CST2013: Materials / Tabulated Surface Impedance

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The built-in lossy metal material model assumes that the skin depth is much smaller than the metal thickness, which is not the case at low frequencies or for thin metal layers. This macro allows to generate tabulated surface impedance data that is accurate for such cases. At low frequencies, the data calculated by this macro tends to the true DC resistance and at high frequencies, the data approaches the lossy metal material. Thus, data generated by this macro can be used for broadband calculations.

In addition, the macro also allows to consider the dispersive effects of layered materials, frequency-dependent permeabilities, or surface roughness.

General Settings

Material folder: The material folder in which the material will be stored.

Material name: The material name.

Number of frequency samples: The number of samples in the table.

Logarithmic sampling: If this is checked, the frequency samples will be distributed logarithmically. If unchecked, they will be distributed linearly.

Error limit for data fit: For time-domain simulations, the data created by this macro needs to be fitted by a set of well-defined functions. (See Material Overview HF, general nth order model.) This error limit describes the largest acceptable error between table data and fit.

Cross Section

The model assumes a one-dimensional geometry where the lateral layer dimensions are much larger than the layer thickness. This is typically a reasonable assumption, especially towards higher frequencies. The largest error caused by this assumption occurs at DC. The user may enter the true width-to-height ratio of the layer cross section to correct for this error at DC.

Layer configuration: One, two, or three layers are possible. In the case of three layers, top and bottom layers must be identical.

Width-to-height ratio of total cross section: The ratio of the layer width to its total thickness (sum of all layer thicknesses).

Coated side walls: If this option is checked, the outer layer material is assumed to cover the left and right side walls of the conductor. If unchecked, a sandwich geometry is assumed.

Note: For clarity, the wording in the following paragraphs describes symmetric three-layer configuration with one inner layer and two outer layers (top and bottom). For the two-layer configuration, the "outer" layer becomes the top layer and the "inner" layer becomes the bottom layer. For the one-layer configuration, the "inner" layer is the only layer.

Outer Layer(s)

Thickness1: Thickness of each top and bottom layer in project units.

Conductivity1: Electric conductivity in S/m of outer material.

Mue_r1: Relative permeability of outer material. The user may enter a frequency-dependent expression in which the frequency is represented by the capitalized variable 'F' (not 'f').

Enforce causality for mue: See under "Inner Layer".

DeltaRMS1: Surface roughness (RMS) of the outer layers in um.

Enforce causality for roughness: See under "Inner Layer".

Inner Layer

Thickness2: Thickness of the inner layer in project units.

Conductivity2: Electric conductivity in S/m of the inner material.

Mue_r2: Relative permeability of the inner material. The user may enter a frequency-dependent expression in which the frequency is represented by the capitalized variable 'F' (not 'f').

Enforce causality for mue: To ensure causality, real and imaginary part of mue need to fulfil the Kramers-Kronig relation. Depending on the frequency-dependent expression used for mue_r, this relation might be violated. For example, measured data of the real part of mue_r generally leads to non-causal results if the imaginary part is ignored and set to zero. If this option is checked, the macro will construct an imaginary part of mue_r by means of a Hilbert transform of the real part, such that Kramers-Kronig is fulfilled.

Please note that this option may add considerable runtime to the macro execution so it should only be switched on if needed. This option is currently in experimental stage.

In particular for the case of a constant, purely real mue_r (e.g., mue_r=1), Kramers-Kronig is fulfilled and this option should NOT be used.

DeltaRMS2: Surface roughness (RMS) of the inner layer in um.

Enforce causality for roughness: This macro uses the Hammerstad-Jensen model to describe the effect of surface roughness on the conductivity. The Hammerstad-Jensen model is an empirical model for the real part of the conductivity kappa and generally leads to violation of Kramers-Kronig. If this option is checked, the macro will construct an imaginary part of kappa by means of a Hilbert transform of the Hammerstad-Jensen-modified real part, such that Kramers-Kronig is fulfilled. Please note that this option may add

considerable runtime to the macro execution so it should only be switched on if needed. This option is currently in experimental stage.

Create Material: This button starts the macro execution. The table data will be calculated and the material will be added to the model. If a material with the same name already exists, it will be replaced by the new data.

Exit: Closes the macro.