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| style="width:360px;" | Radiation and scattering problems involving metals and homogeneous dielectric materials
|}
 
== The Composition of Physical Structure ==
 
[[Image:MAT1.png|thumb|400px|A structure made up of a PEC plate and different dielectric materials.]]
Your '''Physical Structure''' in [[EM.Cube]] consists of a number of CAD objects you draw in the project workspace. In all [[EM.Cube]] modules, you use [[CubeCAD]]'s common drawing tools and/or its import capability to construct your geometrical structure. In order to perform an electromagnetic simulation, you need to assign material properties to all of your CAD objects in the project workspace. The drawn CAD objects are organized together based on their common properties under one or more object groups or nodes in the '''Navigation Tree'''. The grouping of CAD objects is essentially based on their material composition and their associated boundary conditions.
 
Among [[EM.Cube]]'s computational modules, [[EM.Tempo]] is the most comprehensive in view of material variety offering. [[EM.Ferma]] and [[EM.Libera]] offer PEC and dielectric material groups similar to [[EM.Tempo]]. [[EM.Illumina]] offers PEC, PMC and impedance surfaces. [[EM.Terrano]] groups objects into material [[Block Types|block types]] that are characterized by their ray interaction properties. [[EM.Picasso]] groups objects based on their trace location (i.e. Z-coordinate) in the substrate layer hierarchy.
 
== Variety of Material Types in EM.Cube ==
 
From an electromagnetic analysis point of view, materials are categorized by the constitutive relations or boundary conditions that relate electric and magnetic fields. [[EM.Cube]] offers a large variety of material types listed in the table below:
{| class="wikitable"
|-
! scope="col"| Material Type
! scope="col"| Supporting Module(s)
|-
| Perfect Electric Conductor (PEC)
| [[EM.Tempo]], [[EM.Illumina]], [[EM.Ferma]], [[EM.Picasso]], [[EM.Libera]]
|-
| Perfect Magnetic Conductor (PMC)
| [[EM.Tempo]], [[EM.Illumina]], [[EM.Picasso]]
|-
| Dielectric
| [[EM.Tempo]], [[EM.Ferma]], [[EM.Picasso]], [[EM.Libera]], [[EM.Terrano]]
|-
| Impedance Surface
| [[EM.Illumina]]
|-
| Conductive Sheet
| [[EM.Picasso]]
|-
| Anisotropic Material
| [[EM.Tempo]]
|-
| Dispersive Material
| [[EM.Tempo]]
|-
| Inhomogeneous Material
| [[EM.Tempo]]
|-
| Thin Wire
| [[EM.Tempo]], [[EM.Libera]]
|}
 
== Constitutive Parameters of a Material Medium ==
 
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 (&sigma;<sub>m</sub>) having units of &Omega;/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 &epsilon;<sub>0</sub> = 8.854e-12 F/m, &mu;<sub>r</sub> = 1.257e-6 H/m, and &epsilon;<sub>r</sub> and &mu;<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>j&omega;t</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 &omega; = 2&pi;f, 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''': &epsilon;<sub>r</sub> = &mu;<sub>r</sub> = 1 and &sigma; = &sigma;<sub>m</sub> = 0
* '''Perfect Electric Conductor (PEC)''': &epsilon;<sub>r</sub> = &mu;<sub>r</sub> = 1, &sigma; = &infin;, &sigma;<sub>m</sub> = 0
* '''Perfect Magnetic Conductor (PMC)''': &epsilon;<sub>r</sub> = &mu;<sub>r</sub> = 1, &sigma; = 0, &sigma;<sub>m</sub> = &infin;
Kazem Sabet
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