Layered Impedance Boundary Condition

The is an extension of the that allows to model a sequence of geometrically thin layers on top of a substrate. It is used on exterior boundaries where the field is known to penetrate only a short distance outside the boundary. In brief, this feature combines a with an of the type:

The layer stack is built using a . For each layer in the , the transfer and surface impedances are obtained from the layer thickness and the 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. The mathematical details relative to the field propagation in the layer stack can be found in the Layered Transition Boundary Condition section.

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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.


	The Layered Impedance Boundary Condition is based on the assumption that in the thin layers and in the substrate the wave propagates essentially in the normal direction. Thus, the wave could be incident in the normal direction or the wave could be refracted to propagate in a direction close to the normal direction. The latter condition is fulfilled for a good conductor. The thickness of the layer should be less than the radius of curvature for the boundary.

Shell properties

The section displays which is coupled to the .

Clear the check box in order to select a specific from the list. The feature is then applicable only on the boundaries where the chosen is defined.

You can visualize the selected and the layers that constitute it by clicking the and buttons.

The thickness of the should be set as follows, depending on the type of material:

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For a general , added through a or a , the is set in the section of the window. Several layers may be defined in the table, and the should be defined for each of them. The total thickness of the is the sum of all the layers thicknesses.

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When the is a , the is set in the section in the window. Alternatively it can be set in the section of the property group window.

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In a node, the layer is set in the section by adding a property group from the section in the material window. This automatically adds a subnode under the node, transforming it into a .

Layer PROPERTIES

The section specifies the material properties of the thin layers constituting the stack located on top of the substrate. Select an — (the default), , , , , , or . See the Wave Equation, Electric node, Electric Displacement Field section, for all settings.

The defaults use the values . In this case, the material properties are taken layer by layer from the existing on those boundaries where the feature is enabled. Otherwise, choose and enter a value or an expression. In the latter case all layers constituting the chosen will take on the same given value for the selected material property.

SUBSTRATE PROPERTIES

The section specifies the material properties of the thick domain that is not included in the model, being approximated by an . Select a from the list of materials that have been introduced in the model previously. Select an — (the default), , , , , , or . See the Wave Equation, Electric node, Electric Displacement Field section, for all settings.

The defaults use the values . In this case, the material properties are taken from the specified . Otherwise, choose and enter a value or an expression.

See Skin Depth Calculator to evaluate the skin depth of a homogeneous material.