Layered Transition Boundary Condition
The Layered Transition Boundary Condition is an extension of the Transition Boundary Condition that allows to model a sequence of thin metallic layers using a Layered Material. It represents a discontinuity in the tangential electric field. For each layer in the Layered Material, the transfer and surface impedances are obtained from the layer thickness and material properties. The impedances are then used to relate the discontinuity in the tangential electric field to the current flowing on the surface of either side (up/down) of the corresponding layer. Mathematically this reads:
where the index i = 1, 2,..., n refers to the layer number. The system of equations above is solved for each layer in the Layered Material. The index i has been omitted from the expressions of the impedances and the wave vector k in order to improve their readability.
Figure 5-5: The layered material is composed of n layers. The surface currents on the up and downside of each layer are determined from the transfer and surface impedances and are functions of the tangential electric fields.
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For more information, see Layer and Interface Selection Tools.
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See Layered Material, Layered Material Link, Layered Material Stack, Layered Material Link (Subnode), and Single Layer Materials in the COMSOL Multiphysics Reference Manual for details on the definition of layered materials.
Shell Properties
The Shell Properties section displays which layered material(s) the Layered Transition Boundary Condition is coupled to.
Clear the Use all layers check box in order to select a specific layered material from the list. The Layered Transition Boundary Condition feature is then applicable only on the boundaries where the chosen material is defined.
You can visualize the selected layered material and the layers that constitute it by clicking the Layer Cross Section Preview and Layer 3D Preview buttons.
The thickness of the layered material should be set as follows, depending on the type of material:
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In a Material node, the layer Thickness is set in the Material Contents section by adding a Shell property group from the Material Properties section in the material Settings window. This automatically adds a Shell subnode under the Material node, transforming it into a layered material.
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When the layered material is a Single Layer Material, the Thickness is set in the Material Contents section in the Settings window. Alternatively it can be set in the Layer Definition section of the Shell property group Settings window.
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For a general Layered Material, added through a Layered Material Link or a Layered Material Stack, the Thickness is set in the Layer Definition section of the Settings window. Several layers may be defined in the table, and the Thickness should be defined for each of them. The total thickness of the layered material is the sum of all the layers thicknesses.
Layered Transition Boundary Condition
The Layered Transition Boundary Condition section lists the material properties of the thin layered material that this boundary condition approximates:
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Relative permittivity, εr (dimensionless)
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Relative permeability, μr (dimensionless)
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Electrical conductivity, σ (SI unit: S/m)
The defaults use the values From material, taking the properties from the layered material specified for the boundary. Otherwise, choose User defined and enter different values or expressions. In the latter case all layers constituting the layered material will take on the same value for the selected property.