# Glossary of EM.Cube's Materials & Other Physical Object Types

## Anisotropic Material

ICON:

MODULE: EM.Tempo

FUNCTION: Defines an isotropic material object group with four constitutive tensors

TO DEFINE AN ANISOTROPIC MATERIAL GROUP:

1. Right-click on the Anisotropic Materials item in the navigation tree.
2. Select Insert New Isotropic Material... to open up the Isotropic Material dialog.
3. Click the OK button of the dialog to return to the project workspace.

NOTES, SPECIAL CASES OR EXCEPTIONS: EM.Tempo allows you to define a general anisotropic material, whose constitutive parameters, i.e. permittivity (ε), permeability (μ), electrical conductivity (σ) and magnetic conductivity (σm), are all tensorial in nature. Each constitutive parameter in this case is represented by a 3×3 matrix:

A Uniaxial material is a special case of an anisotropic material whose constitutive parameters are all diagonal matrices. Specifying an anisotropic material as Uniaxial in the FDTD Module has a very important computational implication. There are six field update equations for uniaxial materials at each time steps: three for the electric field and three for the magnetic field. In this respect, a uniaxial material is similar to an isotropic dielectric material. On the other hand, a fully anisotropic material with non-zero off-diagonal constitutive matrix elements requires twelve update equations at each time step: three equations for the three components of each of the four vector fields E, D, H and B. As a result, the time loop for fully anisotropic materials takes much longer time than uniaxial materials.

PYTHON COMMAND: None

ANISOTROPIC MATERIAL PARAMETERS

Parameter Name Value Type Units Default Value Notes
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The anisotropic material dialog showing the properties of a uniaxial material.

## Conductive Sheet Trace

ICON:

MODULE: EM.Picasso

FUNCTION: Defines a conductive sheet trace group

TO DEFINE A CONDUCTIVE SHEET GROUP:

1. Right-click on the Conductive Sheet Traces item in the navigation tree.
2. Select Insert New Conductive Sheet Trace... to open up the Conductive Sheet Trace dialog.
3. Besides the color and texture properties, you have to enter values for the Electric Conductivity σ in S/m and the sheet Thickness in the project units.
4. Click the OK button of the dialog to return to the project workspace.

NOTES, SPECIAL CASES OR EXCEPTIONS: In EM.Picasso, you may model imperfect metals using conductive sheet traces, which are an example of impedance surfaces. Keep in mind that you can typically model most lossless metallic traces such as micstorip lines and planar patches using PEC groups. A PEC trace is assumed to have an infinite electric conductivity and a zero metallization thickness. But also remember that since EM.Picasso's simulation engine is based on the 2.5-D method of moments (MoM), lossy embedded dielectric objects with a large σ cannot represent an imperfect metal because can only support vertical currents. A Conductive Sheet Trace group has a finite electric conductivity σ and a small nonzero finite thickness expressed in the project units.

The conductive sheet traces are modeled using the surface impedance boundary condition stated above. If the thickness of the sheet is greater than the skin depth of the metal at the project frequency, then the surface impedance is given by

$Z_s = \dfrac{1+j}{\sigma \delta}, \quad \delta = \sqrt{\dfrac{2}{k_0 Z_0 \sigma}}$

If the thickness t of the sheet is less than the skin depth, then the conductive sheet transition boundary condition is used instead, and the surface impedance is given by

$Z_s = \dfrac{1}{[j k_0 Y_0 (\varepsilon_r - 1) + \sigma] \tau} = \dfrac{1}{\sigma_{tot} \tau}$

PYTHON COMMAND: conductive_sheet_group(label,sigma,thickness)

CONDUCTIVE SHEET PARAMETERS

Parameter Name Value Type Units Default Value Notes
sigma (σ) Real Numeric S/m 5.8e+7 electric conductivity
thickness Real Numeric project units 1.0 finite metallization thickness
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The conductive sheet trace dialog.

## Dielectric Material

ICON:

MODULE: EM.Tempo, EM.Ferma, EM.Libera

FUNCTION: Defines a dielectric material object group with specified constitutive parameters

TO DEFINE A DIELECTRIC GROUP:

1. Right-click on the Dielectric Materials or Dielectric Objects item in the navigation tree.
2. Select Insert New Dielectric... to open up the New Dielectric Material dialog.
3. You have two options to choose from: Uniform and Inhomogeneous.
4. If you choose the uniform option, you have to enter numeric values for relative permittivity εr, electric conductivity σ in S/m, relative permittivity μr, magnetic conductivity σm in Ω/m and mass density in kg/m3. The default values are εr = μr = 1, σ = σm = 0, and ρV = 1. You can also enter numeric values for Thermal Conductivity in W/(m.K) and Specific Heat Capacity in J/(kg.K). These parameters are used for thermal simulation in EM.Ferma.
5. If you choose the inhomogeneous option, you have to enter mathematical or Python expressions in the global (x,y,z) coordinates for all the constituent parameters.
6. Change the color of the material group if necessary.
7. Click the OK button of the dialog to return to the project workspace.

NOTES, SPECIAL CASES OR EXCEPTIONS: The inhomogeneous option is available only in EM.Tempo and EM.Ferma. Although in this mode you may enter numeric values as valid mathematical or Python expressions, beware of the fact that the Python expressions are evaluated at every single mesh point. This may take a very long processing time for large meshes.

PYTHON COMMAND: dielectric_group(label,eps,sigma,mu,sigma_m[,rr,gg,bb])

DIELECTRIC PARAMETERS

Parameter Name Value Type Units Default Value Notes
eps (εr) Real Numeric - 1.0 relative permittivity
sigma (σ) Real Numeric S/m 0.0 electric conductivity
mu (μr) Real Numeric - 1.0 relative permeability
sigma_m (σm) Real Numeric Ohm/m 0.0 magnetic conductivity
loss_tangent Real Numeric - 0.0 dielectric loss tangent
mass_dens (ρV) Real Numeric kg/m3 1.0 volume mass density
thermal_cond Real Numeric W/(m.K) 0.0 thermal conductivity
spec_cap Real Numeric J/(kg.K) 0.0 specific heat capacity
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The dielectric material dialog showing a uniform dielectric material. The dielectric material dialog showing an inhomogeneous dielectric material with a parabolic permittivity profile. In the expression, h is a project variable and rect(z) is the pulse function.

## Dispersive Material

ICON:

MODULE: EM.Tempo

FUNCTION: Defines a dispersive material object group with specified poles

TO DEFINE A DISPERSIVE MATERIAL GROUP:

1. Right-click on the Dispersive Materials item in the navigation tree.
2. Select Insert New Debye Material... or Insert New Drude Material... or Insert New Lorentz Material... or Insert New Generalized Metamaterial... or to open up one of the four Dispersive Material dialogs.
3. You have to define each pole of the dispersive material individually. You can add as many poles as you want using the Add Pole button of the dialog.
4. Click the OK button of the dialog to return to the project workspace.

NOTES, SPECIAL CASES OR EXCEPTIONS: EM.Tempo currently offers four types of dispersive material:

1. Debye Material
2. Drude Material (Unmagnetized Plasma)
3. Lorentz Material
4. Generalized Metamaterial

The FDTD simulation engine uses the Auxiliary Differential Equation (ADE) method to model dispersive materials. EM.Cube allows you to define an arbitrary number of poles for each of the above dispersive material types. Keep in mind that all the objects belonging to the same dispersive material group have the same dispersion properties.

The complex permittivity of a Debye material with N poles is given by:

$\varepsilon (\omega) = \varepsilon_\infty + \sum_{p=1}^N \dfrac{\Delta \varepsilon_p}{1 + j\omega \tau_p}, \quad \Delta \varepsilon_p = \varepsilon_{sp} - \varepsilon_\infty$

where $\varepsilon_{\infty}$ is the value of the permittivity at infinite frequency, $\tau_p$ is the relaxation time corresponding to the pth pole having the unit of seconds, and $\varepsilon_{sp}$ is the value of the static permittivity (at DC) corresponding to the pth pole. $\Delta \varepsilon_p = \varepsilon_{sp} - \varepsilon_{\infty}$ represents the change in permittivity due to the pth pole.

Unmagnetized plasmas are typically modeled as Drude materials. The complex permittivity of a Drude material with N poles is given by:

$\varepsilon(\omega) = \varepsilon_{\infty} - \sum_{p=1}^N \dfrac{{\omega_p}^2}{\omega^2 - j\omega \nu_p}$

where $\omega_p$ and $\nu_p$ are the angular plasma frequency and angular collision frequency corresponding to the pth pole, respectively, and both are expressed in rad/s. For an unmagnetized plasma, $\varepsilon_{\infty} = 1$.

The complex permittivity of a Lorentz material with N poles is given by:

$\varepsilon(\omega) = \varepsilon_{\infty} - \sum_{p=1}^N \dfrac{\Delta \varepsilon_p {\omega_p}^2}{\omega^2 - 2j\omega \delta_p - {\omega_p}^2}, \quad \Delta \varepsilon_p = \varepsilon_{sp} - \varepsilon_{\infty}$

where $\omega _p$ and $\delta_p$ are the angular resonant frequency and angular damping frequency corresponding to the pth pole, respectively, and both are expressed in rad/s. Similar to a Debye material, $\Delta \varepsilon_p = \varepsilon_{sp} - \varepsilon_{\infty}$ represents the change in permittivity due to the pth pole.

The Debye, Drude and Lorentz dispersive materials are all isotropic dielectric materials having a scalar relative permittivity that varies with the frequency. A generalized metamaterial in EM.Tempo is defined as a uniaxial dispersive material that has three relative permittivities εr,xx, εr,yy, εr,zz and three relative permeabilities μr,xx, μr,yy, and μr,zz. These six quantities can independently be functions of the frequency in general or non-dispersive. Moreover, you can define poles of different kind for each constitutive parameter. The pole type can be Debye, Drude or Lorentz.

PYTHON COMMAND: None

DISPERSIVE MATERIAL PARAMETERS

Parameter Name Value Type Units Default Value Notes
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The Debye dispersive material dialog. Defining the parameters of a Debye-Type pole in the "Add Pole" dialog.
 The Drude dispersive material dialog. Defining the parameters of a Drude-Type pole in the "Add Pole" dialog.
 The Lorentz dispersive material dialog. Defining the parameters of a Lorentz-Type pole in the "Add Pole" dialog.
 The generalized metamaterial dialog. Defining the parameters of a Drude-Type pole for εr,xx in the "Add Pole" dialog.

## Embedded Dielectric Object Set

ICON:

MODULE: EM.Picasso

FUNCTION: Defines an embedded dielectric object set group

TO DEFINE AN EMBEDDED DIELECTRIC SET:

1. Right-click on the Embedded Object Sets item in the navigation tree.
2. Select Insert New Dielectric Set... to open up the New Dielectric Object Set dialog.
3. From the drop-down list labeled Host Layer, select the substrate layer to embed the new object set.
4. Enter values for relative permittivity εr and electric conductivity σ in S/m. The default values are εr = 1 and σ = 0, representing an air void.
5. Click the OK button of the dialog to return to the project workspace.

PYTHON COMMAND:

pec_via_group(label,host_layer)

EMBEDDED DIELECTRIC SET PARAMETERS

Parameter Name Value Type Units Default Value Notes
eps (εr) Real Numeric - 1.0 relative permittivity
sigma (σ) Real Numeric S/m 0.0 electric conductivity
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The embedded dielectric object set dialog.

## Embedded PEC Via Set

ICON:

MODULE: EM.Picasso

FUNCTION: Defines an embedded PEC via object set group

TO DEFINE A PEC VIA SET:

1. Right-click on the Embedded Object Sets item in the navigation tree.
2. Select Insert New PEC Via Set... to open up the New PEC Vias Set Dialog.
3. From the drop-down list labeled Host Layer, select the substrate layer to embed the new via set.
4. Change the color or texture of the via set if desired.
5. Click the OK button of the dialog to return to the project workspace.

PYTHON COMMAND:

pec_via_group(label,host_layer)

EMBEDDED PEC VIA SET PARAMETERS

Parameter Name Value Type Units Default Value Notes
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The PEC via set dialog.

## Ferrite Material

ICON:

MODULE: EM.Tempo

FUNCTION: Defines a ferrite material

TO DEFINE A FERRITE MATERIAL GROUP:

1. Right-click on the Gyrotropic Materials item in the navigation tree.
2. Select Insert New Ferrite Material... to open up the New Ferrite dialog.
3. Enter values for the DC Bias Magnetic Field and Saturation Magnetization.
4. If necessary, change the default values of attenuation factor, permittivity and electric conductivity.
5. Change the color of the material group if desired.
6. Clicking the Plot button generates plots of the components of the permeability tensor over the frequency range of the project.
7. Click the OK button of the dialog to return to the project workspace.

PYTHON COMMAND: None

VOXEL DATABASE PARAMETERS

Parameter Name Value Type Units Default Value Notes
DC Bias Magnetic Field Real Numeric A/m 100000 Assumed to be Z-directed
Saturation Magnetization Real Numeric A/m 50000 Assumed to be Z-directed
Attenuation Factor Real Numeric - 0 -
eps (εr) Real Numeric - 1.0 relative permittivity
sigma (σ) Real Numeric S/m 0.0 electric conductivity
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The Ferrite material dialog.

## Fixed-Potential PEC

ICON:

MODULE: EM.Ferma

FUNCTION: Defines an equi-potential perfect electric conductor object group with a specified voltage

TO DEFINE A FIXED-POTENTIAL PEC GROUP:

1. Right-click on the Fixed-Potential PEC Objects item in the navigation tree.
2. Select Insert New Fixed-Potential PEC... to open up the Fixed-Potential PEC dialog.
3. Besides the color and texture properties, you have to enter a value for the fixed Voltage in Volts. The default voltage is 0V.
4. Click the OK button of the dialog to return to the project workspace.

PYTHON COMMAND: pec_voltage_group(label,voltage)

FIXED-POTENTIAL PEC PARAMETERS

Parameter Name Value Type Units Default Value Notes
voltage Real Numeric Volts 0 -
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The fixed-potential PEC dialog.

## Fixed-Temperature PTC

ICON:

MODULE: EM.Ferma

FUNCTION: Defines an iso-thermal perfect thermal conductor object group with a specified temperature

TO DEFINE A FIXED-TEMPERATURE PTC GROUP:

1. Right-click on the Fixed-Temperature PTC Objects item in the navigation tree.
2. Select Insert New Fixed-Potential PEC/PTC... to open up the Fixed-Temperature PTC dialog.
3. Besides the color and texture properties, you have to enter a value for the fixed Temperature in degrees C. The default voltage is 0°C.
4. Click the OK button of the dialog to return to the project workspace.

PYTHON COMMAND: pec_voltage_group(label,voltage)

FIXED-TEMPERATURE PTC PARAMETERS

Parameter Name Value Type Units Default Value Notes
temperature Real Numeric Deg C 0 -
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The fixed-temperature PTC dialog.

## Gyrotropic Material

ICON:

MODULE: EM.Tempo

FUNCTION: Defines a gyrotropic material (either a ferrite or a magnetoplasma)

TO DEFINE A GYROTROPIC MATERIAL GROUP:

1. Right-click on the Gyrotropic Materials item in the navigation tree.
2. Select either Insert New Ferrite Material... or Insert New Magnetoplasma... to open up the New Ferrite dialog or New Magneoplasma dialog, respectively.
3. For a ferrite material, follow the procedure at Ferrite Material.
4. For a magnetoplasma material, follow the procedure at Magnetoplasma Material.
5. Change the color of the material group if desired.
6. Click the OK button of the dialog to close it.

NOTES, SPECIAL CASES OR EXCEPTIONS: In the case of a magnetoplasma, the user has two options, either to specify the DC magnetic field or the angular cyclotron frequency. Once either of the two parameter is specified, the value of the other parameter is computed and displayed.

PYTHON COMMAND: None

FERRITE MATERIAL PARAMETERS

Parameter Name Value Type Units Default Value Notes
DC bias magnetic field Real Numeric A/m 105 assumed to be Z-directed
saturation magnetization Real Numeric A/m 5×104 assumed to be Z-directed
attenuation factor Real Numeric - 0 must be between 0 and 1
relative permittivity Real Numeric - 1 -
electric conductivity Real Numeric S/m 0 -
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled

MAGNETOPLASMA MATERIAL PARAMETERS

Parameter Name Value Type Units Default Value Notes
angular plasma frequency Real Numeric rad/s 3.14×107 -
collision frequency Real Numeric 1/s 105 -
DC bias magnetic field Real Numeric A/m 105 assumed to be Z-directed
angular cyclotron frequency Real Numeric rad/s 8837887.024 must be specified if the DC magnetic field check box is unchecked
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The ferrite material dialog. The magnetoplasma material dialog.

## Impedance Surface

ICON:

MODULE: EM.Illumina

FUNCTION: Defines an impedance surface object group

TO DEFINE AN IMPEDANCE SURFACE GROUP:

1. Right-click on the Impedance Surfaces item in the navigation tree.
2. Select Insert New Impedance Surface... to open up the impedance Surface dialog.
3. Besides the color and texture properties, you have to enter values for the real and imaginary parts of Surface Impedance. The default values are 0 + j0 Ω, representing a PEC surface.
4. Click the OK button of the dialog to return to the project workspace.

NOTES, SPECIAL CASES OR EXCEPTIONS: An impedance surface is a surface on which the tangential electric and magnetic fields are governed by the surface impedance boundary condition (SIBC):

$\mathbf{\hat{n}} \times \mathbf{\hat{n}} \times \mathbf{E} = -Z_s \mathbf{J_s} = -Z_s \mathbf{\hat{n}} \times \mathbf{H}$

where $Z_s$ is the surface impedance in Ohms and $\mathbf{\hat{n}}$ is the unit outward normal on the given surface.

PYTHON COMMAND: impedance_surface_group(label,z_real,z_imag)

IMPEDANCE SURFACE PARAMETERS

Parameter Name Value Type Units Default Value Notes
resistance Real Numeric Ohm 0.0 real part of surface impedance
reactance Real Numeric Ohm 0.0 imaginary part of surface impedance
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The impedance surface dialog.

## Impenetrable Surface

ICON:

MODULE: EM.Terrano

FUNCTION: Defines an impenetrable surface block group

TO DEFINE AN IMPENETRABLE SURFACE GROUP:

1. Right-click on the Impenetrable Surfaces item in the navigation tree.
2. Select Insert New Block... to open up the Impenetrable Surface dialog.
3. In the material table, the default setting shows Brick with a relative permittivity of εr = 4.44 and an electric conductivity of σ = 0.001S/m.
4. You can change the default material composition by selecting and highlighting it in the table and clicking the Add/Edit button of the dialog.
5. In the Material Layer Properties dialog, either enter new values for εr and σ or click the Material button of this dialog to open EM.Cube's Materials List and select one of its entries.
6. You can add several layers to your impenetrable surface composition. In that case, you need to define a thickness for each layer. The bottommost layer always has an infinite thickness representing an unbounded half-space medium as seen by an incident ray.
7. After you complete the definition of all layers, click the OK button of the dialog to return to the project workspace.

PYTHON COMMAND: impenetrable_surface_group(label,epsilon,sigma[,rr,gg,bb])

IMPENETRABLE SURFACE PARAMETERS

Parameter Name Value Type Units Default Value Notes
epsilon Real Numeric - 4.44 relative permittivity
sigma Real Numeric S/m 1e-3 electric conductivity
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The impenetrable surface dialog.

## Magnetoplasma Material

ICON:

MODULE: EM.Tempo

FUNCTION: Defines a magnetoplasma material

TO DEFINE A FERRITE MATERIAL GROUP:

1. Right-click on the Gyrotropic Materials item in the navigation tree.
2. Select Insert New Magnetoplasma... to open up the New Magnetoplasma dialog.
3. Enter values for the Angular Plasma Frequency and Collision Frequency.
4. The box labeled "Specify the Z-directed DC Magnetic Field" is checked by default. In that case, you need to enter a value for the DC magnetic field.
5. If you uncheck the magnetic field box, then you need to enter a value for Angular Cyclotron Frequency.
6. Change the color of the material group if desired.
7. Clicking the Plot button generates plots of the components of the permittivity tensor over the frequency range of the project.
8. Click the OK button of the dialog to return to the project workspace.

PYTHON COMMAND: None

VOXEL DATABASE PARAMETERS

Parameter Name Value Type Units Default Value Notes
Angular Plasma Frequency Real Numeric rad/s 31400000 -
Collision Frequency Real Numeric 1/s 100000 -
DC Magnetic Field Real Numeric A/m 40 Assumed to be Z-directed
Angular Cyclotron Frequency Real Numeric rad/s 8837887.024 Disabled when specifying the DC magnetic field
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The Magnetoplasma material dialog.

## Penetrable Surface

ICON:

MODULE: EM.Terrano

FUNCTION: Defines a penetrable surface (thin wall) block group of a specified thickness

TO DEFINE AN PENETRABLE SURFACE GROUP:

1. Right-click on the Penetrable Surfaces item in the navigation tree.
2. Select Insert New Block... to open up the Penetrable Surface dialog.
3. In the material table, the default setting shows Brick with a relative permittivity of εr = 4.44, an electric conductivity of σ = 0.001S/m and a thickness of 0.5 project units.
4. You can change the default material composition by selecting and highlighting it in the table and clicking the Add/Edit button of the dialog.
5. In the Material Layer Properties dialog, either enter new values for εr and σ or click the Material button of this dialog to open EM.Cube's Materials List and select one of its entries. You can also change the Wall Thickness from this dialog.
6. You can add several layers to your penetrable wall composition. An incident ray first penetrates the topmost layer and finally exits the bottommost layer.
7. After you complete the definition of all layers, click the OK button of the dialog to return to the project workspace.

PYTHON COMMAND: penetrable_surface_group(label,epsilon,sigma,thickness[,rr,gg,bb])

PENETRABLE SURFACE PARAMETERS

Parameter Name Value Type Units Default Value Notes
epsilon Real Numeric - 4.44 relative permittivity
sigma Real Numeric S/m 1e-3 electric conductivity
thickness Real Numeric project units 0.5 finite thickness of thin walls
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The penetrable surface dialog.

## Penetrable Volume

ICON:

MODULE: EM.Terrano

FUNCTION: Defines a penetrable volume block group

TO DEFINE AN PENETRABLE VOLUME GROUP:

1. Right-click on the Penetrable Volumes item in the navigation tree.
2. Select Insert New Block... to open up the Penetrable Volume dialog.
3. From the Interface drop-down dialog, choose one of the four options: Standard Material, Rain, Fog, Vegetation.
4. The default interface type is the standard material Brick with a relative permittivity of εr = 4.44, an electric conductivity of σ = 0.001S/m.
5. You can change the default material composition by entering new values for εr and σ. Or click the Material button of this dialog to open EM.Cube's Materials List and select one of its entries.
6. If you choose the Rain option, you have to enter a value for Rain Rate in mm/hr.
7. If you choose the Fog option, you have to enter a value for Fog Density in g/m^3.
8. If you choose the Vegetation option, Weissberger's model will be used and there is no parameter to set.
9. After you complete the definition of all layers, click the OK button of the dialog to return to the project workspace.

NOTES, SPECIAL CASES OR EXCEPTIONS: Inside a penetrable volumes, the rays travel through a non-air medium. As a result, they experience different phase velocities and possibly additional losses. Therefore, the attenuation and propagation constants of the material medium are used for wave computations:

$\gamma = \alpha + j\beta = \alpha + j\frac{\omega}{c}\sqrt{\epsilon_r}$

where α and β are the attenuation and propagation constants in Neper/m and radian/m, respectively, ω = 2*πf, εr is the relative permittivity of the medium and f the operational frequency.

There are four types of penetrable volumes:

• Standard material
• Rain
• Fog
• Vegetation

Standard material blocks reflect, transmit and diffract impinging rays. The ray reflection and edge diffraction mechanisms are identical to the cases of impenetrable or penetrable surfaces with the same material properties. The transmitted rays, however, travel in the material medium until they exit the other side of the penetrable volume object. This is different than the case of penetrable surfaces, where the transmitter ray is assumed to travel the very short thickness of a wall before entering the free space again, and the specular points of the entering and exiting rays are taken to be the same.

Of the above list, rain, fog and vegetation media only attenuate the incoming ray and do not generate reflected or diffracted rays. A rain medium is characterized by the Rain Rate expressed in mm/hr, and a fog medium is characterized by the Fog Density expressed in gr/m3. EM.Terrano uses Weissberger's model for the calculation of attenuation due to propagation in a vegetation medium. This model is only applicable when there is foliage obstruction (blockage by dense, dry and leafy trees) in a line-of-sight link. Weissberger's model is valid in the frequency range from 230MHz to 95GHz and provides accurate results for foliage depths up to 400m. It expressed the propagation loss as

$L = \left\{ \begin{array}{lr} 0.45 f^{0.284}d & d\lt14\text{m} \\ 1.33 f^{0.284}d^{0.588} & 14\text{m} \le d \le 400\text{m} \end{array} \right.$

where L is the total loss in dB, d is the depth of the foliage and f is the operational frequency in GHz.

PYTHON COMMAND: penetrable_volume_group(label,epsilon,sigma[,rr,gg,bb])

PENETRABLE VOLUME PARAMETERS

Parameter Name Value Type Units Default Value Notes
eps Real Numeric - 4.44 relative permittivity
sigma Real Numeric S/m 1e-3 electric conductivity
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The penetrable volume dialog.

## Perfect Electric Conductor (PEC)

ICON:

FUNCTION: Defines a perfect electric conductor object group

TO DEFINE A PEC GROUP:

1. Right-click on the PEC Objects or PEC Traces item in the navigation tree.
2. Select Insert New PEC... to open up the New PEC Dialog.
3. The only properties of a PEC group you can modify is its color and texture.
4. Click the OK button of the dialog to return to the project workspace.

PYTHON COMMAND: pec_group(label)

PEC PARAMETERS

Parameter Name Value Type Units Default Value Notes
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The PEC dialog.

## Perfect Magnetic Conductor (PMC)

ICON:

MODULE: EM.Tempo, EM.Illumina

FUNCTION: Defines a perfect magnetic conductor object group

TO DEFINE A PMC GROUP:

1. Right-click on the PMC Planes or PMC Surfaces item in the navigation tree.
2. Select Insert New PMC... to open up the New PMC dialog.
3. The only properties of a PMC group you can modify is its color and texture.
4. Click the OK button of the dialog to return to the project workspace.

PYTHON COMMAND: pmc_group(label)

PMC PARAMETERS

Parameter Name Value Type Units Default Value Notes
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The PMC dialog.

## Permanent Magnet

ICON:

MODULE: EM.Ferma

FUNCTION: Defines a permanent magnet group with a specified magnetization vector

TO DEFINE A PERMANENT MAGNET GROUP:

1. Right-click on the Permanent Magnets item in the navigation tree.
2. Select Insert New Permanent Magnet... to open up the Permanent Magnet Source dialog.
3. Enter a value for relative permeability μr, which has a default value of 1.
4. You have two options for Magnetization to choose from: Uniform and Inhomogeneous.
5. If you choose the uniform option, you have to enter three numeric values for the three components of the magnetization vector Mx, My and Mz in A/m.
6. If you choose the inhomogeneous option, you have to enter three expressions for the three components of the magnetization vector Mx, My and Mz in the global (x,y,z) coordinates.
7. Click the OK button of the dialog to return to the project workspace.

NOTES, SPECIAL CASES OR EXCEPTIONS: A permanent magnet is typically a ferromagnetic material with a fixed intrinsic magnetization vector. As a result, it can be used as a source in an magnetostatic problem. When a permeable material has a permanent magnetization, the following relationship holds:

$\mathbf{B(r)} = {\mu} (\mathbf{H(r)} + \mathbf{M(r)} )$

where M(r) is the magnetization vector. In SI units system, the magnetic field H and magnetization M both have the same units of A/m.

It can be shown that for magnetostatic analysis, the effect of the permanent magnetization can be modeled as an equivalent volume current source:

$\mathbf{J_{eq}(r)} = \nabla \times \mathbf{M(r)}$

If the magnetization vector is uniform and constant inside the volume, then its curl is zero everywhere inside the volume except on its boundary surface. In this case, the permanent magnetic can be effectively modeled by an equivalent surface current density on the surface of the permanent magnetic object:

$\mathbf{J_{s,eq}(r)} = \mathbf{M(r)} \times \hat{\mathbf{n}}$

where $\hat{\mathbf{n}}$ is the unit outward normal vector at the surface of the permanent magnet object. Note that the volume of the permanent magnet still acts as a permeable material in the magnetostatic analysis.

PYTHON COMMAND: magnet_group(label,mu,Mx,My,Mz)

PERMANENT MAGNET PARAMETERS

Parameter Name Value Type Units Default Value Notes
mu (μr) Real Numeric - 1.0 relative permeability
Mx Real Numeric A/m 0.0 X-component of magnetization vector
My Real Numeric A/m 0.0 Y-component of magnetization vector
Mz Real Numeric A/m 1.0 Z-component of magnetization vector
 The permanent magnet dialog.

## Point Radiator Set

ICON:

MODULE: EM.Terrano

FUNCTION: Defines a base location set group to be associated with a transmitter or receiver set

TO DEFINE A BASE LOCATION SET GROUP:

1. Right-click on the Base Locataions item in the navigation tree.
2. Select Insert New Point Set... to open up the base Location Set dialog.
3. The only property of a base location set is its color, which you can change from this dialog.
4. Click the OK button of the dialog to return to the project workspace.
5. By default, the transmitter set is assumed to be made up of vertical half-wave radiators.
6. You may also force the transmitters to adjust their Z-coordinates based on the underlying terrain surface.
7. Click the OK button of the dialog to return to the project workspace. The new round symbols appear representing the transmitter set.
8. You can open the property dialog of the transmitter set and change the radiator type to User Defined Antenna. In that case, click the Import Pattern button of the dialog to set the file path for a far-field radiation pattern data file of ".RAD" type. You can also additionally rotate the imported radiation pattern about its local X-, Y- and Z-axes.
9. An imported radiation pattern file typically contains a total radiated power parameter at its file header. By default, this value is overridden and the Custom Power check box is checked. A default total power of 1W is assigned to each transmitter, which you can change to any arbitrary value. Or you may uncheck Custom Power to use the imported value of the total radiated power.

POINT RADIATOR SET PARAMETERS:

Parameter Name Value Type Units Default Value Notes
radiator type options: vertical half-wave dipole, user define antenna - vertical half-wave dipole -
pattern file file path - Models\DPL_STD.RAD imported far-field radiation pattern data file with a ".RAD" file extension for the case of user defined antenna
rot_x real numeric degrees 0 additional rotation angle of the imported radiation pattern about the local X-axis
rot_y real numeric degrees 0 additional rotation angle of the imported radiation pattern about the local Y-axis
rot_z real numeric degrees 0 additional rotation angle of the imported radiation pattern about the local Z-axis

 The base location set dialog.

## Point Scatterer Set

ICON:

MODULE: EM.Terrano

FUNCTION: Defines a point scatterer set group to be used as one or more targets in a radar simulation

TO DEFINE A POINT SCATTERER SET GROUP:

1. Right-click on the Point Scatterers item in the navigation tree.
2. Select Insert New Scatterer Set... to open up the Point Scatterer Set dialog.
3. You can change the color of the scatterer set from this dialog.
4. In the section titled "Polarimetric Scattering Matrix Data File", use the Import... button to browse the folder on your computer. Clicking the Import... button opens the Windows Explorer window. Select a file with a ".DAT" file extension, whose name ends in polar_scat.
5. Click the OK button of the dialog to return to the project workspace.

PYTHON COMMAND: scatterer_group(label,polar_scat_file[,rr,gg,bb])

POINT SCATTERER SET PARAMETERS:

Parameter Name Value Type Units Default Value Notes
scattering matrix file file path - Models\POLAR_SCAT.DAT imported polarimetric scattering matrix data file with a ".DAT" file extension and a name ending in "polar_scat"
 The point scatterer set dialog.

## Slot Trace

ICON:

MODULE: EM.Picasso

FUNCTION: Defines a slot trace object group on an infinite PEC ground plane

TO DEFINE A SLOT TRACE GROUP:

1. Right-click on the Slot Traces item in the navigation tree.
2. Select Insert New Slot Trace... to open up the New Slot Trace dialog.
3. The only properties of a slot trace group you can modify is its color and texture.
4. Click the OK button of the dialog to return to the project workspace.

PYTHON COMMAND: slot_group(label)

SLOT TRACE PARAMETERS

Parameter Name Value Type Units Default Value Notes
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The slot trace dialog.

## Terrain Surface

ICON:

MODULE: EM.Terrano

FUNCTION: Defines a terrain surface block group

TO DEFINE A TERRAIN SURFACE GROUP:

1. Right-click on the Terrain Surfaces item in the navigation tree.
2. Select Insert New Terrain... to open up the Terrain Surface dialog.
3. In the material table, the default setting shows Rock with a relative permittivity of εr = 5 and an electric conductivity of σ = 0.001S/m.
4. You can change the default material composition by selecting and highlighting it in the table and clicking the Add/Edit button of the dialog.
5. In the Material Layer Properties dialog, either enter new values for εr and σ or click the Material button of this dialog to open EM.Cube's Materials List and select one of its entries.
6. You can add several layers to your terrain surface composition. In that case, you need to define a thickness for each layer. The bottommost layer always has an infinite thickness representing an unbounded half-space medium as seen by an incident ray.
7. After you complete the definition of all layers, click the OK button of the dialog to return to the project workspace.

PYTHON COMMAND: terrain_group(label,epsilon,sigma[,rr,gg,bb])

TERRAIN SURFACE PARAMETERS

Parameter Name Value Type Units Default Value Notes
epsilon Real Numeric - 5 relative permittivity
sigma Real Numeric S/m 5e-3 electric conductivity
Locked mesh density Real Numeric cells/effective wavelength 30 Only if "Lock Mesh" enabled
 The terrain surface dialog.

## Thin Wire

ICON:

MODULE: EM.Tempo, EM.Libera

FUNCTION: Defines a thin wire object group with a specified wire radius

TO DEFINE A THIN WIRE GROUP:

1. Right-click on the Thin Wires item in the navigation tree.
2. Select Insert New Thin Wire... to open up the Thin Wire dialog.
3. Enter a value for the Wire Radius.
4. Click the OK button of the dialog to return to the project workspace.

THIN WIRE PARAMETERS

Parameter Name Value Type Units Default Value Notes
Wire radius Real Numeric project units 0.3 -
Locked mesh density Real Numeric cells/effective wavelength 50 "Lock Mesh" enabled by default
 The thin wire dialog.

## Virtual Object Group

ICON:

MODULE: EM.Terrano

FUNCTION: Defines a virtual object group that is invisible to the simulation engine

TO DEFINE A VIRTUAL OBJECT GROUP:

1. Right-click on the Virtual Objects item in the navigation tree.
2. Select Insert a Virtual Material... to open up the Virtual Material dialog.
3. Virtual materials have only one property, which is their color. You can the change from this dialog.
4. Click the OK button of the dialog to return to the project workspace.

PYTHON COMMAND: virtual_group(label)

VIRTUAL OBJECT PARAMETERS: None

 The virtual object set dialog.

## Volume Charge

ICON:

MODULE: EM.Ferma

FUNCTION: Defines a volume charge source group with a specified charge density

TO DEFINE A VOLUME CHARGE GROUP:

1. Right-click on the Volume Charges item in the navigation tree.
2. Select Insert New Volume Charge... to open up the Volume Charge Source dialog.
3. You have two options to choose from: Uniform and Inhomogeneous.
4. If you choose the uniform option, you have to enter a numeric value for Charge Density in C/m^3.
5. If you choose the inhomogeneous option, you have to enter an expression for Charge Density in the global (x,y,z) coordinates.
6. Click the OK button of the dialog to return to the project workspace.

PYTHON COMMAND: charge_group(label,density)

VOLUME CHARGE PARAMETERS

Parameter Name Value Type Units Default Value Notes
density Real Numeric C/m^3 -1e-5 volume charge density with a positive or negative sign
 The volume charge source dialog.

## Volume Current

ICON:

MODULE: EM.Ferma

FUNCTION: Defines a volume current source group with a specified current density vector

TO DEFINE A VOLUME CURRENT GROUP:

1. Right-click on the Volume Currents item in the navigation tree.
2. Select Insert New Volume Current... to open up the Volume Current Source dialog.
3. You have two options to choose from: Uniform and Inhomogeneous.
4. If you choose the uniform option, you have to enter three numeric values for the three components of volume current density Jx, Jy and Jz in A/m^2.
5. If you choose the inhomogeneous option, you have to enter three expressions for the three components of volume current density Jx, Jy and Jz in the global (x,y,z) coordinates.
6. Click the OK button of the dialog to return to the project workspace.

PYTHON COMMAND: volume_current_group(label,Jx,Jy,Jz)

VOLUME CURRENT PARAMETERS

Parameter Name Value Type Units Default Value Notes
Jx Real Numeric A/m^2 0.0 X-component of volume current density vector
Jy Real Numeric A/m^2 0.0 Y-component of volume current density vector
Jz Real Numeric A/m^2 1.0 Z-component of volume current density vector
 The volume current source dialog.

## Volume Heat Source

ICON:

MODULE: EM.Ferma

FUNCTION: Defines a volume heat source group with a specified heat density

TO DEFINE A VOLUME HEAT SOURCE GROUP:

1. Right-click on the Volume Heat Sources item in the navigation tree.
2. Select Insert New Volume Heat Source... to open up the Volume Heat Source dialog.
3. You have two options to choose from: Uniform and Inhomogeneous.
4. If you choose the uniform option, you have to enter a numeric value for Heat Density in W/m^3.
5. If you choose the inhomogeneous option, you have to enter an expression for Heat Density in the global (x,y,z) coordinates.
6. Click the OK button of the dialog to return to the project workspace.

PYTHON COMMAND: charge_group(label,density)

VOLUME HEAT SOURCE PARAMETERS

Parameter Name Value Type Units Default Value Notes
density Real Numeric W/m^3 -1e-5 volume heat density with a positive or negative sign
 The volume heat source dialog.

## Wire Current

ICON:

MODULE: EM.Ferma

FUNCTION: Defines a wire current source group with a specified current and wire radius

TO DEFINE A WIRE CURRENT GROUP:

1. Right-click on the Wire Current item in the navigation tree.
2. Select Insert New Wire Current... to open up the Wire Current dialog.
3. Enter a value for the total Current flowing in the wire in Amperes as well as a value for Wire Radius in the project units.
4. You may assume that the wire current consists of multiple turns or multiple bundled wires. The default number of turns is 1, but you can change it.
5. The current flowing in the wire is directional. You may need to check the box labeled Reverse Current if you prefer the opposite direction.
6. Click the OK button of the dialog to return to the project workspace.

NOTES, SPECIAL CASES OR EXCEPTIONS: EM.Ferma allows you to define idealized wire current sources. You can use this source type to model filament currents or coils. Wire currents are defined using only line and polyline objects. You also need to define a current value I in Amperes and a wire radius r in the project units. The line or polyline object is then approximated as a volume current with a current density of J = I/(πr2) flowing along the line or polyline side's direction.

 If you draw curve CAD objects under a wire current group, they will be permanently converted to polyline objects before running the simulation engine.