Rough surfaces impede current flow compared to smooth surfaces.Īll real surfaces, however, have some roughness, which may be significant. Curved boundaries will be resolved to within the accuracy of the finite element mesh used, the geometric discretization error, as discussed here. A planar boundary is assumed to be geometrically perfect. So far, with both the TBC and the IBC, we have assumed that the surfaces are perfect. The Transition boundary condition computes a surface current on either side of the boundary. For an example of using this boundary condition, see the Beam Splitter tutorial, which models a thin layer of silver via a complex-valued permittivity. Additionally, the total losses through the thickness of the film are computed. That is, the TBC will lead to a drop in the transmitted electric field.įrom a computational point of view, the number of degrees of freedom on the boundary is doubled to compute the electric field on either surface of the TBC, as shown below. These are used to relate the current flowing on the surface of either side of the film. The TBC takes the material properties as well as the thickness of the film as inputs, computing an impedance through the thickness of the film as well as a tangential impedance.
#Qucs simulation sharp transitions trouble skin#
The TBC can be used even if the thickness is many times greater than the skin depth. The Transition boundary condition (TBC) is appropriate for a layer of conductive material with a thickness relatively smaller than the characteristic size, and curvature, of the objects being modeled. We will instead want to use the Transition boundary condition. Now, what if we are dealing with an object that has one dimension that is much smaller than the others, perhaps a thin film of material like aluminum foil? In that case, the skin depth in one direction may actually be comparable to the thickness, so the electromagnetic fields will partially penetrate through the material. Sharp-edged objects such as wedges will have some inaccuracy at the corners, but this is a local effect and also an inherent issue whenever a sharp corner is introduced into the model, as discussed in this previous blog post. The IBC becomes increasingly accurate as L_c / \delta \rightarrow \infty however, it is accurate even when L_c / \delta \gt > 10 for smooth objects like spheres. For an example of the appropriate usage of the IBC and a comparison with analytic results, please see the Computing Q-Factors and Resonant Frequencies of Cavity Resonators tutorial. Additionally, the IBC computes losses due to the finite conductivity. Thus, we can avoid meshing the interior of these domains and save significant computational effort. With the Impedance boundary condition (IBC), we are able to avoid modeling Maxwell’s equations in the interior of any of the model’s metal domains by assuming that the currents flow entirely on the surface. The Impedance boundary condition is appropriate if the skin depth is much smaller than the object. From the point of view of the electromagnetic wave, this is true, since L_c \gg \delta means that the wave does not penetrate through the object. In this situation, it is appropriate to use the Impedance boundary condition, which treats any material “behind” the boundary as being infinitely large. So, from a modeling point of view, we can treat the currents as flowing on the surface. Although there are currents flowing inside of the object, the skin effect drives these currents to the surface. That is, the object is much larger than the skin depth. Let’s consider an object in which L_c \gg \delta. Depending on the situation, the characteristic size can be defined as the ratio of volume to surface area or as the thickness of the thinnest part of the object being simulated. There are different ways of defining L_c. Now that we have the skin depth, we will want to compare this to the characteristic size, L_c, of the object we are simulating. The skin depth, along with your knowledge of the dimensions of the part, will determine if it is possible to use the Impedance boundary condition or the Transition boundary condition. \nabla \times \left( \mu_r^īefore you even begin your modeling in COMSOL Multiphysics, you should compute or have some rough estimate of the skin depth of all of the materials you are modeling.
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