Coils & circuits

Exciting your model: coils, turns, fill factor, windings, and the RLC circuit editor.

Coils

A coil is created empty, then attached to the region(s) it excites as a separate step — add one from the Model Tree's Coils list, then attach regions to it either from each region's own Set Coil field or by right-clicking selected regions on the canvas and choosing Set Coil (with a Swap Direction option to flip which regions carry current in and which carry it out, for a go/return pair of slots).

Double-click a coil to open Coil Properties:

• Number of Turns;
• Current Type — DC, AC, Pulsed or Custom, each with its own parameters (AC: amplitude, frequency, phase, DC offset; Pulsed: amplitude, frequency, pulse width, offset; Custom: an editable time/current table with a live plot, the only way to drive an arbitrary waveform);
• Enable eddy-current — models induced eddy currents within the coil's own conductor, not just the current you impose;
• Use calc. resistance — when ticked, Nabla derives the coil's resistance from its geometry, turns and Coil Fill Factor rather than you typing a value in;
• Additional Resistance and Additional Inductance — extra lumped R/L added on top (of the calculated value, or used alone if calculated resistance is off) to represent whatever the 2D cross-section cannot capture, such as external wiring.

A coil is auto-named CL_N from its position in the coil list; deleting a coil renumbers the ones after it. Coil Properties edits exactly one coil at a time even if several are selected in the tree — unlike Region Properties, there is no bulk-edit here, so a change to turns or current type has to be repeated per coil (or set once at the phase level, see Phase excitation, which pushes the same value to every coil in a phase for you).

Turns, fill factor and calculated resistance

Coil Fill Factor (0–1) is the fraction of a slot's cross-section that is actually copper rather than insulation and air. With Use calc. resistance on, Nabla scales a single turn's region resistance by the number of turns squared and divides by the fill factor — the standard result of N series turns sharing one slot's copper cross-section, where each turn's effective area is the slot area times the fill factor divided by N. Getting the fill factor right matters more than it might look: since resistance scales with its reciprocal, a fill factor that is too optimistic under-predicts copper loss.

Windings

The Machines module builds a coil per slot for you from a small set of winding parameters instead of you defining each one by hand: choose Distributed or Concentrated layout, and Single-layer or Double-layer, plus the number of phases, turns per coil section, coil pitch (chording), and the winding's own filling factor (the slot-level equivalent of a manual coil's fill factor, used for the same copper-loss estimate at the winding level). An end-winding extension length lets the analytical end-winding resistance and inductance below account for the straight run beyond the slot before the conductor turns back — see End-winding resistance and inductance.

Phase excitation

A machine winding is driven per phase rather than per coil: set each phase's current directly (DC/AC/Pulsed/Custom, the same choices as a manual coil), or define it as Id/Iq — a magnitude and an advance angle in the rotor's own reference frame, the natural way to specify a synchronous machine's operating point. Editing a phase pushes its turns, current, resistance and inductance down to every coil in every parallel branch of that phase, splitting resistance/inductance evenly across the parallel paths so the model stays consistent without editing each underlying coil by hand.

A phase's coils are organised into an explicit Parallel Branches count: set how many parallel paths the phase's total current splits across, and Phase Properties shows how many coils fall into each branch (in series within a branch) so the winding stays internally consistent. Entering a phase current divides it by the number of parallel branches before it reaches any single coil — the value you type is always the phase's total current, never one branch's share of it.

End-winding resistance and inductance

The 2D cross-section only models the straight, in-slot part of a winding; the loop connecting one slot to the next outside the lamination stack (the end-winding) is added analytically from the winding geometry — a semicircular-loop model for inductance and a matching resistance from the same bundle geometry and the winding's filling factor. Both are on by default and can be switched off independently if you would rather compare against a purely 2D result.

Circuits

The Circuit Editor tab is a small schematic canvas for wiring coils together with lumped RLC elements, sources and switches, wherever the 2D field solve alone is not the whole circuit you want to model (a diode bridge feeding a coil, a snubber, several coils in series or parallel with an external source). Available elements:

• Wire — connects two component terminals;
• Voltage Source and Current Source — DC/AC/Pulsed/Custom, the same waveform choices as a coil;
• Resistance, Capacitance, Inductance — plain lumped values;
• Switch — a resistance when closed and a (very large) resistance when open, driven by an editable time/state table so it can open or close at a chosen instant;
• Ground — the reference node every circuit needs;
• a defined Coil can itself be dropped onto the schematic and wired in alongside the other elements.

Each element is click-to-place on the schematic canvas, then wired by drawing Wire segments between terminals. Any placed element (and a wire) can be rotated in fixed 90° steps and removed with Delete once selected. Values are entered in base SI units regardless of the model's length unit: Resistance in Ohm, Capacitance in Farad, Inductance in Henry; a Switch's closed- and open-state resistances (Ron / Roff) default to a very small and a very large value respectively (1µΩ / 1 MΩ) rather than being an ideal short or open, which keeps the circuit matrix well-conditioned.

A Custom source (coil or circuit) and a Switch are both driven by an editable time/value table with an "Add Item" button and a live plot:

• a Custom source's table is (time, current or voltage) pairs, linearly interpolated between them for the plot and the solve; points must be entered in increasing time order (editing a point's time clamps it between its neighbours) and the first point's time only has to be ≥ 0, not exactly zero;
• a Switch's table is (time, state) pairs plotted as a step function rather than interpolated — state 0 is open (Roff) and 1 is closed (Ron), so the switch snaps at each listed time rather than ramping.

Enable Enable circuit solver in the Solver settings for the circuit to be solved together with the field, rather than the coil currents being taken as fixed sources.

Next steps

• Motion — moving a coil-bearing region.
• Solving — enabling the circuit solver and eddy currents.
• Back to the contents.