The RLC (Resistive-Inductive-Capacitive) Coil Group node is an advanced coil feature that takes advantage of the A-V formulation of the Magnetic and Electric Fields features to take into account in-plane electric current flow in the coil’s current balance. This feature combines the magnetic model of a Single Turn Coil (in Coil group mode) with a multiple-terminal electrical model for the in-plane current. This node can be used to approximate in 2D a coil in which (due to capacitive coupling or other phenomena) there is relatively significant current flow in the in-plane directions.

Apply this feature to a group of domains representing the cross sections of the coil turns on the modeling plane. Since the electric potential is assumed to be constant in the cross section of each turn, the V variable must be removed in the selected domains by applying an Ampère’s Law node. The feature applies an external current density flowing orthogonally to the plane, and also imposes a voltage constraint on the boundary of each cross section, computed from the coil and the excitation properties. The feature also enforces a balance of the current flowing out-of-plane and the current leaking in the plane between the coil turns.

In order to apply the correct voltage at each coil turn, it is necessary to precisely define the order in which the domains are connected. The RLC Coil Group feature assumes that all domains are of the same shape and are disposed on a two-dimensional Bravais lattice; that is, that there exist two vectors a and b (called primitive vectors) such that given two lattice points r1 and r2 the following relation holds:

with n and m being integers. One-dimensional lattices (linear lattices) are also supported by this feature.

The RLC Coil Group node can automatically determine two lattice vectors (or one, in the case of a linear lattice) from the geometry and position of the selected domains. The choices Row-wise and Column-wise in the Ordering settings use this functionality. The two choices control how the vectors a and b are chosen.

Since the primitive vectors of a Bravais lattice are not unique, the lattice recognition algorithm could find two vectors different from the desired one. In this case, it is possible to manually specify User defined lattice vectors.

By default, the RLC Coil Group feature assigns the first turn index (closest to the reference potential) to the turn with the smallest n and m. When using the automatic recognition algorithm, this usually corresponds to the coil turn with smallest x and y (or r and z in axisymmetry). The other coil turns are numbered in order of increasing m first, and then increasing n. Refer to the diagram in the node’s Settings window for a visual explanation.

If Winding is set to Alternated, the direction of increasing m is reversed each time n changes value. Again, refer to the diagram for a visual explanation.

The RLC Coil Group feature expands the model applied by a Single-Turn Coil domain feature by including a current balance for each turn and constraints for the voltage. The feature introduces n state variables (where n is the number of coil turns) with the dimensions of voltages: V1, V2,..., Vn. The i-th coil turn (i = 1,..., n) has an applied potential difference

where V0 is the value specified as the Ground voltage in the Settings window, that drives an out-of-plane external current density computed as in the Single-Turn Coil case:

The current flowing in-plane is balanced with the difference of the currents between two adjacent turns. If Ii is the out-of-plane current flowing in the i-th turn,

The coil current ICoil is computed from the coil excitation in the same way as for the Single-Turn Coil feature.

The settings in this section is very similar to the ones described in the Single-Turn Coil node. The only addition is the Ground voltage input. Specify in the text box the voltage at one end of the coil (SI unit: V). The voltage at the other end depends on the excitation type. This setting is useful, for example, to connect in series two coil groups.

This section specifies the information needed to identify the Bravais lattice on which the coil turns are placed The feature automatically detects the two primitive vectors of the lattice if Ordering is set as Row-wise (the default) or Column-wise. For User defined use the diagram as a guide to manually enter the Primitive vectors a and b (SI unit: m) of the lattice. The diagram shows how the domains are ordered for each choice.

Select a Winding style — Regular (the default) or Alternated. Look at the diagram for an illustration of these options.