Planar Transformer
Planar Transformer: Theoretical Foundations
Overview
Teacher! Today's topic is about planar transformers, right? What are they like?
A thin transformer where the windings are formed by PCB wiring patterns. It has excellent high-frequency characteristics and high reproducibility. Adopted in onboard chargers and server power supplies.
I see... Using wiring patterns for windings seems simple at first glance, but it's actually quite profound, isn't it?
Governing Equations
Discretization Method
How do you actually solve these equations on a computer?
We use spatial discretization by the Finite Element Method (FEM). We assemble the element stiffness matrices and construct the global stiffness equation.
We perform transformation to the weak form (variational form) and use formulation by the Galerkin method using test functions and shape functions. The choice of element type (low-order elements vs. high-order elements, full integration vs. reduced integration) directly affects the trade-off between solution accuracy and computational cost.
Matrix Solution Algorithms
What exactly are matrix solution algorithms?
Solve the simultaneous equations using direct methods (LU decomposition, Cholesky decomposition) or iterative methods (CG method, GMRES method). For large-scale problems, preconditioned iterative methods are effective.
| Solver | Classification | Memory Usage | Applicable Scale |
|---|---|---|---|
| LU decomposition | Direct method | O(nยฒ) | Small to medium scale |
| Cholesky decomposition | Direct method (symmetric positive definite) | O(nยฒ) | Small to medium scale |
| PCG method | Iterative method | O(n) | Large scale |
| GMRES method | Iterative method | O(nยทm) | Large scale / Non-symmetric |
| AMG preconditioner | Preprocessing | O(n) | Very large scale |
So, if you cut corners on the finite element method part, you'll pay for it later. I'll keep that in mind!
Implementation in Commercial Tools
So, what software can be used for planar transformers?
| Tool Name | Developer/Current | Main File Format |
|---|---|---|
| JMAG-Designer | JSOL Corporation | .jmag, .jproj |
| Ansys Maxwell | Ansys Inc. | .aedt, .maxwell |
| COMSOL Multiphysics | COMSOL AB | .mph |
Vendor Lineage and Product Integration History
Does each software have a dramatic origin story?
JMAG-Designer
What exactly is JMAG?
Developed by Japan's JSOL Corporation. An electromagnetic field analysis tool specialized for electrical equipment design.
Current affiliation: JSOL Corporation
Ansys Maxwell
Tell me about "Ansys Maxwell"!
Ansoft Maxwell. Low-frequency electromagnetic field analysis. Integrated into Ansys in 2008.
Current affiliation: Ansys Inc.
After hearing this, I finally understand why the Japanese one is important!
COMSOL Multiphysics
Tell me about "COMSOL Multiphysics"!
Founded in Sweden in 1986. Started as FEMLAB with MATLAB integration, later renamed COMSOL. Strong in multiphysics.
Current affiliation: COMSOL AB
File Formats and Interoperability
Are there any points to note when transferring data between different software?
| Format | Extension | Type | Overview |
|---|---|---|---|
| STEP | .stp/.step | Neutral CAD | 3D CAD data exchange format compliant with ISO 10303. Supports geometry + PMI. |
| IGES | .igs/.iges | Neutral CAD | Early CAD data exchange standard. Has issues with surface data compatibility. Transition to STEP is progressing. |
| JT | .jt | Lightweight 3D | Lightweight 3D format developed by Siemens. Standardized as ISO 14306. |
When converting models between different solvers, attention must be paid to the correspondence of element types, compatibility of material models, and differences in the representation of loads and boundary conditions. Particularly, high-order elements and special elements (cohesive elements, user-defined elements, etc.) often cannot be directly converted between solvers.
I see... Formats seem simple at first glance, but they're actually quite profound, aren't they?
Practical Considerations
Are there any "field wisdom" things not found in textbooks?
Verifying mesh convergence, validating the appropriateness of boundary conditions, and performing sensitivity analysis of material parameters are extremely important.
- Mesh dependency verification: Confirm convergence with at least 3 levels of mesh density.
- Boundary condition validity: Setting physically meaningful constraint conditions.
- Result verification: Comparison with theoretical solutions, experimental data, and known benchmark problems.
I've grasped the overall picture of planar transformers! I'll try to be mindful of it in my work starting tomorrow.
Yeah, you're doing great! Actually getting your hands dirty is the best way to learn. If you have any questions, feel free to ask anytime.
Planar TransformerโThe Design Philosophy of "Thin Power Supplies" Where PCB Copper Foil Becomes Windings
A planar transformer uses the copper foil wiring of a PCB as windings, distributing the windings across a multi-layer PCB structure to create an ultra-thin transformer. Because the winding cross-section becomes a constant sheet, skin effect and proximity effect are minimized (the copper foil is thin so current spreads uniformly across the surface), and copper loss at high frequencies is lower than with conventional wire windings. Commercialized by Philips (now NXP) in the 1990s, it is now a core technology for high-efficiency, thin designs in communication equipment, automotive power supplies, and medical devices. FEM analysis evaluates the complex current paths and magnetic field distribution of the 3D PCB laminated structure to design the optimal winding layout.
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