Properties

Properties define the material or simulation behaviors of geometrical shapes (known as primitives). A property can be a metal, a thin conducting sheet, a dielectric metarial, a magnetic material, or a lumped element (resistor, capacitor, inductor).

Non-physical simulation entities such as excitation sources, probes, and field dump boxes are also properties, they’re used to enable a specific function at a location or a shape. Hence, one can consider simulation entities to be geometrical objects made of special materials.

Relationship to Primitives

A property is always used to derive one or more geometrical shapes, known as primitives. Together, they form physical and non-physical objects in the CSXCAD model. In principle, any properties can derive any primitives. For example, an excitation source is added to the model by creating a property via AddExcitation(), and deriving a Box primitive from it via AddBox().

Important

To create a meaningful object, remember to always derive at least one Primitives (such as a Box) from any property.

Metal

A metal is a modeled as a Perfect Electric Conductor (PEC) with infinite conductivity.

Internally, the PEC is implemented by forcing the tangential electric field in this region to be zero, which is characteristic of an ideal conductor that can’t be penetrated by electric field lines. If resistive losses are unimportant, one can use PEC rather than a realistic material model for simplicity and efficiency.

Example

It’s added by the AddMetal() method in Matlab/Octave, or by the AddMetal() method in Python.

Create a Perfect Electric Conductor named plate:

OctavePython

csx = InitCSX();
csx = AddMetal(csx, 'plate');
% derive primitives via AddBox(), AddCylinder(), etc.

Thin Conducting Sheet

A Thin Conducting Sheet is a simplified model of a resistive conductor, and is the standard choice for modeling resistive metal sheets, plates, and traces.

Modeling thin metal sheets is challenging in FDTD. To capture effects like surface current (skin effect) requires an impractically high resolution mesh. Thus, Thin Conducting Sheet treats the metal as a zero-thickness 2D plane. The resistive loss in metals is simulated using a simplified, behavioral model to “fit” the observed loss rather than the full physics.

Important

• A Thin Conducting Sheet can only be used to create a zero-thickness geometrical object, the created 3D shape (primitive) must degenerate to a 2D plane (i.e. the same start and stop coordinates must be identical on one axis, such as [-10, -10, 5], [10, 10, 5] for a XY plane at z == 5).

• Surface roughness modeling is currently not supported.

Example

It’s added by the AddConductingSheet() method in Matlab/Octave, or by the AddConductingSheet() method in Python.

The following example creates a Thin Conducting Sheet material named copper_foil, with a conductivity of 59.6e6 S/m and a simulated thickness of 35 µm (the shape created from it must be a 2D plane with zero thickness). This is typical for a 1-oz circuit board:

OctavePython

csx = InitCSX();
csx = AddConductingSheet(csx, 'copper_foil', 59.6e6, 35e-6);
% derive primitives via AddBox(), AddCylinder(), etc.

General Material

A general material is defined by a relative permittivity \(\epsilon_r\), a relative permeability \(\mu_r\), an electric conductivity \(\kappa\), and a hypothetical magnetic conductivity \(\sigma\).

Warning

Kappa (\(\kappa\)) always stands for electric conductivity in openEMS. It’s not to be confused with electric permittivity \(\epsilon\), which is sometimes also denoted as \(\kappa\) in the literature (e.g. high-κ dielectric). This convention is never used in openEMS, its use in simulation code is strongly discouraged.

All parameters are constants that don’t vary with frequency. It can model dielectric materials (such as circuit board substrate), magnetic materials (such as magnetic cores), resistive materials, and 3D metals. Due to the constant-property assumption, this model is not realistic. But it produces acceptable results in simpler applications, and has no simulation overhead.

See also

Dispersive Materials

Example

It’s added by the AddMaterial() method in Matlab/Octave, or by the AddMaterial() method in Python.

Create a plexiglass material:

OctavePython

csx = InitCSX();
csx = AddMaterial(csx, 'plexiglass');
csx = SetMaterialProperty(csx, 'plexiglass', 'Epsilon', 2.22);
% derive primitives via AddBox(), AddCylinder(), etc.

Anisotropic Material

A material property such as permittivity may differ along the X, Y, and Z axes, This is known as an anisotropic material. If only one axis has a different value from the conventional value (two values in total), it’s known as uniaxial anisotropy. If two axes have different values (three values in total), it’s known as biaxial anisotropy.

In optics, many crystals exhibit a phenomenon known as birefringence due to the anisotropic refractive indexes. In high-speed electronics, the propagation delays of signals on an FR-4 circuit board have measurable differences depending on the excitation mode (single-ended vs. differential) due to anisotropic permittivity of the fiberglass-epoxy mixture.

To model anisotropic effects, set the respective material property as an array [x, y, z].

Important

A material can be anisotropic and dispersive (described later) at the same time, but the simultaneous use of both material models is currently untested.

Example

The Y2SiO5 (YSO) crystal is a dielectric material with biaxial anisotropy at both microwave and optical frequencies [1].

OctavePython

csx = InitCSX();
csx = AddMaterial(csx, 'yso');

% YSO (Y2SiO5) crystal, 8 - 22.3 GHz, room temperature.
% source: https://arxiv.org/abs/1503.04089
csx = SetMaterialProperty(csx, 'yso', 'Epsilon', [9.60, 11.22, 10.39]);
% derive primitives via AddBox(), AddCylinder(), etc.

Weighting Function

A material property can be a function of position (spatial coordinates) by modulating its constant value by a weighting function via SetMaterialWeight() (Octave) or SetMaterialWeight() (Python). The weighting function is a string, which contains the expression parsed by the fparser library, so the string should be a legal fparser expression with proper syntax.

In the following example, a material with a permittivity that alternates between 1 and 2 in space is defined:

OctavePython

csx = InitCSX();
csx = AddMaterial(csx, 'material');
csx = SetMaterialProperty(csx, 'material', 'Epsilon', 1);

% '(x > 0)' is a fparser expression, evaluates to 0 or 1
csx = SetMaterialWeight(csx, 'material', 'Epsilon', ['(sin(4 * z / 1000 * 2 * pi) > 0) + 1']);

See also

See Symbolic Expression Parser: fparser for weighting function syntax.

Magnetic Conductivity

Magnetic Conductivity is a hypothetical material property in computational electromagnetics by assuming the existence of magnetic charges (magnetic monopoles) and magnetic conduction currents.

Faraday’s law in Maxwell’s curl equations is modified to the following form [2]. \(\kappa\) and \(\sigma\) are the electric and magnetic conductivity terms, respectively.

\[\begin{split}\begin{aligned} \begin{cases} \nabla \times \mathbf{H} = \space\space\space \kappa \mathbf{E}+ \epsilon \dfrac{\partial \mathbf{E}}{\partial t} \\ \nabla \times \mathbf{E} = -\sigma \mathbf{H} - \mu \dfrac{\partial \mathbf{H}}{\partial t} \end{cases} \end{aligned}\end{split}\]

The modified Faraday’s law allows one to introduce both electric and magnetic conduction losses, which simplifies certain aspects of a simulation. For example, the Perfect Magnetic Conductor (PMC) boundary condition is a wall with \(\sigma \to \infty\), which allowing cutting a symmetrical simulation domain by half by implicitly enforcing field symmetry. The Perfectly Matched Layer’s internal implementation makes use of magnetic conductivity to enable EM wave absorption.

Tip

In the physical universe, magnetic monopoles don’t exist according to our best knowledge, the modified Faraday’s law degenerates to the standard form by setting \(\sigma = 0\).

User simulations can also take advantage of this advanced feature, an example of a custom localized EM wave absorber for transmission line simulations can be found in matlab/examples/transmission_lines/MSL.m, which combines electric conductivity, magnetic conductivity, and two custom weighting functions, creating a hypothetical “tapered conductivity” and achieving low reflections. It demonstrates a non-standard and advanced simulation by a clever combination of different features:

Octave

% this "pml" is a normal material with graded losses
% electric and magnetic losses are related to give low reflection
% for normally incident TEM waves
finalKappa = 1 / abs_length ^ 2;
finalSigma = finalKappa * MUE0 / EPS0;
csx = AddMaterial(csx, 'fakepml');
csx = SetMaterialProperty(csx, 'fakepml', 'Kappa', finalKappa);
csx = SetMaterialProperty(csx, 'fakepml', 'Sigma', finalSigma);
csx = SetMaterialWeight(csx, 'fakepml', 'Kappa', ['pow(z-' num2str(length - abs_length) ',2)']);
csx = SetMaterialWeight(csx, 'fakepml', 'Sigma', ['pow(z-' num2str(length - abs_length) ',2)']);

Lumped Element

Lumped elements are ideal resistors, capacitors and inductors with sizes assumed to be negligible. They’re especially useful for modeling surface-mount circuit components.

Example

It’s added by the AddLumpedElement() method in Matlab/Octave, or by the AddLumpedElement() method in Python. If argument caps is enabled, a small PEC plate is added to each end of the lumped element to ensure electrical contact to the connected lines.

Create a lumped 1 pF capacitor in y direction:

OctavePython

csx = InitCSX();
CSX = AddLumpedElement(CSX, 'capacitor', 'y', 'Caps', 1, 'C', 1e-12);
% derive primitives via AddBox(), AddCylinder(), etc.

Important

Axis Alignment. Lumped elements must have an orientation aligned to the X, Y, or Z axis. If a misaligned resistor or capacitor must be used, rather than modeling it as a lumped element, constructing a distributed element based on a hypothetical material (via AddMaterial() with an artificial conductivity or permittivity) may be a workaround.

For most of the project history, a lumped element can only be an isolated resistor or capacitor (even inductors are not implemented). In the latest development version of openEMS (v0.0.37, unreleased), a contributed new extension has been submitted to openEMS, allowing the lumped element to be an entire RLC circuit, with resistance, capacitor, inductance values simultaneously. It’s controlled by the parameter LEtype in Python’s AddLumpedElement(). A value of 0 denotes a parallel RLC circuit, when a value of 1 denotes a series RLC circuit. It’s not implemented by the Matlab/Octave binding as of now.

Limitation: Parasitic Ambiguity

Lumped elements are ideal throughout the region occupied by the derived primitives. However, the intermediate connections between a lumped element to the external circuit still introduce parasitic effects (e.g., inductance from the overall loop area, partial inductance of terminal leads or mounting height). Full-wave simulations inherently capture them through the electric and magnetic fields in space.

Furthermore, the existence and modeling of parasitics effects can be context-dependent and ambiguous. It’s not always clear whether a parasitics effect should be explicitly modeled as a lumped element (such as an LC circuit), implicitly modeled using the geometries, or modeled as a combination of both.

Due to these ambiguities, it’s recommended to run simple test cases to determine the best way to model a lumped component for your application. To learn more, see Lumped Elements.

Dispersive Materials

Debye, Drude, Lorentz materials are advanced models to model dispersive materials. They’re added by the functions AddDebyeMaterial() and AddLorentzMaterial().

Nearly all real-world materials exhibit a phenomenon known as dispersion. That is, the speed of light in the medium depends on the EM wave’s frequency. In optics, it manifests as a frequency-dependent refractive index. In RF/microwave engineering, it appears as a frequency-dependent permittivity and permeability. In metamaterial research, one can even deliberately introduce dispersion to control electromagnetic wave propagation in unusual ways.

As a result, while the basic material model with constant permittivity and permeability is sufficient if dispersion is negligible, more demanding simulations call for dispersion models for accurately calculating a material’s wideband response.

See Dispersive Materials for detailed descriptions.

Probes and Dumps

Technically, excitation sources, probes, and field dump boxes are also Properties. The associated geometrical shape determines the locations of these excitations, probes and dumps.

They’re added by Matlab/Octave functions AddExcitation(), AddPlaneWaveExcite(), AddProbe(), and AddDump(). In Python, they’re added by AddExcitation(), AddProbe() and AddDump().

To learn more, see Excitation Sources and Field Dump.

Bibliography

[1]

N. C. Carvalho, J.-M. L. Floch, J. Krupka, and M. E. Tobar, “Multi-mode technique for the determination of the biaxial Y2SiO5 permittivity tensor from 300 to 6 Kelvin,” arXiv, 2015.

[2]

John B. Schneider. Understanding the FDTD Method., page 66, equation 3.53.