Skin Effect and Ohmic Losses

Note: The material parameters for the skin effect are defined with the DI card. The SK card then uses the label defined at the DI card.

High frequency approximation skin effect

The required parameters are $μ_{r}$ , $\tan δ_{u}$ and $σ$ (defined with the DI card). If applied to surfaces then also the thickness d is required.

The following restrictions apply:

A good conductivity is required, satisfying the condition $σ ≫ ω ε_{0}$ .
For wires the skin depth must satisfy the condition $δ_{skin} < ϱ$ where $ϱ$ is the wire radius. The surface impedance is given by $Z_{s}^{'} = \frac{1}{2 π ϱ} \sqrt{\frac{j ω μ}{σ}}$ .
For metallic surfaces the skin depth must satisfy the condition $δ_{skin} < \frac{d}{2}$ . The surface impedance is given by $Z_{s} = \frac{1}{2} \sqrt{\frac{j ω μ}{σ}}$ .

The required parameters are $μ_{r}$ , $\tan δ_{u}$ and $σ$ (defined with the DI card). If applied to surfaces then also the thickness d is required.

The following restrictions apply:

A good conductivity is required, satisfying the condition $σ ≫ ω ε_{0}$ .
For wires the skin depth must satisfy the condition $δ_{skin} > ϱ$ where $ϱ$ is the wire radius. The surface impedance is given by $Z_{s}^{'} = \frac{1}{π ϱ^{2} σ}$
For metallic surfaces the skin depth must satisfy the condition $δ_{skin} > \frac{d}{2}$ . The surface impedance is given by $Z_{s} = \frac{1}{σ d}$ .

The required parameters are $μ_{r}$ , $\tan δ_{u}$ and $σ$ (defined with the DI card). If applied to surfaces then also the thickness d is required.

The following restrictions apply:

A good conductivity is required, satisfying the condition $σ ≫ ω ε_{0}$ .
For wires with wire radius $ϱ$ the surface impedance is given by
(1) $Z_{s^{'}} = \frac{1 - j}{2 π ϱ σ δ_{s k i n}} \frac{J_{0} [(1 - j) \frac{ϱ}{δ_{s k i n}}]}{J_{1} [(1 - j) \frac{ϱ}{δ_{s k i n}}]}$
where J₀ and J₁ are Bessel functions.
For a sheet of thickness, d, with properties $ε_{c}$ , $μ_{c}$ with $ε_{c} = ε + \frac{σ}{j ω}$ the wave propagation constant in the sheet is given by $β_{c} = ω \sqrt{μ_{c} ε_{c}}$ and the wave impedance in the sheet by $η_{c} = \sqrt{\frac{μ_{c}}{ε_{c}}}$ . The reflection coefficient at the interface between the sheet and the environment is defined as $Γ = \frac{E^{-}}{E^{+}} = \frac{η_{o} - η_{c}}{η_{o} + η_{c}}$ . The surface impedance is given by
(2) $Z_{s^{'}} = η_{c} \cdot \frac{1 + Γ e^{- j 2 β_{c} d}}{1 - Γ e^{- j 2 β_{c} d} + (Γ - 1) e^{- j β_{c} d}}$