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Defining Circuit Components and Excitations

In this section, you will learn about:

  • Adding passive and active circuit elements to your EMPro project
  • Other excitations you can include, such as plane waves and Gaussian beams

This section focuses on the steps associated with creating and defining valid components and excitations in an EMPro project.

Circuit Components are discrete components which may be used almost anywhere in the problem space. Examples include resistors, capacitors, inductors, voltage sources, current sources, switches and diodes. The definitions associated with these components are defined within the Circuit Component Definition Editor.

There are three primary input excitation forms in EMPro. The first type of excitation can be applied at one or more discrete locations with a voltage or current source. The second and third excitations are applied externally in the form of incident plane waves, for scattering calculations, or Gaussian beams, for optical frequency calculations. The External Excitation Editor governs both plane wave and Gaussian beam excitations.

The Waveform Editor governs the time variation of all three types of excitations. A waveform may be defined as a pulse for broadband calculations, a sinusoidal source, or a user-defined waveform. A waveform definition must be applied to a defined excitation for it to be valid.

The following four sections outline the various aspects of creating and defining components and excitations.

Component Tools

This section will document the capabilities of Component Tools, found in the first drop-down menu in the Geometry workspace window. The Component Tools dialog enables users to add discrete components to the EMPro project. These discrete components include voltage sources, current sources, feeds, lumped resistors (R), capacitors (C), inductors (L), diodes, non-linear capacitors, and switches. Discrete sources (such as voltage and current sources) are locations at which the electric field is modified by the addition of some type of input waveform.

Each circuit component has its own specific set of definitions (i.e., spacial orientation, polarity, alignment), which are included in the Circuit Components dialog. Definitions such as resistance, inductance, capacitance, etc. are specified in the Circuit Component Definition Editor so that they can be reused for multiple components if necessary. To access this editor, navigate to the Definitions:Circuit Component Definitions branch of the Project Tree and double-click on the component's Circuit Component Definition object.

The following illustration shows the various components available within the Circuit Components dialog box.

Adding a new component with Component Tools

Adding a New Component

Once Circuit Components is visible in the first-drop down button of the Geometry workspace window, clicking Create With New will prompt a drop-down menu to appear. This menu includes:

  • Passiveload
  • Feed
  • Switch
  • Non-Linear Capacitor
  • Diode

Selecting any of these components will prompt a similar series of tools to place the desired component into the simulation space. The following sections will detail the definitions associated with these tools.

For more information about any one of these discrete sources, refer to Circuit Component Definition Editor.

Circuit Components can also be added by right-clicking in the Project Tree as shown below.

Accessing the Component Tools dialog from the Project Tree

Connections Tab

When choosing one of the new New Circuit Components... menus, two tabs appear. In the Connections tab, you can easily specify the location of a component by using existing object vertex points. One defines circuit components in solid space (connected to e.g. two objects) and not in the mesh space. The actual component, however, can only span one mesh cell and must adapt to changing mesh densities local to the component definition. This mesh cell is always in the middle of the feed as defined in solid space. The other cells between the two endpoints defined in this tab are automatically filled with a PEC wire. For many applications, as when feeding a monopole at its base, one needs to make sure that the feed starts exactly at the first mesh cell from the wire endpoint. This can be achieved by making the solid feed shorter or equal to one grid cell size and having one endpoint be attached to the wire vertex.

One can use the placement tool (white arrow icon) to easily pick off vertex points from different objects. Make sure to look at the bubble up help instructions. For example, if a wire is attached to the top of a box object, you can click this icon, then hover over the wire until its edge and vertex points are highlighted, and then click "l" (lower-case L) to temporarily unlock it so that the bottom vertex can be snapped to.

Properties Tab

In the Properties tab, the name of the component, alignment, and polarity is defined. The component(s) can be aligned with either the X-, Y-, or Z-axes, by selecting X, Y, or Z, respectively. Otherwise, the default Auto selection will automatically align the component based on Endpoint 1 and Endpoint 2 defined in the Connections tab.

The check box, This Component Is A Port, can be selected to assign the component as a port. When this box is selected, EMPro will automatically add a Port sensor at this location.

The check box, Evenly Spaced In Orthogonal Directions, can be selected to enforce proper grid creation in the region around components. This option should be selected except in special cases.

Note

Keep in mind that a port that contains only passive components cannot be the active port. Lumped reactive elements should not be used in the active port specification.

For more information about port sensors and the data that they collect, refer to Sensor Tools Port Sensors.

The figure below displays the Properties tab for editing a feed.

Editing component properties

If a component is added before it is defined in the Circuit Component Definition Editor, a default definition will be created so that the component is valid. Simply double-click on this default definition in the Definitions branch of the Project Tree to edit its properties. Likewise, if the component requires a waveform definition, a default definition will be added to this branch.

Adding a Component Using an Existing Definition

The Create With drop-down menu functions similarly to the Create With New drop-down menu described above, except that a pre-existing component definition is applied to the component that is to be added. For this reason, the Create With menu is not active until a component definition has already been created within the Create With New dialog. It is thus a list all of the pre-existing component definitions that hav already been added to the project. This menu makes it easy to add identical components to a project.

Circuit Component Definition Editor

The Circuit Component Definition Editor is used to define the parameters associated with discrete components. Components such as voltage sources, current sources, feeds, lumped resistors (R), capacitors (C), inductors (L), diodes, non-linear capacitors, and switches are defined in this window.

It is important to recognize the purpose of the Circuit Components interface versus that of the Circuit Component Definition Editor. The former places the physical component into the project (and creates an object in the Project Tree that represents the actual component), while the latter creates a Circuit Component Definition object for the parameters of that component (or components) that can be used over and over again by dropping it onto multiple components.

The Circuit Component Definition Editor is accessed by double-clicking on any object found in Definitions: Circuit Component Definitions branch of the Project Tree. The interface shown in the figure below is a sample setup for a feed. Note that the Type of component determines the diagram in the editor.

The Circuit Component Definition Editor

Passive Load

When a component with no source is desired, the user may create it by selecting Passive Load. Passive components include lumped resistors (R), inductors (L), and capacitors (C). A passive component is one that does not add any energy to the problem space.

Passive loads may be combined at the same location with a single active component, such as a voltage or a current source. Since passive lumped loads do not radiate energy, they may be added to the calculation when either Planewave or Gaussianbeam excitations are selected.

For more information about these excitations, refer to the External Excitation Editor.

The RLC elements lumped at component locations can be combined with each other either in series or parallel. For passive components used with a voltage or current source, the RLC components will be in series with the voltage source or in parallel with the current source. The Series and Parallel choices refer only to how the RLC components are combined with respect to each other. For the series load combination, all of the lumped circuit elements are in series and are located on one FDTD mesh edge. For a parallel load combination, all of the lumped circuit elements are in parallel and are located on one FDTD mesh edge. The selected configuration is shown schematically in this window.

Below a sample setup for a Passive Load within the Circuit Component Definition Editor is shown.

Editing a load within the Circuit Component Definition Editor

Displacement of Current and Lumped Elements

There are physical limitations to the lumped element approximation in FDTD. Each FDTD mesh cell includes a volume of free space. That free space volume has capacitance, and a displacement current flows through it. f a lumped RLC element is specified that results in a high impedance, the free space displacement current may be significant relative to the current through the lumped elements in EMPro. In this situation, if the displacement current is neglected, the result is non-physical and Maxwell's equations cannot be satisfied. So for lumped element calculations in EMPro, the displacement current is included even though the corresponding mesh cell capacitance is not indicated on the port circuit schematic.

To determine the relative significance of the displacement current, one can calculate the capacitance of the FDTD mesh cell. For a -directed component, the capacitance of the cell is given by ,
where,
, , and are the mesh cell dimensions and the permittivity of the material at that cell location, usually that of free space, 8.854e-12 .

This is discussed on page 192 of the Kunz and Luebbers FDTD book.

As long as the impedance of this mesh cell capacitor is large compared with the impedance of the RLC lumped element circuit, its inclusion in the EMPro calculation has a negligible effect. If the RLC lumped element circuit has an impedance comparable or larger than the mesh cell capacitance, then the inclusion of this capacitance keeps the result stable and physically correct.

For calculating impedances, a frequency corresponding to the sine wave frequency or the highest frequency of interest within the spectrum of the excitation waveform should be used.

Similarly, a lumped inductor should not be less than the inductance of the FDTD cell, given by , where is the permeability of that point in space and is the mesh cell length in the direction of the inductor.

Feed

An active source, or Feed, usually refers to an active component together with any passive components that are at the same cell edge. An active component is a cell edge on which the electric field is modified by the addition of some type of input waveform. Voltage and current sources are active components.

If a voltage or current source is included, the amplitude of the input waveform may be specified as well as the polarity. The phase of the source may be specified if the input waveform is a sinusoid, otherwise this option will be unavailable.

Note

For all voltage and current source specifications, the amplitudes specified are peak values, not RMS.

A time delay may also be specified for voltage and current sources when a Gaussian, Gaussian Derivative, or Modulated Gaussian waveform is used. The time delay is specified in timesteps and is applied to the beginning of the source waveform. For example, if a time delay of 200 timesteps is specified for a given source port, the input waveform at that port will begin 200 timesteps later than the defined waveform. This functionality allows for any number of Gaussian excitations to be applied at different times throughout a simulation.

The voltage across the FDTD mesh edge (electric field times edge length) and the FDTD mesh edge current include the effects of both the RLC components at that mesh edge and the voltage/current source. A voltage source, , in series with a source resistance, is illustrated below. The voltage across the FDTD mesh edge is determined by the voltage source in combination with the source resistance, so that the mesh edge voltage differs from the source voltage by the voltage drop across the source resistance.

Feed schematic, including FDTD mesh edge voltage, V, and current, I

Multiple Voltage and/or Current Sources

For calculations with multiple voltage and/or current sources, such as antenna arrays or multi-port S-parameter calculations, multiple feeds may be specified. They are specified in the Simulations workspace window before the calculation is run.

Note

For more information about setting up an S-parameter simulation, refer to S-parameters Simulation Setup.

For antenna calculations, all feeds are normally excited. However, for S-parameter calculations only one feed can be excited for a particular EMPro calculation. For broadband feeds, each source function must have the same pulse width but may have different amplitudes. Alternatively, they may instead all use the same user-supplied file of voltage versus time. The polarity can be adjusted by clicking the desired button. This may be useful in controlling the sign of the phase terms in S-parameter calculations. For each feed, independent source resistances may be specified. For sinusoidal excitations, each feed can be specified with a different magnitude and phase.

Specifying the Source Resistance

For most EMPro calculations, active sources will consist of a voltage source with a series source resistance. This is the default configuration for feeds. The default value for the source resistance is , since that is the most common reference. If an S-parameter calculation is made, the S-parameters will be in reference to the port resistance.

Note

S-parameters can be calculated for any reference impedance by changing the value of the resistance at each port.

If the value of the source resistance is not determined by the desired S-parameter reference, then for most calculations the source resistance should be chosen to match the structure being driven. This will strongly excite the structure and also dissipate resonances most efficiently. For example, for a microstrip with characteristic impedance, a source resistance of would typically be a good choice.

For antenna calculations, determining a good approximation to an actual antenna feed is not always simple. Many antennas are fed with coaxial cable. For most EMPro calculations the coaxial cable itself need not be meshed, since it is only used to feed the antenna and the fields inside of it are not of primary interest. The simplest approach to simulating this is to locate a port in line with the center conductor of the coaxial cable where the cable is connected to the antenna. The impedance calculated by EMPro will then be at this point in the antenna.

Note

The port resistance typically should be set equal to the characteristic impedance of the coaxial cable used to feed the physical antenna. This will automatically refer S-parameters to this resistance value.

For broadband calculations, to reduce the number of timesteps needed for the transients to dissipate, include a source resistance equal to the characteristic impedance of the coaxial cable being approximated. This is similar to driving an actual circuit or antenna using a matched source.

For some situations, it is desirable to match a voltage or current source to a reactive load. In this situation the RLC capabilities of EMPro components can be utilized.

If the coaxial cable or other feed geometry is important to the calculation, EMPro may be used to mesh the cable itself. In this situation it is important to determine the characteristic impedance of the coaxial cable as meshed, and to match the port resistance to the characteristic impedance.

Another important advantage to including a source resistance is reducing the number of FDTD timesteps necessary for convergence of the electromagnetic calculation. This is especially important for resonant devices, such as many antenna and microstrip circuits. With a "hard" source consisting of a voltage source without series resistance, a resonant microstrip antenna may require 64,000 timesteps for the transients to dissipate. The addition of a source resistance might reduce this to 4,000 timesteps. Similar time savings may be encountered for microwave circuits.

Diode

A Diode can be defined by specifying the following:

  • Saturation Current ( )
  • Junction Potential ( )
  • Depletion Capacitance at zero bias ( )
  • the sum of Transit Time ( ) for holes and electrons
  • Emission Coefficient ( )
  • junction Grading Coefficient ( )
  • the Forward Coefficient ( ), which determines when the junction is heavily forward biased

For stability consideration, voltages applied to the diode should not exceed 15 volts.

Note

Further information regarding the FDTD diode formulation may be found in Bibliography.

The figure below shows editing dialog for a Diode within the Circuit Component Definition Editor.

Editing a diode within the Circuit Component Definition Editor

Nonlinear Capacitor

The Non-Linear Capacitor contains parameters which correspond to the following equation:

where:

is instantaneous cell edge capacitance

is instantaneous cell edge voltage

is static (low ) capacitance

is infinite capacitance

is voltage magnitude

is a scaling voltage

, and are coefficients

  • A non-linear capacitor may be combined with a parallel resistor.

The next figure shows editing dialog for a Non-Linear Capacitor within the Circuit Component Definition Editor.

Editing a nonlinear capacitor within the Circuit Component Definition Editor

Switch

A special feature of EMPro is its ability to include timed and programmable Switch components. This allows a change in the configuration of the geometry during a calculation. Any number of switches may be introduced into the geometry, with each switch being specified as a separate component. Switch states may be changed only once during a calculation.

The initial state of the switch, whether open or closed, may be specified as well as the timestep where the switching action begins. The switching action is spread over a variable number of timesteps to reduce switching transients. The switch transition should on the order of 60 timesteps.

To define the properties of the switch, select Open or Closed to define the switch's initial state in the Circuit Component Definition Editor. Click |+| to add a transition and define the Start Time, Duration, and Transition type of the switch by double-clicking on the default values provided in the chart in the editor.

The following figure shows editing dialog for a multiple transition Switch within the Circuit Component Definition Editor.

Editing a switch within the Circuit Component Definition Editor

A switch may be programmed to allow multiple open/close transitions during a simulation by adding subsequent entries to this initial definition. A switch transition consists of the timestep at which the switch will activate and the duration (in timesteps) that the Gaussian switching function will be applied. Simply click the button found above the definitions chart to add one or more switch transitions and define the Start Time, and Duration that the transition will occur. The transition type will be automatically generated based on the start time of each transition. Furthermore, the Sort button will automatically sort the transition from the earliest to latest occurring state.

During the switch transition, the electric field at the switch is changed from the open switch value to zero when closed (or vice versa) following a Gaussian function. This method provides stability for the EMPro calculation. In order to apply the Gaussian switching function, the value of the electric field at the switch location is first calculated as if the switch were not present. This value is then multiplied by the Gaussian function with the appropriate argument based on the time since the switch state was changed. For a closed switch, the multiplier is zero, for an open switch it is one, and for intermediate times during the transition the value is that for the normalized Gaussian function. For this reason, the function of the switch depends on the material that exists at the mesh location. Usually this is free space, but it might also be dielectric.

The use of timed switches is for situations where only the actual transient results directly calculated by EMPro are of interest. The introduction of the switching action violates the assumptions of linear system theory, so that applying Fourier transformations to the transient results produced in an EMPro calculation with one or more switches which change state will not result in valid impedances, S-parameters, steady-state far-zone fields, or other results involving Fourier transformation, even if the transient results finally decay to zero. Transient far-zone fields will be valid, however.

External Excitation Editor

The External Excitation Editor window is used to define an External Excitation to be applied to an FDTD simulation. There are two types of external excitations, which are detailed in the following sections: Planewave, and _Gaussianbeam.

The following figure shows the External Excitation Editor. Note that a Waveform must be applied for the external excitation to be valid. In this interface, a plane wave excitation is defined.

The External Excitation Editor

To access the editor, double-click on an existing object in the External Excitations branch of the Project Tree. If no external excitations are defined, right-click on this branch and select New External Excitation.

Plane Wave

The first external excitation definition form available within the External Excitation Editor is the incident plane wave. The plane wave parameters are enabled when the source type is set to Planewave in the Simulations workspace window.

Note

For more on how to set up a simulation, refer to Creating a New Simulation.

A Plane Wave source is assumed to be infinitely far away so that the constant field surfaces are planar and normal to the direction of propagation. Calculations of radar cross section or scattering may be performed using this source. All calculations with the incident plane wave input are performed in scattered-field, but total-field values may also be computed.

The incident direction defined by Incident Phi and Incident Theta must be specified by angle. Incident Phi is measured from the X-axis to the Y-axis while Incident Theta is measured from the Z-axis to the XY plane. The incident waveform may be phi- or theta-polarized. The electric field values in the XY , and Z directions are displayed under the Incident Amplitudes heading in this window and are updated each time the polarization or incident direction is modified.

Selecting Scattered-Field Versus Total-Field Plane Wave

Total-field values may be saved and displayed since they can be determined by adding the specified incident field with the computed scattered field. Scattered fields cannot be sampled inside the total-field region and vice versa. Calculations of radar cross section or scattering are based on fields inside the scattered-field region.

The interface between the total-field and scattered-field regions must be free space. For non-periodic boundaries, the six sides of the total-field region interface are located eight cells into the FDTD mesh. When periodic boundaries are specified, certain sides for the interface may be turned off and the total-field region may extend to the boundary. These definitions are specified in the Simulation workspace window.

Note

For a discussion of these definitions, refer to Specifying Field Formulation.

In most cases, total-field plane wave is preferable to scattered-field plane wave. Below, two examples of an electric field propagating (from right to left) through a shelled geometry of Perfect Electric Conductor (PEC) material. The image on the left represents a scattered plane wave source, while the image on the right shows a total-field plane wave source. Since the box is PEC material, the electric field within the bounds of the box should be zero, and therefore, the total-field plane wave source is more valid.

The E-field of a scattered-field (left) vs. total-field (right) plane wave source

In some cases, however, the total-field plane wave source will also create inconsistencies in the calculations.

The next figure shows the resultant electric field when an object crosses the total-field/scattered-field interface (intersection represented by the white arrows). This will produce incorrect results. To fix this problem, the interface may be moved so that it is sufficient distance from the geometry. However, to move the interface, the bounding box of the project must be increased which will also increase the memory requirements of the project. Alternatively, a scattered-field plane wave can be used with the understanding that the region within the shelled geometry is incorrect.

Incorrect results due to an object crossing the interface

The following figure demonstrates a similar problem where the interface is too close to the bounds of the object. In this case the fields fall within the "shadow" region of the object and are not calculated correctly. The image on the left shows the effect of the shadow region early in the field sequence. The image on the right shows the incorrect field values later in the sequence at the interface between the total-field/scattered-field interface. The interface, like in the previous example, must be adjusted if total-field plane wave is to be used.

Incorrect results when a field propagates within the Shadow Region of the geometry

Gaussian Beam

The second external excitation definition available within the External Excitation Editor is the Gaussian Beam source. The focused Gaussian beam is characterized by an incident electric field that has a two-dimensional, radially-symmetric Gaussian distribution in planes normal to the incident direction. It converges to maximum intensity at the focus point. As with the plane wave source, all calculations with a Gaussian beam source are performed in scattered-field, though total-field values may also be saved and displayed also. Unlike the plane wave and discrete sources, the Gaussian beam source requires that the source waveform be sinusoidal.

Note

Examples where this type of source is useful include structures used at optical frequencies and situations where it is desired to illuminate only a portion of the geometry.

The Gaussian beam is specified by Incident Direction, Polarization, Waveform and waveform Amplitude, as described for the plane wave source above, and by focal point (Focus X, Focus Y, Focus Z) and Focus Radius. The Focus Radius is the beam radius, , at the focal point, in the plane normal to the direction of travel and containing the focus, at which the field strength drops to  -8.686 dB of its maximum value.

In the next illustration we see the dialog for defining a Gaussian beam in the External Excitation Editor. To use this excitation as the source for a calculation, it must be specified within the Simulation workspace window.

Note

For more information about the Simulations workspace window, refer to Creating a New Simulation.

Defining a Gaussian Beam source in the External Excitation Editor

In other planes normal to the direction of travel, is the radius at which the field strength drops to of its maximum value in that plane and is given by:

where:

is the free space wavelength and, for simplicity, the direction of travel is assumed to be parallel to the Z-axis and the focus in the plane.

Since passive lumped loads do not radiate energy, they may be added to the calculation when either Planewave or Gaussian beam excitations are selected.

Note

All active ports will be set to passive lumped loads when either of these excitations are selected.

Waveform Editor

The Waveform Editor is used to edit waveforms that can be used in conjunction with an External Excitation or a Feed to inject energy into the space for an FDTD simulation. When used in a simulation, a waveform's field value at each timestep is applied to the field in the space as part of the field update calculation.

To create a Waveform, right-click on the Definitions:Waveforms branch of the Project Tree and select New Waveform Definition. Double-clicking on a Waveform under the same branch will open that waveform for editing.

There are six types of waveforms available:

  • Broadband
  • Gaussian
  • Gaussian Derivative
  • Modulated Gaussian
  • Ramped Sinusoid
  • User-Defined

The choice of waveform should be based on the desired output, as some waveforms are more appropriate than others for specific problems. For broadband calculations, the Broadband or one of the Gaussian-type waveforms should be used, since they will inject energy into the space in a wide band of frequencies. The Ramped Sinusoid may be chosen for cases where steady-state results are desired at a single frequency. The User Defined waveform can be used when none of the other choices meet the requirements of the simulation.

Broadband

When broadband results are desired, it is almost always the case that the Broadband waveform type should be used. This waveform provides a Gaussian pulse with the largest frequency content possible for the specific FDTD space when Excite All Possible Frequencies is selected (see the following figure). Alternatively, the user can clamp the upper end of the frequency range by selecting Excite Up To A Maximum Frequency and choosing a frequency response magnitude and corresponding frequency. In this case, note that the waveform frequency response is truncated in the simulation to the maximum allowed, even if a wider frequency response is specified in this editor. The figure below shows a Broadband waveform in the Waveform Editor.

Note

For more information on waveform frequencies, refer to the Waveform Editor.

Defining a Broadband waveform in the Waveform Editor

Gaussian

The Gaussian waveform provides broadband input and is also suitable for use when broadband results are desired. The width of the pulse is user-specified.
The following figure shows a Gaussian pulse in the Waveform Editor.

Note

For more information on specifying the width of the pulse, refer to Notes on Choosing Waveform Parameters.

Defining a Gaussian pulse in the Waveform Editor

Since the Gaussian pulse has a non-zero average value, it should not be used for a Feed when there is a closed path (loop) of perfect conductor connected to the Feed unless the feed also contains resistance. This is because the Gaussian has a DC (zero-frequency) component which starts a steady current flowing in the loop that will never decay through loss or radiation. The symptom of this will be a source current that has an average value not equal to zero. If this occurs, the Gaussian Derivative or Modulated Gaussian pulses can be used or a non-zero source resistance specified for the Feed.

Gaussian Derivative

The Gaussian Derivative is nearly identical to the Gaussian except that it has a zero average value and thus the DC component is removed. For the same simulation, the pulse width of a Gaussian Derivative should be set somewhat greater than what would be set for a Gaussian since the Gaussian Derivative will have a wider frequency spectrum for the same pulse width. The following figure shows a Gaussian Derivative in the Waveform Editor.

Note

For more information on pulse width, refer to Notes on Choosing Waveform Parameters.

Defining a Gaussian Derivative waveform

Modulated Gaussian

The Modulated Gaussian should be used only when a specific frequency range is desired. This is useful in structures where low frequencies could excite non-radiating modes which could resonate and invalidate results. This waveform is a sinusoid with a Gaussian envelope, with the sinusoid centered in the envelope so that the average of the pulse is zero.

In the figure below we see a Modulated Gaussian in the Waveform Editor.

Defining a Modulated Gaussian waveform

The Pulse Width for the Modulated Gaussian may be adjusted to enclose a specific frequency range. This is useful, for example, in waveguide simulations so that only frequencies in the band of single-mode operation are excited. It is also useful when band-limited devices are being simulated. For example, a broadband antenna, such as a spiral, may be designed for a specific frequency range. Exciting the antenna at frequencies outside this range may greatly increase the simulation time needed for convergence since the out-of-band energy cannot readily radiate or be otherwise dissipated by the antenna structure.

Note

For more information on pulse width, refer to Notes on Choosing Waveform Parameters.

Ramped Sinusoid

The Ramped Sinusoid is useful when only one frequency is of interest. When this waveform is used, a single frequency simulation is performed that provides additional result types over broadband simulations. The "ramped" part of the waveform is used and automatically configured to avoid introducing energy at any frequency other than that of the sinusoid into the simulation.

Since the Ramped Sinusoid is different than the other waveforms, it requires some special considerations. It is recommended that the length of a simulation be at least five cycles of the sinusoid when not using automatic convergence. In some cases, such as extremely low frequencies, running five cycles may not be practical, in which case even just a fraction of a cycle may be used.

The figure below shows a Ramped Sinusoid in the Waveform Editor.

Defining a Ramped Sinusoid waveform

User Defined

An arbitrary source voltage vs. time may be specified using the User Defined waveform type. A time record of the waveform is imported from a user-defined text file and used directly as the discretized waveform for the simulation. The file format is as follows:

  • The first line must be an integer, which is the number of timesteps in the waveform.
  • The first data point corresponds to the first timestep, and zero will be used for the waveform for timesteps beyond the provided data (the user-defined waveform is zero-padded).
  • The remainder of the file contains two floating-point numbers on each line, one line for each successive timestep. The values of these numbers depend upon whether the waveform is being used for a voltage source or incident plane wave (it is incumbent upon the user to fulfill this requirement; EMPro does not validate the data).
    • For a voltage source, the two numbers are the normalized voltage and its time derivative at the source at that timestep.
    • For an incident plane wave, the two numbers are the normalized electric field magnitude (in Volts/meter) and the time derivative of the electric field.

The frequency response of the User Defined waveform is computed from the input time data. The next figure shows a User Defined waveform in the Waveform Editor.

Defining a User Defined waveform

Choosing Waveform Parameters

For obtaining broadband results, the usual choice for a waveform should be the Broadband waveform. However, for certain situations, a specific pulse type may be desired. For these cases, when choosing the pulse width and/or frequency for a waveform, the constraints of the FDTD method must be kept in mind. The time rate of change of a pulse or the sine wave frequency must be low enough so that the waveform is accurately sampled. This results in the frequency being constrained by:

where:

is the speed of light, and

is the largest grid edge length in the space.

This prevents the waveform from introducing energy at frequencies too high for the FDTD method to produce accurate results. The pulse width should also not be so large (and thus the frequency content so low) that the calculation is not excited at frequencies for which accurate and useful results might be obtained. There must be sufficient energy in the pulse in the frequency range of interest for results to be above the numerical noise. For simulations with very small cells compared to the shortest wavelength of interest, pulse widths may be set much larger than the default size to reduce the number of timesteps needed for convergence and to increase stability.

If dielectric materials are present in the FDTD space, wavelengths are reduced inside those materials since the velocity of propagation is less than the speed of light in free space. A reasonable rule of thumb for lossless or low-loss dielectrics is that the maximum frequency for the spectrum of the pulse should be reduced by the square root of the relative permittivity ( ) times the relative permeability ( ), or equivalently, the_Pulse Width_, , should be increased by this factor:

where :

represents the corrected pulse width, and

represents the uncorrected pulse width.

For loose dielectrics or conductors, the frequency and pulse width should be adjusted proportionally to the change in wavelength in the material relative to the free space. Of course, the maximum frequency for reliable results is also reduced as the frequency spectrum of the excitation pulse is reduced.

For example, suppose part of the simulation space is free space and part is a low-loss dielectric with a relative permittivity of 4.0. Further suppose the cell size is 1 cm. At 10 cells per wavelength, one would expect reasonable results up to 3 GHz with a Gaussian pulse 32 timesteps wide (for a uniform grid). But since part of the space has a dielectric material, with the same cell size the Gaussian Pulse Width should be doubled to 64 timesteps to reduce the frequency spectrum bandwidth. Correspondingly, the maximum frequency for reliable results would be decreased from 3 GHz ;to 1.5 GHz.

When using the Broadband waveform, EMPro chooses (in the case of automatic pulse width selection) or limits the pulse width (in the case of user-specified frequency content) of the Gaussian pulse based on the restrictions above. When using a waveform with user-specified pulse widths, it checks to make sure the frequency limit, as described above, is not exceeded. If it is, an error is given when the simulation is created.

Static Voltage Points

The Static Voltage Points feature is used to create and place a voltage point on an object made of PEC material. These points are used by the Laplace static solver to initialize the starting E field within the problem space to voltage values assigned by the user. With no static voltage points defined, the initial E field at the beginning of the FDTD computation is set to 0 V/m at each cell edge.

To use this feature, right-click the Static Voltage Points branch of the Project Tree and select New Static Voltage Point. A static voltage point is added to the project. Double-click the new point to edit the points properties.

Static Voltage Points are specified by graphically picking or manually entering the location of the static voltage point and by specifying the voltage. Click the Done button to apply your changes.

Note that only one entry per conducting object is necessary. Duplicate entries will overwrite the voltage preset value. PEC outer boundaries and any untagged metal objects will be preset to 0V . If the boundary is PML, the fields at a PML boundary will be initialized appropriately to prevent non-physical reflections at the interface. Additionally, static voltage points can be used by themselves to excite an object containing PEC materials, or in conjunction with an external excitation or a discrete source. The following figure displays the available parameters for a static voltage point:

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