A power transformer can meet its turns-ratio and inductance targets yet overheat once installed in a converter. Core loss, winding loss, leakage inductance, connections and cooling interact, making transformer design a coupled electromagnetic, thermal and mechanical problem.
This technical paper adapts Chema Molina’s Frenetic newsletter articles “Magnetics Are Hard. F***ing Hard. — Part I” and “Transformer design is Hard—very Hard—Part II”, with supporting Ferroxcube material data and research on ferrite-core loss modelling. The central engineering task is to establish a thermally stable, electrically suitable construction before optimising size or cost.
Why electrical calculations are only the starting point
Transformer design begins with the converter’s electrical requirements, but it cannot end with a nominal inductance or calculated flux excursion. The physical construction determines how the component distributes loss and transfers heat into its surroundings.
Winding placement changes the magnetic field within the winding window. Insulation separates conductors electrically while also influencing the available copper space and heat-flow paths. Terminations add resistance and exchange heat with the PCB or busbars. A heatsink or cooling plate changes the thermal boundary conditions.
These effects connect otherwise separate design decisions. Moving a winding may change leakage inductance, conductor loss and winding-to-core heat transfer simultaneously. Increasing copper area may reduce DC resistance but require a different winding arrangement. A construction change intended to solve an electrical problem can therefore create a thermal problem elsewhere.
Transformer design optimisation should consequently compare complete constructions rather than isolated parameter improvements. A viable candidate needs compatible electrical behaviour, loss distribution, temperature and mechanical implementation.
Establish thermal feasibility before optimisation
The first meaningful design milestone is a transformer that reaches an acceptable steady operating temperature under its relevant operating conditions.
A room-temperature loss calculation followed by a single temperature-rise calculation does not establish this. The calculated temperature changes the properties used to calculate the losses. Those updated losses then change the temperature again.
The necessary calculation sequence is:
- Calculate core, winding and relevant connection losses.
- Calculate the resulting core and winding temperatures.
- Update temperature-dependent material and conductor properties.
- Recalculate losses and temperatures.
- Continue until the solution converges, or until the candidate exceeds its permissible operating conditions.
The important result is not simply convergence of the numerical solver. It is convergence to a physically acceptable operating point.
Why temperature feeds back into loss
Copper resistance increases with temperature. For an unchanged current waveform, this increases resistive heating. Ferrite loss has a different temperature dependence: its curve depends on the material, frequency and flux excursion, and it need not increase monotonically.
A transformer can therefore contain opposing temperature effects. Warming may initially reduce the core-loss contribution while increasing winding loss. At another operating point, both contributions may rise together.
The core and windings also exchange heat. A winding can become hotter even when its own calculated loss remains unchanged, because the core transfers more heat into it. Conversely, a cooled winding structure may remove part of the core’s heat.
A coupled thermal model of magnetics needs to preserve these heat-flow paths. Treating the core and winding as unrelated temperature-rise calculations can obscure the actual hotspot and the mechanism controlling it.
Stable temperature is not sufficient by itself
A stable solution may still be unsuitable if it exceeds the limits of the winding insulation, bobbin, encapsulant, connections or magnetic material.
The ferrite Curie temperature is particularly easy to misinterpret. It concerns the transition in magnetic behaviour; it is not the transformer’s permissible continuous operating temperature. Insulation and construction limits can govern operation well before that transition.
The useful acceptance criterion is therefore an acceptable stable temperature throughout the construction—not merely a temperature below the ferrite’s Curie point.
Ferrite loss versus temperature: use the material-specific curve
A ferrite material does not have a universal optimum operating temperature. Its loss-temperature relationship must be evaluated at the relevant frequency and flux density.
Ferroxcube 3C95 provides a useful example. Its material documentation characterises a comparatively flat loss-temperature response over a broad temperature range. This differs from treating every power ferrite as having a pronounced loss minimum at one particular temperature.
The tabulated 3C95 material characteristics include:
| Characteristic | Approximate value | Conditions |
|---|---|---|
| Specific power loss | 350 kW/m³ | 25 °C; 100 kHz; 200 mT |
| Specific power loss | 290 kW/m³ | 100 °C; 100 kHz; 200 mT |
| Saturation flux density | 530 mT | 25 °C; 10 kHz; 1200 A/m |
| Saturation flux density | 410 mT | 100 °C; 10 kHz; 1200 A/m |
These are material characteristics under the stated conditions, not measured losses or operating limits for a completed transformer.
The loss and saturation data also illustrate why temperature cannot be handled through a single correction factor. At the tabulated conditions, specific core loss is lower at the higher temperature, while the saturation flux-density value is also lower. A thermal change can therefore ease one design constraint while tightening another.
For selection, the practical question is not whether a material performs favourably at one temperature. It is whether its loss behaviour and magnetic characteristics remain compatible with the converter’s operating range and available cooling.
Why core shape matters to loss prediction
Material loss data provide an essential starting point, but applying them to a finished core introduces another modelling step.
The simplest approach treats loss density as uniform throughout the magnetic volume. That approach becomes less representative when the field distribution varies substantially within the core or when dimensions influence electromagnetic behaviour.
Three mechanisms deserve particular attention:
- Flux crowding: local magnetic flux density can differ from the value obtained from an effective cross-sectional area.
- Eddy-current loss: electrical properties and geometry influence currents induced within the ferrite.
- Dimensional resonance: the interaction between material properties and physical dimensions can alter internal field distributions.
Consequently, multiplying a reference loss density by core volume is a modelling assumption, not a geometry-independent physical rule.
Separate the material model from the field model
A material model describes how ferrite responds to electromagnetic excitation. A field model describes how that excitation is distributed through a particular core.
Both are needed when geometry-dependent effects become significant.
The Combined Field and Material Model, or CFM², provides a research example of this separation. Its field component covers ring, E- and U-core geometries and includes electromagnetic resonance. Its material component represents permeability, permittivity and conductivity as functions of excitation.
The engineering significance is broader than any one implementation: accurate material data cannot compensate for an unsuitable field distribution model, and a detailed geometric model cannot compensate for unsuitable material properties.
For design work, this means retaining the exact material grade and actual core geometry throughout the calculation chain. Substituting a generic ferrite description weakens the connection between the calculated result and the intended component.
Winding loss depends on construction, not just copper area
DC resistance captures only part of the winding-loss problem.
Alternating fields redistribute current within conductors and between neighbouring conductors. Skin and proximity effects make conductor geometry and winding arrangement important. Where an air gap is present, its fringing field can introduce additional local conductor loss.
These mechanisms help explain why selecting a larger conductor does not necessarily solve an AC winding-loss problem. The conductor may have lower DC resistance while remaining poorly positioned within the alternating magnetic field.
Fringing-field loss modelling connects the gap geometry, winding-window field and conductor loss. Its practical value is in locating the cause of heating rather than treating the winding as a uniform resistor.
Leakage inductance belongs in the construction specification
Leakage inductance is another consequence of field distribution. It depends on how the windings couple and therefore on their placement, separation and arrangement.
Its importance is circuit-dependent. In a resonant converter, it can interact with the resonant network. In a phase-shifted full-bridge converter, it influences the converter’s switching behaviour.
A winding change should therefore trigger a linked assessment of:
- Leakage and magnetising inductance.
- DC and AC winding loss.
- Insulation arrangement.
- Local field exposure.
- Thermal contact and heat-removal paths.
Optimising these independently can produce a construction that satisfies each simplified calculation but fails when the effects are combined.
The transformer model must include its installation boundary
A transformer does not operate in thermal isolation.
Terminals, PCB copper, busbars, mounting hardware and cooling interfaces can all exchange heat with it. Electrical connections may also generate heat of their own. Their influence becomes particularly important when they are close to the winding or connected to a cooling structure.
A model can consequently match one installation and disagree with another even when the magnetic assembly is unchanged.
The solution is to define the model boundary explicitly. It should distinguish:
| Model element | Required representation | Design consequence |
|---|---|---|
| Core | Material, geometry, loss distribution | Core heating and magnetic margin |
| Windings | Construction and loss distribution | Winding hotspots |
| Connections | Electrical loss and thermal paths | Terminal heating and heat exchange |
| Cooling interfaces | Contact and heat-removal conditions | Installed temperature |
| Surroundings | Mounting, enclosure and nearby heat sources | System-level thermal behaviour |
A boundary condition should describe the installed physical arrangement rather than provide a convenient route to a lower calculated temperature.
This is particularly relevant to planar magnetics with heatsinks or cooling plates. The mechanical interface is part of the thermal design, not an accessory added after the electromagnetic calculation.
What simulation and experimental results actually establish
Simulation results need to be classified by what they represent.
An electromagnetic model may estimate inductance, field distribution and loss. A thermal model may predict temperatures from those losses and its boundary conditions. A coupled model updates the loss calculation as temperature changes.
Each stage answers a different question. Agreement in inductance does not establish agreement in loss. Agreement in total loss does not establish agreement in hotspot temperature.
The newsletter’s laboratory examples illustrate this distinction qualitatively: thermal predictions for planar magnetics with cooling structures agreed reasonably with some tested configurations but diverged in another. That experience is not a general numerical accuracy rating for finite-element analysis.
Likewise, an error observed in one construction cannot be transferred to a different material, winding arrangement or cooling assembly.
Compare matched physical quantities
A useful model-to-hardware comparison should preserve the relationship between the calculated and measured quantities.
Examples include:
- Core temperature at the corresponding physical location.
- Winding temperature rather than an unrelated external surface temperature.
- Loss at the same electrical operating condition.
- Leakage inductance for the same winding and connection arrangement.
- Thermal behaviour with the same mounting and cooling configuration.
A single matching temperature can conceal an incorrect loss distribution. Excessive calculated core loss and insufficient calculated winding loss might still produce an apparently plausible external temperature.
The objective is therefore validation of the model’s relevant mechanisms, not simply agreement with one convenient measurement.
Design-in notes for engineers
A practical workflow should keep electrical, thermal and mechanical decisions connected.
- Define operating conditions before comparing candidates. Include the conditions that drive flux excursion, winding current and temperature, rather than assuming nominal operation is the most demanding.
- Use the exact ferrite grade. Evaluate its loss-temperature behaviour and magnetic characteristics over the intended operating range.
- Preserve construction detail. Winding placement, insulation, terminations and assembly tolerances belong in the design definition.
- Update losses with temperature. Continue the coupled calculation until it reaches an acceptable stable operating point.
- Separate loss sources. Retain core, winding and connection losses so that a hotspot can be traced to a mechanism.
- Reassess parasitics after construction changes. Leakage inductance and winding loss should not be treated as fixed while winding geometry changes.
- Model the installed cooling path. Include the relevant contacts, mounting and connection structures.
- Establish a feasible baseline before optimisation. Size and cost comparisons are meaningful only between constructions that meet the same operating requirements.
Before schematic, layout or production release, validate the relevant electrical behaviour and thermal operating points in representative hardware with the intended construction and cooling arrangement.
Summary
Transformer design is a coupled problem because the same construction controls magnetic fields, electrical losses and heat transfer. Temperature then feeds back into the properties used to calculate those losses.
Material data remain essential, but they must be applied with the correct excitation, geometry and temperature dependence. Simulation is most useful when its boundaries match the installation and its outputs can be compared with corresponding hardware measurements.
The resulting design process is iterative: establish feasibility, understand the loss distribution, reach an acceptable thermal equilibrium, and only then optimise the construction.
Further reading
- How Modern Tools Model Magnetic Components
- Optimization of 500W LLC Transformer – Case Study
- LLC Transformer Design: 2 kW Integrated Inductor
Source
This technical paper is an edited and extended adaptation of Chema Molina’s Frenetic newsletter article “Transformer design is Hard—very Hard—Part II” (2026), together with Part I. Supporting technical context comes from Ferroxcube’s material documentation and ETH Zurich’s ferrite-loss modelling research. Final component selection and qualification should use the applicable manufacturer specifications.
References
- Transformer design is Hard—very Hard—Part II, Chema Molina, Dr. Molina Newsletter, 2 November 2026.
- Magnetics Are Hard. F**ing Hard. — Part I, Chema Molina, Dr. Molina Newsletter.
- 3C95 / 3C97: Extreme Ferrites for Extreme Conditions, Ferroxcube, March 2022.
- Physical Modelling of Core Losses in Ferrite Cores, Théophane Dimier, doctoral thesis, ETH Zurich, 2024.
