In this section, you will learn how to:
- Add materials to your EMPro project
- Define materials and apply them to geometric objects
Once objects are created and situated correctly in the simulation space, material definitions must be added or else the project will not be considered valid. The electrical and magnetic materials available within EMPro are detailed in this section.
The Material Editor window is the main interface used to define materials to be applied to objects in a simulation. The series of tabbed windows within the editor are used to define a material based on its constitutive parameters. After adding materials to the project, simply drag-and-drop the material in the Project Tree onto the desired geometry to apply it to that object.
The following section describes the options under each tab within the Material Editor.
Adding a New Material
To add a new material, right-click Definitions: Materials branch of the Project Tree and select New Material Definition, as seen in the following illustration. A Material object will be added to this branch. Depending on the project preferences, the Material Editor window will appear automatically. If not, simply double-click on this object to bring up the editor. Similarly, double-click on any existing Material icon to edit an existing material within the Material Editor.
For more information about project preference definitions, refer to Application Preferences.
Adding a New Material Definition to the project
Once the Material Editor window is open, type in the name of the new material in the Name dialog box. Define the Type of material as Physical or Freespace. Freespace is the most basic material definition. Every other type of material is included within the Physical definition, in which case the Electric and Magnetic types should be assigned in their respective drop-down lists below.
There are five electrical and magnetic material types available in EMPro.
- Perfect Conductor
- Diagonally Anisotropic
- Anisotropic (Electric only)
Although frequency-independent materials require the least memory during FDTD simulations, there are some cases in which frequency-independent materials are not appropriate. Frequency-dependent or dispersive materials should be used in these instances. Some common examples of frequency-dependent materials are high water content materials such as human tissues, and metals excited at optical frequencies. EMPro has the capability of simulating electric and magnetic Debye and Drude materials such as plasmas, Lorentz materials, and anisotropic magnetic ferrites, as well as frequency-independent anisotropic dielectrics and nonlinear diagonally anisotropic dielectrics. These additional sub-types are specified within the Isotropic, Diagonally Anisotropic and Anisotropic definitions.
The following sections will detail the various types of materials.
Freespace is the most basic material. By default, the EMPro problem domain is initialized to free space. This material sets relative permittivity and permeability to one, and conductivities to zero.
The following figure shows the Material Editor when the Freespace material is defined. Notice that no Electric or Magnetic tab is available, since both are defined as Freespace material.
Defining a Freespace material
A Perfect Conductor has infinite conductivity and all fields found within it are zero. It has the same settings as the Freespace material, as seen in the figure above. It should typically be used as an approximation when a good conductor is needed in an electromagnetic calculation and losses aren't important. Attempting to include the effects of a good conductor (rather than perfect conductor) may be difficult since the wavelength inside the good conductor will become very small, requiring extremely small FDTD cells to provide adequate sampling of the field values inside the material. This can, however, be overcome by checking the Surface Conductivity box in the Edit Material dialog box.
You can read more about the Surface Conductivity box in the Complex Permittivity, Loss Tangent and Surface Conductivity Correction Overview section.
EMPro includes several Isotropic materials:
- Sampled (FDTD only)
- Nonlinear (FDTD only)
The next figure shows the Material Editor when an Isotropic material is defined. Note that only the Electric tab is available since Magnetic is defined as Freespace. If you define Magnetic as another type, a Magnetic tab would be available as well.
Defining an Electric Material
Nondispersive material properties do not vary with frequency. The continuous-time expressions of Maxwell equations for linear, isotropic, and nondispersive materials that will be discretized in EMPro are:
represents the electric permittivity,
represents the electric conductivity,
represents the magnetic permeability, and
represents the magnetic conductivity.
Defining a Nondispersive material
For a Debye/Drude material, the electrical Conductivity () in , Infinite Frequency Relative Permittivity ( ), Number Of Poles, Static Relative Permittivity ( ), and Relaxation Time ( ) in seconds must be specified. For a Debye material, must equal zero. A non-zero conductivity value results in a Drude material.
This is discussed in detail in Chapter 8 of the Kunz and Leubbers text .
Defining a Debye/Drude material
These parameters cannot be set arbitrarily or instability can occur in FDTD simulations. One constraint is that the FDTD timestep must be small enough to accurately calculate the transient behavior of the material. If the timestep is 3% of the relaxation time or smaller, the time variation of the material parameters should be sufficiently resolved. Typically, the timestep is a very small fraction of the relaxation time. In order to be clear about the signs in the following discussion, note that we are using the engineering time variation of:
and we are defining the complex permittivity as:
For the FDTD calculation to be stable, the imaginary (loss) part () of the complex permittivity, including the effect of the conductivity term, must be positive for all frequencies from zero frequency to infinite frequency. This condition results in a passive material. If is negative, then the material has gain and FDTD simulations will become unstable as the field amplitudes grow.
See equation 8.29 of the Kunz and Leubbers text .
For a Debye material (), stability is assured by setting to a larger value than . In order to have realistic behavior at high frequencies, should be no less than one and should not be much larger than one. Thus the condition for strictly Debye material to be stable for FDTD simulations is:
If the conductivity is not zero, then the material has Drude behavior. There are different conditions that can be satisfied for the imaginary part of the complex permittivity to be positive so that FDTD simulations produce stable results. If the static permittivity is greater than the infinite frequency permittivity then the conductivity can have any positive value. This results in the simplest set of conditions for a stable Drude Material:
These conditions are, however, too restrictive to specify general Drude materials. The more general Drude conditions are:
whereis the Freespace Permittivity of 8.854e-12 !img227.png!.
More general conditions for Drude materials can be determined from the discussion in Chapter 8, Section 3 the Kunz and Leubbers text .
A Djordjevic material is implemented in a number of substrate models to fulfill the causality requirement. The Djordjevic material ensures causality by using the following formula to describe the complex permittivity as a function of frequency:
where fL and fH are the model parameters
is the permittivity value when frequency approaches infinity and a is a constant factor. These two parameters are calculated by EMPro from Er, TanD, FreqForEpsrTanD, LowFreqForTanD, and HighFreqForTanD, which are substrate model parameters entered by the user. FreqForEpsrTanD is the frequency at which for given Er and TanD the equations (1) and (2) are equivalent. Specifically,
In other words, FreqForEpsrTanD represents the frequency at which Er and TanD have been measured, given the fact that the permittivity is frequency dependent in the physical world.
Below is an example illustrating the permittivity profile and how it is related to substrate model parameters. The horizontal axis in both plots is frequency (Hz).
Graph Shows Real Part of Permittivity
Solid Plot Shows Imaginary Part of Permittivity. Dashed Plot Shows TanD.
The corresponding parameters are:
Er = 4.6
TanD = 0.03
FreqForEpsrTanD = 1 GHz
HighFreqForTanD = 1 THz
LowFreqForTanD = 1 kHz
Stability in Lorentz materials for FDTD simulations should be obtained as long as Conductivityand the FDTD timestep is 3% of the relaxation time or less. The limits on the material parameters are:
Defining a Lorentz material
This material enables you to enter multiple relative permittivities and conductivities at one time. It will behave like a nondispersive material when the calculation engine is called and the Wideband Eval Frequency dictates what parameters to use.
This is not a dispersive material and will not automatically be converted to one.
Defining a Sampled material
The relative permittivity of a nonlinear isotropic dielectric material satisfies:
is relative permittivity
E is instantaneous cell edge E-field
is static (low ) relative permittivity
is infinite relative permittivity
is the E magnitude above which the material becomes non-linear
is a scaling term
, and are coefficients
Nonlinear materials are not supported in FEM simulations.
Defining a Nonlinear material
The definitions for a Diagonally Anisotropic are equivalent to those corresponding definitions detailed for Isotropic materials, except the definitions in each of the principle directions are independently specified.
Frequency-independent Anisotropic materials are defined in EMPro by the relative permittivity,, and Conductivity, , tensors.
Defining an Anisotropic material
The parameters below Conductivity represent the terms ofand the parameters below Permittivity (Infinite Frequency) represent the terms of as follows:
The conductivity and permittivity for frequency-independent anisotropic dielectric materials are represented byand , unlike the equations for linear, non-dispersive, frequency-dependent, isotropic materials. These are used in the time-domain FDTD update equations in place of and :
The value of complex permittivity may need to be calculated for some materials. The real part of the complex permittivity may be used for the relative permittivity. The conductivity can be calculated from the imaginary part of the complex permittivity by multiplying by a desired output frequency value (in radian frequency), as shown by:
The loss tangent can be entered directly into EMPro when it is known, typically for good dielectrics. The FDTD engine can then calculate the conductivity as a function of frequency using:
Surface Conductivity Correction
The fields inside a good conductor decay exponentially with a decay rate given by the skin depth. In order to get accurate results for the fields inside a good conductor, it would be neccessary to generate a mesh that has a cell size that is smaller than the skin depth. At high frequencies, this would require very small cells and is thus computationally expensive. Both the FDTD and FEM simulators offer a choice to approximate the fields inside good conductors to reduce this expense. These choices are controlled by the Surface Conductivity Correction box. By default, the Surface Conductivity Correction box is not selected.
In FDTD simulations, the default behavior is to model the fields inside conductors. This gives the proper loss modeling at low frequencies, but underestimates the losses at high frequencies unless the FDTD grid creates small cell sizes along the inside surface of good conductors. An accurate accounting of the high frequency losses can be obtained by checking the Surface Conductivity Correction box and specifying a nominal frequency about which the calculated losses will be most accurate.
In FEM simulations, the default behavior is to not model the fields inside conductors. Instead, an approximate surface impedance model is used on the surface of conductors. This gives the correct loss modeling at high frequencies. It also gives the correct DC losses for conductors with a uniform cross section. Slightly more accurate DC and low frequency losses for structures of varying cross section can be obtained by checking the Surface Conductivity Correction box. However, this can significantly degrade the accuracy of the high frequency losses from FEM simulations.
The Evaluation Frequency parameter that appears with the Surface Conductivity Correction box selected is ignored for FEM simulations.
EMPro also includes several types of magnetic materials. Many of these materials are simply the magnetic counterpart to the dielectrics described in Electric Materials. All restrictions noted in the Electric Materials section apply to their magnetic counterparts.
The figure below shows the Material Editor when a Magnetic Isotropic material is defined. Note that only the Magnetic tab is available since Electric is defined as Freespace. If Electric was defined as another type, a Electric tab would be available as well.
Defining a Magnetic material
See Nondispersive in the Electric Materials section.
See Debye/Drude in the Electric Materials section.
The first parameter related to magnetized ferrites is the Applied Field, (). Enter its value in units of . This number will be used to calculate the Larmor precession frequency ( ),
whereis the gyromagnetic ratio ( ).
Next, enter the Internal Magnetization () in units of . This number is used to calculate the saturation frequency ( ), .
Then, use the Damping Coefficient to account for damping in the ferrite or of any absorption of power due to the ferrite. Finally, enter the direction of the biasing field using the spherical direction fields THETA and PHI.
Ferrite materials are not supported in FEM simulations.
Defining an Magnetized Ferrite material
See Sampled in the Electric Materials section.
See Nonlinear in the Electric Materials section.
See Diagonally Anisotropic in the Electric Materials section.
Use the Appearance tab to assign the aesthetic properties of each defined material. Colors and other properties can be assigned to the faces, edges, and vertices of objects that contain the material so that they can be easily distinguished from other materials in the project.
The Physical Parameters tab governs the definitions most commonly associated with biological tissue. These definitions are thus necessary when performing biological calculations. These values are computed automatically for tissues in Agilent Technologies high fidelity meshes.