The Coil node can be used to model coils, cables, and other conductors subject to a lumped excitation, such as an externally applied current or voltage. The Coil feature transforms this lumped excitation into local quantities (electric field and electric current density), and computes lumped parameters of interest such as impedance, and inductance.
The Coil feature supports three different
Conductor models:
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Single conductor, which models a conductive body such as a wire, busbar, or other metallic object in which the current flows freely due to the material’s conductivity. This model can be used when the current flow has a well-defined beginning and end (for example, connections to an external source) or is closed in a loop.
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Homogenized multiturn, which models a bundle of electrically thin wires tightly wound together but separated by an electrical insulator. In this scenario, the current flows only in the direction of the wires. Induced currents flowing in other directions are considered negligible.
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Homogenized litz coil, which is a variant of the multiturn model where the effects of helical twisting and multiple strands per turn are accounted for.
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In 3D, the has to be complete in the sense that selecting only part of a contiguous conductor will lead to unphysical results. If the current loop is not complete, Ampère’s law may be violated.
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The Coil feature is available both for domain and for boundary selections. In the latter case, it represents a flat coil or a conductor with a thickness negligible compared to the other dimensions. Various subnodes can be added to the
Coil node in certain cases.
The global Harmonic Perturbation subnode is available from the context menu (right-click the parent node and select it from the
Global menu) or from the
Physics toolbar,
Attributes menu. The subnode can be used to apply a harmonic perturbation to the coil excitation.
In 2D and 2D axisymmetric components, the Coil feature supports the
Coil group functionality. This can be activated by selecting the corresponding checkbox.
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The Coil group option assumes that the selected domains represent cross sections of the same conductor going in and out of the modeling plane. These domains are expected to have the same areas. The same total current will be imposed in each domain, even if the domain areas are not equal. If the areas are unequal, the computed concatenated flux, coil voltage and inductance will be incorrect. For cases with varying cross section areas, it is recommended to use separate coil features that are coupled using The Electrical Circuit Interface.
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Refer to the Modeling Coils section in the modeling guide for more information about this node.
The Material type setting decides how materials behave and how material properties are interpreted when the mesh is deformed. Select
Solid for materials whose properties change as functions of material strain, material orientation and other variables evaluated in a material reference configuration (material frame). Select
Nonsolid for materials whose properties are defined only as functions of the current local state at each point in the spatial frame, and for which no unique material reference configuration can be defined. Select
From material to pick up the corresponding setting from the domain material on each domain. Since
Coil features model conductors or bundles of wires, the correct choice is usually
Solid.
Enter a Coil name. This name is appended to the global variables (current, voltage) defined by this coil, and it can be used to identify the coil in a
Coil Geometry Analysis study step.
Select the Conductor model for the coil. The choices correspond to rather different physical models, although the setup is similar. The
Single conductor model (the default) is appropriate for fully resolved conductors with skin and proximity effects included. The
Homogenized multiturn model represents a bundle of electrically thin wires that are not geometrically resolved but included as an
effective medium. Skin and proximity effects can be included in a lumped sense, using the
Harmonic loss effective loss model or a
Mutually coupled circuit. The
Homogenized litz coil is a variant of the multiturn model where the effects of helical twisting and multiple strands per turn are accounted for. The choice of conductor model affects the controls that are visible in the GUI and the available subnodes for the Coil feature.
This section is available when selecting Homogenized multiturn or
Homogenized litz coil as the
Conductor model in 3D, and is used to specify the coil geometry (the orientation of the wire bundle).
Select a Coil Type —
Numeric (the default),
Circular,
Linear, or
User defined. The different alternatives are described in the following sections. Also see
Using Coils in 3D Models for more information.
When Single conductor is selected as the
Conductor model, the coil behaves as if
Coil Type is
Numeric, including the presence of the
Geometry Analysis subnode.
In a Numeric coil, the current flow is computed automatically in a
Coil Geometry Analysis study step. Use the
Geometry Analysis subnode to set up the problem.
In a Circular coil, the wires are wound in circles around the same axis. Use the
Coil Geometry subnode to select a group of edges forming a circle or a part of a circle around the coil’s axis. From the selected edges, the coil axis is computed and the direction of the wires is taken to be the azimuthal direction around the axis, as marked by the red arrows. The coil length used is computed as the coil volume divided by the coil cross sectional area, unless the
Use robust geometry analysis method box is checked. When the robust method is used, the coil length is simply the length of the selected edges.
In a Linear coil, all the wires are parallel and straight lines. Use the
Coil Geometry subnode to select an edge or a single group of connected edges that maps out the local coil direction. The direction of the wires and the coil length is taken to be the direction and the length of the edge(s), as marked by the red arrow. Avoid selecting multiple parallel edge groups as that will result in an incorrect coil length.
For User defined manually specify the direction of the wires as a vector field and the length of the coil. Use the
User Defined Coil Geometry subnode to specify the coil geometry.
The Coil group checkbox is only available for 2D and 2D axisymmetric components. Select this checkbox to enable the
Coil group mode for this feature. With this setting, the domains or domain groups in this feature’s selection are considered series-connected. Selecting this checkbox activates the
Domain Group subnode. See
Coil Groups for more information.
Select a Coil excitation —
Current (the default),
Voltage,
Circuit (voltage),
Circuit (current), or
Power (2D and 2D axisymmetric components only).
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Current forces a total current flowing in the coil wire. Enter a Coil current Icoil (SI unit: A). The default is 1 A. See the box below for study limitations on this setting.
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Voltage applies a total voltage across the coil enter a Coil voltage Vcoil (SI unit: V). The default is 1 V.
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Circuit (current) works similarly to the Current excitation, but in this case the inputs are provided by a circuit connection.
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Circuit (voltage) works similarly to the Voltage excitation, but in this case the inputs are provided by a circuit connection.
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Power (only available for 2D and 2D axisymmetric components) forces the coil input power (cycle-average in frequency studies) to the specified value. Choosing this option makes the problem nonlinear. For Power enter a Coil power Pcoil (SI unit: W). The default value is 1 W.
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When using the Current, Circuit (current), and Power options, the coil feature sets up a control problem for the coil voltage and current. Due to its complexity, the following limitations apply:
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The Power option is only available for 2D and 2D axisymmetric components.
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The Current and Circuit (current) options should be used with care in Time Dependent study steps. One should avoid applying a current step excitation (for example a fixed nonzero current) as that will lead to unphysical results and/or numerical instability.
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This section is available only when Homogenized multiturn or
Homogenized litz coil is selected as the
Conductor model. In this case, the coil represents a bundle of electrically thin wires separated by an insulating material. Additional settings can be specified.
Enter the Number of turns N. The default is 10. This is the number of wires constituting the coil cross-section. The coil resistance is affected by this number and so is the current density in the coil. Together with the
Current setting the number of turns defines the number of Ampère-turns in the coil.
The Wire properties can be specified using the following options:
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From conductivity allows for specifying the coil wire conductivity σ and a coil wire cross-section area. The area needs to be the area of the actual conductor, without varnish or insulation. Several standards are supported.
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From resistivity; specify the wire resistance per unit length ρwire. This option is typically used for litz wires, where the resistance per unit length is taken from measurements or a specification sheet provided by the supplier.
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From resistance and mutually coupled circuit; specify the coil resistance Rcoil, the mutual inductance Mcir, and the source of the mutually coupled circuit current Icir. If the latter is set to Series R and L, also specify the mutually coupled circuit resistance Rcir and the mutually coupled circuit inductance Lcir. If it is set to User defined, just specify Icir directly.
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The Wire properties are used to determine the intrinsic resistance of the coil wire or litz wire. Usually, this amounts to the DC resistance. If a frequency-dependent AC resistance is used — for instance from a litz wire specification sheet — it will include both the DC resistance and additional resistance from loss terms caused by skin and proximity effects within the strand bundle that forms the litz wire. This intrinsic AC resistance is a property of the (litz) wire itself.
If the wire is then wrapped around a magnetic core with a nonzero conductivity it will lead to additional eddy currents and additional loss. The total loss will determine the final coil AC resistance as perceived by the power source. Depending on the coil geometry, core type, and nearby conductors this resistance may be different from the AC resistance used to specify the wire properties.
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Available for the Homogenized litz coil conductor model only. The
Litz wire DC resistance per unit length ρdc is typically around 3–10% higher than the DC resistance of a bundle of untwisted strands with the same bundle length and cross sectional copper content. This is because the helical path length of the individual strands is a bit longer than the bundle length. The effect can be compensated for by specifying the DC resistance as measured or as provided by the litz wire specification sheet. When unknown, an increase of 6% is a fair estimate.
Enter the Number of strands n as included in the litz wire. This parameter is used together with the
Strand conductivity, and the
Strand area to determine the untwisted DC resistance and the copper packing density.
Enter a Conductivity σ (SI unit: S/m). The default value is approximately the conductivity for copper, 6·10
7 S/m. This parameter represents the conductivity of the metal wires forming the coil and will be used for determining the lumped resistance and the loss. Note that this is not the bulk conductivity of the material as perceived by free eddy currents, which is instead set to a very low value comparable to the
Free space stabilization conductivity. Intrinsic parasitic inductive effects such as skin and proximity effects in the coil itself are instead modeled in a lumped fashion, using the
Harmonic loss effective loss model or a
Mutually coupled circuit.
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For Filling factor, enter the filling factor f. This dimensionless factor sets the fraction of the cross-section occupied by the metal (usually copper), also known as the packing density. Use this setting to specify the wire or strand area when the area is unknown or is yet to be determined, and the coil geometry is a reasonably accurate representation of the real device. The value is expected to be below 0.9, which is the densest packing for circles. The option is not available for boundary coils.
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For From diameter, enter the diameter of the individual wire or strand d (SI unit: m). The cross-section area of the round wire will be computed from it. The default value of d is 1 mm.
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For Standard wire gauge, enter the SWG size. Sizes between 7/0 and 50 are available. The default size is 0.
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For American wire gauge (Brown & Sharpe), enter the AWG size. Sizes between 0000 and 40 are available. Sizes such as 0000 can be also written as 4/0. The default size is 0.
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For User defined, enter the value of the cross section area a (SI unit: m 2). The default is 1 mm 2.
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When using the options From diameter, Standard- or American wire gauge, or User defined, there is a risk of the filling factor passing the 0.9 threshold unnoticed. If the coil geometry in the model is an accurate representation of the real device (not an approximate prototype or a proof of concept) this may indicate a design flaw or a modeling error; the coil should not contain more metal than physically possible. Higher values are allowed, however, for experimentation, sweeping, or optimization purposes. Use the coil filling factor variable in postprocessing to verify coil integrity.
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For domain coils where the wire or strand properties are specified using the conductor area and wire conductivity, the Include harmonic loss option is available for computing the coil’s intrinsic AC loss in the frequency domain (enabled by default). For stationary and transient studies, it reverts back to DC behavior — for including intrinsic AC loss in a Transient analysis, consider using the
Mutually coupled circuit option.
When the frequency, the wire or strand size (and distance) with respect to the skin depth, the fill factor and the wire conductivity are known, it is possible to include intrinsic AC losses in the coil (or litz wire) based on a continuum skin and proximity effect model, see
Ref. 1. At frequencies where the skin depth approaches the strand size, the intrinsic loss starts to dominate and the resistance of the coil can become orders of magnitude larger than the DC resistance.
Specify a Wire resistance per unit length ρwire in
Ω/m. The default value is 30
Ω per 1000 feet. This option is typically used for litz wires, where the resistance per unit length is taken from measurements or a specification sheet provided by the supplier. Other common sources are analytic litz wire models (that can be typed directly into the expression field for
ρwire) or 2D finite element models that fully resolve the strands and output the frequency-dependent AC resistance in the form of a lookup table.
Only available for the Homogenized multiturn conductor model. Specify the total
Coil resistance. This will typically be the total DC resistance. When a frequency dependence is included in the expression, it will be the
intrinsic AC resistance — For more information, see
Wire Properties. The default value is 50
Ω.
Only available for the Homogenized multiturn conductor model. When the
From resistance and mutually coupled circuit option is chosen, the coil resistance
Rcoil and the inductance will approach the DC values in the low frequency regime. When the frequency increases, the magnetic fields are still described by Ampère’s law where the integrated current density in each coil section is the coil current multiplied by the number of turns. However, the presence of
Icir will affect the total potential that generates the coil current as an extra load opposed to the main coil current.
This may be seen as an effect of the interaction between the outermost and innermost parts of the current density in each coil turn. Therefore, with properly tuned values of Rcir and
Lcir, it is possible to mimic the increased resistance due to skin and proximity effects between the individual turns in the multiturn coil. Finding these values is typically done by fitting the parameters (using a sweep, or optimization) such that the coil shows the same time-average behavior as a fully resolved 2D model.
For domain coils in 2D and 2D axisymmetry, symmetry factors can be entered at the coil’s main level (note that for coils in 3D these factors are typically set in the Geometry Analysis subnode). If the model represents only a part of the full device because of the use of symmetry, these factors can be used to compensate for parts of the coil missing. Attached circuits and lumped quantities such as the inductance or the resistance will then behave as if the model represents the full device.
Enter the Coil length multiplication factor FL and
Coil area multiplication factor FA (dimensionless integer numbers) to compensate for the difference in turn length, and the difference in conductor (or bundle) thickness.
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To model a fully resolved litz wire (or litz coil) in 2D, add all the strands as individual circles in the geometry and mesh. Use a Single conductor coil to fully resolve the skin and proximity effects, and use a coil group to put all the strands in series — enforcing the same current in each of them. Then, set FL equal to 1/n and FA equal to n, where n is the number of strands. This will effectively turn the series connection into a parallel connection, while still enforcing the same current in all strands. In order to model a litz coil without resolving the strands, use the Homogenized litz coil effective conductor model, and enable Include harmonic loss.
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This section is available only for the Single conductor coil model. It allows to set the resistive bulk properties. In this case, the coil represents a solid (fully resolved) conductor and the conductivity of the material is required to compute the current density flowing in it. This section is identical to the one in the
Ampère’s Law node.
For a domain coil, the Constitutive Relation B-H and
Constitutive Relation D-E sections can be used to specify the magnetic and dielectric bulk properties of the medium. When the
Single conductor model is selected, these options are essentially the same as those used in the
Ampère’s Law node.
When the Homogenized multiturn or
Homogenized litz coil model is selected, the number of options is restricted to better match the assumptions that the effective material model is based on; a densely packed strand bundle with magnetic and dielectric bulk properties close to those of
Free space. The chosen settings now represent the average properties of both the wires and the insulation, or epoxy resin.
To display this section, click the Show More Options button (
) and select
Stabilization in the
Show More Options dialog. This section is available only in 3D components when using
Homogenized multiturn as the
Conductor model and it contains advanced settings relative to the accuracy and stabilization of the solution.
The Accurate coil voltage calculation checkbox enables a current filtering functionality that improves the accuracy of the computed electric field and the induced coil voltage, at the cost of a slightly increased number of degrees of freedom. This functionality is only applicable for time dependent and frequency domain studies, and is active by default.
For the purpose of stabilizing the solution, the coil feature can apply a small electric conductivity to the coil domain. Use the Stabilization combo box to specify the value of the conductivity. Choose
Automatic (the default) to use a conductivity automatically computed by the coil. In frequency domain studies, the conductivity is chosen so that the skin depth in the coil is much larger than the coil length (see the sections
Coil Geometry and
User Defined Coil Geometry below). It is deduced from the formula
by setting the skin depth δ, equal to the coil length. In other study types the conductivity is set to 1 S/m.
If None is chosen, no conductivity is used in the coil domain. Choose
User defined to specify the
Electric conductivity in the coil domain σΩ (SI unit: S/m). The default value is 1 S/m. The purpose of this electric conductivity is only to stabilize the solution. According to the Homogenized multiturn model, the domain should not be conductive and all the currents should flow in the direction of the wires only.
