Maxwell 3D Transient Solution Based on A-Phi Formulation

By default, the Maxwell 3D transient solver is based on T-Omega (W) formulation, which is a powerful method for solving a wide range of low-frequency EM problems. However, there are some areas where the applicability of the method is limited – such as multiple (mixed) source excitations on a single conduction path and capacitive effect (displacement current). For simulation of such problems, the Maxwell 3D Transient A-Phi (F) formulation  is a more suitable solution type.

Comparison of T-Omega and A-Phi Solvers

For more information on the Transient A-Phi formulation, refer to the following sections:

• Limitations
• Boundaries and Excitations
• Rules/Limitations of Excitations on Conduction paths
• Matrix Setup
• Postprocessing Support

• 3D Layout Component

Limitations

The following 3D Transient features is not supported/available for this release:

• Motion-related features

Boundaries and Excitations

Boundaries and Excitations supported are as follows:

• Boundaries supported are Flux Tangential, Insulating, Symmetry, Independent and Dependent Matching, and Resistive Sheet.

  

  Flux Tangential boundaries can only be applied to face objects. Unlike the T-Omega formulation, the Neumann boundary condition on external faces is flux normal for A-Phi formulation. That is why a Flux Tangential boundary condition must be assigned when the magnetic field is tangential to the face.

  

• Excitations supported are Winding (via Coil Terminal), Voltage, and Current. Winding excitation is assigned as in the Transient solver (Refer to Coil Terminals for more information on winding assignments). Voltage and Current excitations are also included on the Excitations > Assign menu:

  

Winding Excitations for A-Phi Formulation

Winding excitation is assigned as in the Transient solver (Refer to Assigning a Winding Setup for a Transient Solver for more information on winding assignments). For winding excitations, the coil terminals must be ordered according to the physical potential distribution. To do this:

1. Right-click on the winding to open the context menu.
2. Click on Order Coil Terminals to open the Order Coil Terminals dialog box.

   

3. Order the terminals by dragging them in the Order Coil Terminals dialog box.

Coil Order

The solver connects the coils according to the coil order specified via Order Coil Terminals. Voltage/current values are assigned to the first terminal, and the last terminal is grounded. To generate the correct potential plot, the terminals should be ordered according to the actual connection of the conductors.

A winding with coil terminals assigned to the external surfaces of the conductors are shown below. The coil terminals are labeled with numbers.

If a winding has more than three external terminals, as in this example, the solver makes the consecutive terminals (except first and last terminal) equipotential (or connected). For example, in Coil Order Case 1, terminals (4,5) and (6,7) have the same potentials . Coil Order Case 2 shows the effect of reordering the coil terminals. Even though Coil Order 1 and 2 have the same terminals, the different order of the terminals gives different potentials, but still the same B, H, and J fields.

For coil terminals defined inside the conductors, the solver defines two potentials for each terminal, and the same connection rule described above applies considering this double potential definition. See Rules/Limitations of Excitations on Conduction Paths for further information about winding excitations.

Voltage Excitations for A-Phi Formulation

For designs with known potentials, select and assign a voltage excitation on each face.

You can also define initial currents for Voltage Excitation by checking the Initial Current box. When initial current is defined, the solver treats it as the current excitation. The default value is 0 A. You should select at least one voltage excitation without enabling the initial currents on a solid conduction path to set a reference potential. (If the path is touching the odd symmetry boundary, where the potential is set to 0 V, or if displacement effect is considered in the problem domain, then this rule does not apply on this path.)

Voltage excitation supports three different excitation models:

• Single Potential: The solver treats the terminal as an equipotential terminal. Only one scalar electric potential DOF (Degree of Freedom) is assigned to the surface, and the value of the DOF is set to the value that you input. This model must be used only at the external boundaries of the problem domain.



• Double Potentials: The solver treats the terminal as a voltage (potential difference) terminal. At the terminal face, two scalar electric potential DOFs are defined and the DOFs are unknown. The difference between those potentials equals the voltage value that you specified. If the voltage value is a positive quantity, higher potential is in the specified direction. This model must be used on faces inside the problem domain.



If you do not define a reference potential on the same conduction path, the potentials at the terminal will be floating, so they are not unique. However, B, J, H, and all other quantities will be unique because they depend on the derivative of the potential.



• Double Potentials with Ground: The solver treats the terminal as voltage (potential difference) terminal. At the terminal face, two scalar electric potential DOFs are defined and both DOFs are known. The difference between those potentials equals to the voltage value that you specified. If the voltage value is a positive quantity, the DOF in the specified direction is set to the specified voltage value, and the DOF in the opposite direction is set to 0. This model must be used on faces inside the problem domain.

Current Excitations for A-Phi Formulation

For designs with known current values, the user selects and assigns a current excitation on each face and also selects the type of conductor: solid or stranded. Current excitation supports three different excitation models for a Solid conductor type based on how the potential DOF is assigned on the face:

• Single Potential: Only one scalar electric potential DOF is assigned to the surface and it is unknown. This model must be used only at the external boundaries of the problem domain.

  

• Double Potentials: At the terminal face, two electric scalar potential DOFs are defined and the DOFs are unknown. There is a potential difference at the terminal. The current will be unidirectional, and it will flow in the specified direction if the current value entered is a positive quantity. This model must be used on faces inside the problem domain.
• Double Potentials with Ground: At the terminal face, two scalar electric potential DOFs are defined. The potential on the opposite side of the specified direction is set to 0. The current will be unidirectional, and it will flow in the specified direction if the current value entered is a positive quantity. This model must be used on faces inside the problem domain.

  

  

Rules/Limitations of Excitations on Conduction Paths

Winding Excitations

For the eddy current simulations with displacement effect off for all objects:

• One or two terminals can be defined on a conduction path: if the path is a loop, then only one coil terminal per coil must be defined, else only two coil terminals per coil must be defined (for both solid and stranded cases).
• More than two coil terminals are not allowed on a conduction path.
• Coil terminals must be ordered according to the physical potential distribution. One potential degree of freedom (DOF) is assigned to each external coil terminal. Two DOFs are assigned to each internal coil terminal. For windings with external coil terminals, there are two coil terminals defined for each conduction path. The potential DOF of the second terminal on a conduction path is linked to the potential DOF of the first terminal on the next conduction path, which means the coils are serially connected. That is why it is essential to create the coil terminals in the order of the actual potential distribution on serially connected coils (conduction paths). The potential on the last Coil Terminal is set to zero. The same rule for linking the DOFs applies to the windings with internal coil terminals.

When the displacement effect is on, the restrictions above will not apply. You can define one external coil terminal per conduction path and needs to ensure that there is a reference potential defined in the design.

Current Excitations

• For stranded current excitation: More than two terminals are not allowed on a conduction path. For a loop conduction path, one terminal is defined. For other conduction paths, you must define two terminals (in and out). A voltage terminal and a stranded current terminal cannot be defined on the same conduction path.
• For solid current excitations: At least one voltage excitation is to be defined as a reference potential on the same conduction path of the current excitation. If a current excitation with Double Potentials with Ground exists in the path, or displacement current is enabled, this requirement does not apply. Multiple current excitations on a conduction path are allowed.

Voltage Excitations

• There must be at least one voltage excitation on a conduction path with current/voltage excitations if displacement effect is not enabled (if the path is not touching the odd symmetry boundary, or there is no current/voltage excitation with Double Potentials with Ground excitation, where the potential is set to 0 V).
• Winding excitation cannot be defined together with voltage or current excitations on the same path.
• On a conduction path there can be multiple solid voltage and current terminals defined.

Independent/Dependent and Odd Symmetry Boundaries

• Excitations cannot be defined on Independent/Dependent boundaries.
• If a conduction path crosses an Odd Symmetry boundary, excitations must be defined at External boundaries because the default electric potential value is zero on the Odd Symmetry boundary. Voltage excitation can be used to set a different potential value on the face intersecting with an Odd Symmetry boundary. Also, any excitation (Coil Terminal, Voltage, or Current Excitation) assignment is allowed on the face intersecting with an Odd Symmetry boundary.
• If a conduction path crosses both Odd Symmetry and Independent/Dependent boundaries, the software's validation process does not allow one external terminal definition on the path. You can select Perform minimal validations under Design Settings to simulate such designs at the your own risk. Full model simulation is highly recommended for such designs.

Matrix Setup

Parametric matrix setup is supported for the A-Phi transient solver. Only one matrix setup can be defined for inductance, capacitance, or DC resistance calculations. For computation of the defined matrix, select Enable Inductance Matrix Computation, Enable Capacitance Matrix Computation, or Enable DC Resistance Matrix Computation in the 3D Design Settings window:

Next, select the signals and grounds for the matrix of interest. For the inductance matrix, the following are restrictions on ground selections:

• Ground selection is not allowed for windings because they are internally grounded.
• Ground selection is not allowed for stranded current excitations because no potential is defined on the conduction path.
• Ground selection is not allowed for current excitations with double potentials and double potentials with ground.
• Ground selection is only available for Voltage excitation with Single Potential model. Ground selection is not allowed for voltage excitations with double potentials and double potentials with ground.

It is highly recommended that ground selection be as in the nominal problem setup, especially for designs with multi-terminal excitations on a conduction path. Other solver types do the matrix computation after the solution of nominal problem so it is fully postprocessed, and you can select different signal/ground/return path configurations. However, the transient solver is computing the matrix at each timestep and the computation is highly dependent on how the current flows on a path, especially for designs with multiple excitations on the path.

The capacitance matrix is computed using the electrostatic energy stored in a system under 1 V excitation for one selected signal and 0 V for all others. Based on the selection of signals and grounds, the solver computes the capacitance matrix of the system. Stranded conductors and floating conductors (no signal or ground assigned) are treated as equipotential surfaces. For the capacitance matrix, the following rule applies for the ground selection:

• There must be at least one ground selection in the Matrix setup if there is no internal zero reference potential defined in the design. Odd Symmetry, winding excitation, and double potentials with ground excitation model are examples of internal grounds.

The resistance matrix is computed with the assumption of a DC conduction solution using the material values at time zero, so it is time independent. For stranded conductors, the solver internally calculates the stranded resistance values. The resistance value (the user typically inputs the stranded resistance value in addition to the source resistance) in the winding excitation setup is not included in the DC resistance matrix.

Postprocessing Support

The A-Phi transient solver supports all the postprocessing features of the transient solver. Additionally, the following features are supported:

• Voltage in the Field Plot and in the Fields Calculator; there are cases where no voltage is defined in an object (in a stranded object, or in an object with no eddy or displacement effect setting).
• Magnetic vector potential in the Fields Calculator:

  

• Voltage and current quantities at the Voltage and Current Terminals; the current computed at any terminal is assumed to be flowing into the problem domain.