CEM
3D Electromagnetics, powered by Palace
Extracting Coil Inductance and Coupling for Circuit and Power Design
- Electronics
- RF & Microwave
- Energy
- Aerospace & Defense
What This Simulation Does
The rings example is the canonical Palace magnetostatic problem: extraction of the inductance matrix for a pair of current-carrying rings in free space. Self- and mutual-inductances are recovered from the stored magnetic energy of the finite-element field solution.
- Curl-curl magnetostatics — Palace solves ∇×(μ⁻¹∇×A) = J for the magnetic vector potential A (B = ∇×A), driving each conductor with a prescribed surface current
- Energy-based inductance — the matrix follows from Wm = ½ Lij Ii Ij, so one solve per source yields the self- and mutual-inductance entries
- Flux linkage — SurfaceFlux (magnetic) through cut planes gives the flux linkage between rings, cross-checking the energy result
Key Parameters
- Problem type: Magnetostatic, length unit L0 = 1 μm
- Material: single vacuum/air region, permeability 1.0
- Boundaries: outer/far-field walls = PEC; Ring 1 and Ring 2 = prescribed SurfaceCurrent
- Postprocessing: domain Energy → inductance; SurfaceFlux (magnetic) → flux linkage; field probe at origin
- Solver: CG + auxiliary-space Maxwell (AMS) preconditioner, tolerance 1e-8, GPU device
The core transferable physics: any set of current-carrying conductors stores magnetic energy and links flux. Solving the magnetostatic field once per source recovers the entire self/mutual inductance network. What changes across applications is the conductor geometry (coils, windings, PCB traces, antennas) and what the inductance controls — resonance, energy transfer efficiency, or EMI coupling.
What Makes This Capability Unique
3D field-accurate inductance.
High-order FEM captures proximity effects and 3D flux paths that closed-form and 2D formulas miss, especially for tightly coupled coils.
Full matrix per source.
One solve per conductor yields self- and mutual-inductances — the exact lumped network for the coupled-circuit model.
Energy and flux cross-check.
Inductance from stored energy is validated against flux linkage through cut planes — two independent estimates for confidence.
AMS-accelerated on GPU.
The auxiliary-space Maxwell preconditioner makes curl-curl solves fast, so coupling-vs-geometry sweeps run in minutes.
Domain Applications
Select a domain to see how this simulation applies, with industry-specific scenarios and ROI.
The Problem
On-chip and on-board inductors, and the mutual coupling between them, set the behavior of oscillators, DC-DC converters, RF front ends, and clock networks. Inductance is geometric and notoriously hard to predict with formulas once conductors are close, multi-turn, or over a ground plane.
Unmodeled mutual inductance between adjacent inductors is a leading cause of oscillator pulling, converter instability, and EMI failures found only at bring-up — each costing weeks of debug and, at worst, a board respin at $50K–$300K.
A magnetostatic inductance extraction gives the exact L-matrix for the circuit model, catching coupling problems before layout freeze.
Applications
| Application | How this simulation maps |
|---|---|
| Integrated inductor design | Self-inductance vs turn geometry for VCOs, LNAs, and matching networks |
| Inductor-to-inductor coupling | Mutual inductance predicts oscillator pulling and converter interaction |
| EMI / loop coupling | Coupling between current loops quantifies radiated/conducted EMI risk |
Quantifiable Business Value
Scenario: A mixed-signal board team hits 1 inductive-coupling bring-up issue per 6 designs, averaging a partial respin. Inductance extraction prevents most of these.
Each avoided bring-up surprise also protects the product launch date — often worth more than the respin cost itself.
Recommended Next Steps
Extract your coils
Replace the rings with your coil/winding geometry and prescribe the surface currents to get the full inductance matrix.
Sweep alignment and geometry
Vary spacing, misalignment, and turn count to map coupling k and self-inductance across the operating envelope.
Feed your circuit model
Drop the extracted L-matrix into your SPICE/system model to close the loop between electromagnetics and circuit performance.
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