A physical structure in [[EM.Cube]] in made up of a number of geometric objects you either draw in the project workspace or import from an external CAD model file. In [[CubeCAD]], geometric objects are grouped together simply by their color. They do not have any physical properties. However, in all of [[EM.Cube]]'s computational modules, you need to assign physical properties to each geometric object. In these modules, geometric objects are grouped together by their common physical properties. The physical properties may differ in different computational modules, but they are typically the same as the material properties or related boundary conditions.
From an electromagnetic modeling point of view, materials are categorized by the constitutive relations or boundary conditions that relate electric and magnetic fields. In general, an isotropic material medium is macroscopically characterized by four constitutive parameters: * Permittivity (ε) having units of F/m* Permeability (μ) having units of H/m * Electric conductivity (σ) having units of S/m* Magnetic conductivity (σ<sub>m</sub>) having units of Ω/m The permittivity and permeability of a material are typically related to the permittivity and permeability of the free space as follows: :<math> \epsilon = \epsilon_r \epsilon_0 </math> :<math> \mu = \mu_r \mu_0, \quad \quad </math> where ε<sub>0</sub> = 8.854e-12 F/m, μ<sub>r</sub> = 1.257e-6 H/m, and ε<sub>r</sub> and μ<sub>r</sub> are called relative permittivity and permeability of the material, respectively. The constitutive parameters relate the field quantities in the material medium: :<math> \mathbf{D} = \epsilon \mathbf{E}, \quad \quad \mathbf{J} = \sigma \mathbf{E} </math> :<math> \mathbf{B} = \epsilon \mathbf{H}, \quad \quad \mathbf{M} = \sigma_m \mathbf{H} </math> where '''E''' and '''H''' are the electric and magnetic fields, respectively, '''D''' is the electric flux density, also known as the electric displacement vector, '''B''' is the magnetic flux density, also known as the magnetic induction vector, and '''J '''and '''M '''are the electric and magnetic current densities, respectively.  The electric conductivity and magnetic conductivity parameters represent the material losses. In frequency-domain simulations under a time-harmonic (e<sup>jωt</sup>) field assumption, it is often convenient to define a complex relative permittivity and a complex relative permeability in the following manner:  :<math> \epsilon_r = \epsilon^{\prime}_r -j\epsilon^{\prime\prime}_r = \epsilon^{\prime}_r -j\frac{\sigma}{\omega \epsilon_0} </math> :<math> \mu_r = \mu^{\prime}_r -j\mu^{\prime\prime}_r = \mu^{\prime}_r - j\frac{\sigma_m}{\omega \mu_0}</math> where ω = 2πf, and f is the operational frequency. It is also customary to define electric and magnetic loss tangents as follows: :<math> \tan \delta = \epsilon^{\prime\prime}_r / \epsilon^{\prime}_r </math> :<math> \tan \delta_m = \mu^{\prime\prime}_r / \mu^{\prime}_r </math> Three special media frequently encountered in electromagnetic problems are: * '''Vacuum''' or '''Free Space''': ε<sub>r</sub> = μ<sub>r</sub> = 1 and σ = σ<sub>m</sub> = 0* '''Perfect Electric Conductor (PEC)''': ε<sub>r</sub> = μ<sub>r</sub> = 1, σ = ∞, σ<sub>m</sub> = 0* '''Perfect Magnetic Conductor (PMC)''': ε<sub>r</sub> = μ<sub>r</sub> = 1, σ = 0, σ<sub>m</sub> = ∞
== Constitutive Parameters of a Material Medium ==
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In general, an isotropic material medium is macroscopically characterized by four constitutive parameters:
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* Permittivity (ε) having units of F/m
* Permeability (μ) having units of H/m
* Electric conductivity (σ) having units of S/m
* Magnetic conductivity (σ<sub>m</sub>) having units of Ω/m
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The permittivity and permeability of a material are typically related to the permittivity and permeability of the free space as follows:
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:<math> \epsilon = \epsilon_r \epsilon_0 </math>
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:<math> \mu = \mu_r \mu_0, \quad \quad </math>
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where ε<sub>0</sub> = 8.854e-12 F/m, μ<sub>r</sub> = 1.257e-6 H/m, and ε<sub>r</sub> and μ<sub>r</sub> are called relative permittivity and permeability of the material, respectively.
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The constitutive parameters relate the field quantities in the material medium:
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:<math> \mathbf{D} = \epsilon \mathbf{E}, \quad \quad \mathbf{J} = \sigma \mathbf{E} </math>
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:<math> \mathbf{B} = \epsilon \mathbf{H}, \quad \quad \mathbf{M} = \sigma_m \mathbf{H} </math>
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where '''E''' and '''H''' are the electric and magnetic fields, respectively, '''D''' is the electric flux density, also known as the electric displacement vector, '''B''' is the magnetic flux density, also known as the magnetic induction vector, and '''J '''and '''M '''are the electric and magnetic current densities, respectively.
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The electric conductivity and magnetic conductivity parameters represent the material losses. In frequency-domain simulations under a time-harmonic (e<sup>jωt</sup>) field assumption, it is often convenient to define a complex relative permittivity and a complex relative permeability in the following manner:
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:<math> \epsilon_r = \epsilon^{\prime}_r -j\epsilon^{\prime\prime}_r = \epsilon^{\prime}_r -j\frac{\sigma}{\omega \epsilon_0} </math>
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:<math> \mu_r = \mu^{\prime}_r -j\mu^{\prime\prime}_r = \mu^{\prime}_r - j\frac{\sigma_m}{\omega \mu_0}</math>
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where ω = 2πf, and f is the operational frequency. It is also customary to define electric and magnetic loss tangents as follows:
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:<math> \tan \delta = \epsilon^{\prime\prime}_r / \epsilon^{\prime}_r </math>
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:<math> \tan \delta_m = \mu^{\prime\prime}_r / \mu^{\prime}_r </math>
Three special media frequently encountered in electromagnetic problems are:
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* '''Vacuum''' or '''Free Space''': ε<sub>r</sub> = μ<sub>r</sub> = 1 and σ = σ<sub>m</sub> = 0
* '''Perfect Electric Conductor (PEC)''': ε<sub>r</sub> = μ<sub>r</sub> = 1, σ = ∞, σ<sub>m</sub> = 0
* '''Perfect Magnetic Conductor (PMC)''': ε<sub>r</sub> = μ<sub>r</sub> = 1, σ = 0, σ<sub>m</sub> = ∞
== Variety of Source Types in EM.Cube ==