>\lambda_{eff} = \tfrac{\lambda_0}{\sqrt{\varepsilon_{eff}}}</math>, where e<sub>eff</sub> is the effective permittivity.
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The effective permittivity is defined differently for different types of traces and embedded object sets. For metal and conductive sheet traces, the effective permittivity is defined as the larger of the permittivity of the two substrate layers just above and below the metallic trace. For slot traces, the effective permittivity is defined as the mean (average) of the permittivity of the two substrate layers just above and below the metallic trace. These definitions of effective permittivity are consistent with the effective propagation constant of [[Transmission Lines|transmission lines]] realized on such trace types. For embedded object sets, the effective permittivity is defined as the largest of the permittivities of all the substrate layers and embedded dielectric sets. In all cases, for the purpose of calculating the effective wavelength, only the real part of the permittivities are considered. The reason for using an effective wavelength so defined for determination of mesh resolution is to make sure that enough cells are placed in areas that might feature higher field concentration.
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Due to the different definitions of effective wavelength in different parts of your planar structure, you will see different mesh resolutions. For example, if you structure has several substrate layers with different permittivities, the mesh of metal traces on layers with a higher permittivity value will feature more cells than the mesh of metal traces on layers with a lower permittivity value even though the mesh density value is the same for the whole structure.
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[[File:PMOM30.png|800px]]
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Mesh of two rectangular patches at two different planes. The lower substrate layer has a higher permittivity.
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=== Customizing A Planar Mesh ===
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You can change the settings of the planar mesh including the mesh type and density from the planar Mesh Settings Dialog. You can also change these settings while in the mesh view mode, and you can update the changes to view the new mesh. To open the mesh settings dialog, either click the '''Mesh Settings''' [[File:mesh_settings.png]] button of the '''Simulate Toolbar''' or select '''Menu > Simulate > Discretization > Mesh Settings...''', or by right click on the '''Planar Mesh''' item in the '''Discretization''' section of the Navigation Tree and select '''Mesh Settings...''' from the contextual menu, or use the keyboard shortcut '''Ctrl+G'''. You can change the mesh algorithm from the dropdown list labeled '''Mesh Type''', which offers two options: '''Hybrid''' and '''Triangular'''. You can also enter a different value for '''Mesh Density''' in cells per effective wavelength (λ<sub>eff</sub>). For each value of mesh density, the dialog also shows the average "Cell Edge Length" in the free space. To get an idea of the size of mesh cells on the traces and embedded object sets, divide this edge length by the square root of the effective permittivity a particular trace or set. Click the '''Apply''' button to make the changes effective.
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[[File:PMOM31.png]]
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The Planar Mesh Settings dialog.
=== Refining Mesh At Discontinuities ===