Chapter 13 closes the electromagnetic design loop by converting winding resistance, AC winding effects, ferrite loss, and parasitic loss into a temperature prediction. A flyback transformer is not successful merely because it meets inductance, turns ratio, flux density, and insulation requirements at room temperature. It must remain within electrical, magnetic, insulation, and material limits at the hottest operating condition.
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Table of Contents
1. Loss and Temperature Must Be Solved Together
Transformer loss creates temperature rise, but temperature also changes transformer loss. Copper resistance rises with temperature. Ferrite core loss can change substantially with temperature. Semiconductor and clamp behavior can alter the waveform presented to the transformer. The thermal design is therefore an iterative problem rather than a final arithmetic step.
The total transformer loss is commonly separated into winding loss and core loss, with additional local contributions from leads, shields, gap-fringing effects, and other construction details.
SOLIDMAG ENGINEERING INSIGHT
Thermal Design Is the Final Check on Every Earlier Choice
Turns, gap, core size, material, conductor, winding arrangement, leakage, and capacitance all influence the loss budget.
If the transformer runs too hot, the correct solution may require revisiting any of those earlier variables rather than simply choosing a higher-temperature insulation class.
2. DC Copper Loss at Operating Temperature
For each winding, the DC copper loss is:
Copper resistance increases approximately linearly with temperature over the normal transformer operating range:
| Variable | Meaning |
|---|---|
| RT | Winding resistance at temperature T |
| RREF | Measured or calculated resistance at reference temperature |
| αCU | Copper temperature coefficient near the reference temperature |
| T | Winding operating temperature |
| TREF | Reference temperature |
This temperature correction can be significant. A winding that meets a DCR target at 25°C may dissipate materially more power near its operating hot spot.
ENGINEERING CAUTION
Use Hot Resistance for Hot Loss
Do not calculate full-load copper loss using only a 20°C or 25°C DCR value. The winding temperature and copper resistance must converge to a self-consistent operating point.
3. AC Winding Loss: Skin Effect, Proximity Effect, and Fringing
The effective resistance seen by the pulsed flyback current is generally higher than the DC resistance. A useful loss formulation is to sum the harmonic components of the current waveform:
For simplified early estimates, an AC-resistance factor can be applied to the temperature-corrected DCR:
The AC-resistance factor depends on frequency, harmonic spectrum, conductor diameter or thickness, number of layers, winding arrangement, and local magnetic field.
Important AC winding-loss mechanisms include:
- Skin effect within the conductor
- Proximity effect from neighboring turns and layers
- Current crowding near layer transitions and terminations
- Gap-fringing fields intersecting nearby conductors
- Unequal sharing among parallel strands
- Foil edge and tab current crowding
SOLIDMAG ENGINEERING INSIGHT
AC Resistance Is a Geometry Result
An AWG table can provide copper area and DC resistance, but it cannot predict the final high-frequency winding resistance.
Accurate AC loss requires the actual winding geometry or a validated analytical, numerical, or measurement-based model.
4. Primary, Secondary, and Auxiliary Winding Loss
Calculate loss for each winding separately because their current waveforms, conductor technologies, lengths, and AC-resistance factors are different.
A low-current auxiliary winding may contribute little direct copper loss, but a high-power auxiliary output can become thermally significant. Likewise, a four-turn secondary can dissipate substantial power because its RMS current is high even though its conductor length is short.
| Winding | Typical Loss Driver |
|---|---|
| Primary | Turns count, RMS current, multilayer proximity loss, temperature-corrected DCR |
| Main secondary | High RMS current, foil/parallel-conductor AC effects, tabs and terminations |
| Auxiliary | Load level, conductor size, regulation-driven placement |
| Shield | Eddy-current or circulating-current risk if poorly implemented |
5. Core Loss Is a Function of Material, Flux Waveform, Frequency, and Temperature
Ferrite core loss is commonly reported as power-loss density under specific waveform, frequency, flux-density, and temperature conditions.
| Variable | Meaning |
|---|---|
| PCORE | Total ferrite core loss |
| Pv | Core-loss density for the material and operating condition |
| Ve | Effective core volume |
A Steinmetz-type approximation is often expressed as:
but the coefficient set, flux definition, waveform type, temperature, and valid operating range must match the selected material data.
ENGINEERING CAUTION
Do Not Apply Sinusoidal Core-Loss Data Blindly to a Flyback Waveform
Flyback flux waveforms are generally nonsinusoidal and may include unequal slopes, zero intervals, DC bias, and variable frequency. Use manufacturer data or a waveform-aware loss model appropriate to the actual material and excitation.
6. Flux Excursion, Frequency, and Core-Loss Tradeoffs
Increasing switching frequency can reduce required energy per cycle and component size, but core loss and AC winding loss generally become more difficult to control.
Reducing flux-density excursion can lower core loss, but doing so often requires:
- More primary turns
- A larger core area
- A different reflected-voltage or duty-cycle strategy
- A different switching frequency
- A different ferrite material
More turns can increase copper length and winding layers, so minimizing core loss can increase copper loss. The optimum transformer normally occurs where the combined electrical, thermal, volume, cost, and manufacturing objectives are balanced.
SOLIDMAG ENGINEERING INSIGHT
Minimum Core Loss Is Not the Same as Minimum Transformer Loss
A low-flux design may have excellent ferrite loss and poor copper loss. A high-flux design may have compact windings and excessive core heating.
Optimize the total transformer rather than one loss component.
Flyback transformer optimization requires balancing several competing loss mechanisms. Increasing primary turns can reduce flux-density excursion and core loss, but it also increases copper length and DC resistance. Increasing switching frequency can reduce magnetic size while increasing AC winding and core-loss penalties.
The lowest-loss region is generally found between the extremes of too few turns, excessive flux-density excursion, and high core loss on one side, and too many turns, excessive copper length, and higher winding loss on the other. The optimum operating point depends on the selected core material, conductor geometry, winding arrangement, switching frequency, thermal environment, and mechanical constraints.
Figure 13-1. Flyback transformer loss map showing the interaction among copper loss, AC winding loss, core loss, switching frequency, flux-density excursion, and turns count.
7. Temperature Dependence of Ferrite Core Loss
Ferrite loss is temperature dependent, but the direction and magnitude of that dependence vary by material and operating point. Some power ferrites exhibit a loss minimum over a particular temperature range, while others rise more strongly at elevated temperature.
Therefore, the core-loss calculation should be repeated using material data at relevant temperatures rather than assuming room-temperature loss density applies everywhere.
At minimum, evaluate:
- Minimum ambient / cold start where relevant
- Nominal operating temperature
- Maximum expected core temperature
- Any temperature region where the material loss changes sharply
The same temperature sweep should also verify the material’s saturation margin because saturation flux density normally decreases with temperature.
8. Other Transformer-Related Losses
Not every loss associated with the transformer appears directly as winding or ferrite loss. Relevant contributors can include:
- Leakage energy dissipated in an RCD clamp or snubber
- Eddy-current loss caused by gap fringing
- Shield loss
- Lead and pin resistance
- Foil-tab and termination loss
- PCB copper associated with high-current winding terminations
- Circulating current caused by unequal parallel conductors
Some of these losses occur outside the transformer body, but they are consequences of transformer design choices and should be included in the converter efficiency and thermal budget.
9. From Power Loss to Temperature Rise
A simple lumped thermal estimate uses thermal resistance:
This is useful for early estimates, but a transformer does not have one uniform temperature or one universal thermal resistance.
Heat leaves the component through several paths:
- Natural or forced convection from the outer surfaces
- Radiation
- Conduction through the core
- Conduction through the bobbin and pins
- Conduction into the PCB
- Conduction through potting or encapsulation
- Airflow through and around the winding window
ENGINEERING CAUTION
One Thermal-Resistance Number Is an Approximation
The winding hot spot, core hot spot, bobbin, and outer surface can all be at different temperatures. Use empirical thermal characterization or a validated thermal model when temperature margin is small.
10. Winding Hot Spot, Core Hot Spot, and Material Limits
The design should identify the hottest credible location rather than relying only on external surface temperature.
| Part | Possible Limiting Mechanism |
|---|---|
| Copper winding | Insulation life, conductor temperature, solder/termination temperature |
| Ferrite core | Material loss, saturation margin, adhesive or coating temperature |
| Bobbin | Polymer temperature rating, mechanical stability, safety approval |
| Tape / sleeving | Insulation-system temperature class and dielectric aging |
| Adhesive / varnish / potting | Thermal rating, expansion, mechanical stress |
| Pins / solder joints | Local I²R heating and solder reliability |
The allowable transformer temperature is therefore determined by the most restrictive approved material, safety requirement, lifetime target, and magnetic-performance limit—not by the copper melting point or a generic insulation-class label.
11. Thermal Feedback and Iterative Convergence
A practical design loop is:
- Assume initial winding and core temperatures.
- Calculate temperature-corrected DCR.
- Calculate AC winding loss.
- Calculate core loss at the assumed material temperature.
- Calculate or estimate temperature rise.
- Update winding and core temperatures.
- Repeat until the temperatures and losses converge.
The iterative nature is important because copper and ferrite loss both depend on temperature.
A stable design should converge to a temperature below all relevant limits with adequate margin across tolerances and operating corners.
SOLIDMAG ENGINEERING INSIGHT
Thermal Margin Should Survive Tolerance Stacking
Do not optimize the nominal design to sit directly on the temperature limit. Production variation in inductance, DCR, core loss, airflow, ambient temperature, and load can all move the real hot spot upward.
12. Find the Worst Thermal Operating Corner
The highest output power is often a severe thermal condition, but it is not automatically the worst condition for every loss mechanism.
Evaluate combinations such as:
- Low line / full load
- High line / full load
- Maximum ambient temperature
- Minimum switching frequency
- Maximum switching frequency
- Minimum magnetizing inductance
- Maximum current-limit threshold
- Worst core-loss material tolerance
- Burst or skip modes if they create unusual thermal cycling
- Startup or overload if duration is significant
Low line may increase primary RMS current. High line may increase some switching-related stresses. Frequency variation can shift both core and winding loss. The thermal corner should be found by calculation and test rather than assumed.
13. Measuring Winding and Core Temperature
Prototype thermal validation should use multiple methods where practical.
Resistance Method for Copper Temperature
Winding resistance can be used to estimate average copper temperature:
where RC is the cold resistance at known temperature TC and RH is the hot winding resistance measured promptly after operation or by a validated in-situ method.
Thermocouples
Fine-gauge thermocouples can measure selected core and winding-surface locations, but placement can alter the local construction and may not reach the true buried hot spot.
Infrared Imaging
Infrared imaging is useful for exposed surfaces and comparative thermal patterns. Emissivity, reflective tape, ferrite finish, varnish, and inaccessible internal windings can affect accuracy.
ENGINEERING CAUTION
Surface Temperature Is Not Automatically Winding Hot-Spot Temperature
An externally measured bobbin or core temperature can be lower than a buried winding hot spot. Use a measurement method appropriate to the location that actually sets the temperature limit.
Transformer temperature is determined not only by total power loss but also by where that loss is generated and how effectively heat can leave the component. Winding copper loss, ferrite core loss, and termination losses create different local hot spots and use different thermal paths to reach the surrounding environment.
Heat leaves the flyback transformer through several parallel mechanisms, including conduction through the copper, ferrite, bobbin, pins, and PCB, convection to ambient air, and radiation from exposed surfaces. Because these paths are not identical for every internal region, the winding hot spot, core hot spot, and external surface temperature can differ significantly.
Figure 13-2. Flyback transformer thermal network showing heat generation in primary winding, secondary winding, ferrite core, and terminations with conduction, convection, radiation, and PCB heat-flow paths.
14. Worked Example — Loss and Temperature for the Chapter 12 Transformer
DESIGN ASSUMPTION
Educational Loss and Thermal Example
This example continues the earlier design and uses illustrative AC-resistance factors, core-loss density, and thermal resistance. Final values must come from the selected material, actual winding geometry, and prototype measurements.
| Parameter | Illustrative Value |
|---|---|
| Primary RMS current | 1.18 A |
| Secondary RMS current | 9.44 A |
| Primary DCR at 25°C | 98.7 mΩ |
| Secondary DCR at 25°C | 1.54 mΩ |
| Assumed winding temperature | 100°C |
| Copper temperature coefficient | 0.00393 /°C |
| Primary AC-resistance factor | 1.35 |
| Secondary AC-resistance factor | 1.60 |
| Auxiliary / lead winding loss allowance | 0.05 W |
| Candidate core volume | 6.3 cm³ |
| Illustrative core-loss density | 95 mW/cm³ |
| Illustrative transformer thermal resistance | 32 °C/W |
| Maximum ambient for example | 50°C |
Step 1 — Correct DCR to 100°C
Step 2 — Calculate Hot DC Copper Loss
Step 3 — Apply Illustrative AC-Resistance Factors
Step 4 — Estimate Core Loss
Step 5 — Estimate Total Transformer Loss
Step 6 — Estimate Temperature Rise
The calculated 87.6°C is lower than the assumed 100°C winding temperature used for the resistance correction. A second iteration would therefore use a temperature closer to 88°C and recalculate the winding resistance and losses.
Step 7 — Estimate Transformer-Only Efficiency Contribution
Using the 60.5 W output level from the earlier worked example:
This is only a transformer loss ratio. It does not include MOSFET, rectifier, clamp, gate-drive, control, capacitor, PCB, or other converter losses.
| Calculated Quantity | Result |
|---|---|
| Primary resistance at 100°C | 127.8 mΩ |
| Secondary resistance at 100°C | 1.99 mΩ |
| Primary winding loss with AC factor | 0.240 W |
| Secondary winding loss with AC factor | 0.285 W |
| Total winding loss incl. allowance | 0.575 W |
| Illustrative core loss | 0.599 W |
| Total transformer loss | 1.174 W |
| Estimated rise with 32°C/W | 37.6°C |
| Estimated temperature at 50°C ambient | 87.6°C |
| Approximate transformer-only efficiency | 98.1% |
SOLIDMAG ENGINEERING INSIGHT
The Worked Thermal Result Must Be Iterated and Measured
The example demonstrates the calculation flow, not a production prediction. AC-resistance factors, ferrite loss density, and thermal resistance are geometry- and material-specific.
The final design should converge analytically and then be validated on a representative transformer in the actual converter.
A practical thermal calculation must combine winding and core losses at the expected operating temperature. Copper resistance increases with temperature, high-frequency effects raise effective winding resistance, and ferrite core loss depends on frequency, flux excursion, material, and temperature.
The worked loss budget combines temperature-corrected primary and secondary copper loss with AC winding factors and ferrite core loss to estimate total transformer dissipation. Applying the estimated thermal resistance then provides a first-pass temperature-rise prediction, which should be iterated with temperature-dependent losses and ultimately verified on the physical transformer in the actual converter.
Figure 13-3. Worked flyback loss budget showing temperature-corrected primary and secondary copper loss, AC winding factors, core loss, total transformer loss, and estimated temperature rise.
15. How to Reduce Transformer Temperature
If the transformer exceeds its thermal target, possible design responses include:
| Design Change | Likely Benefit | Possible Tradeoff |
|---|---|---|
| Increase copper area | Lower DCR | More window fill, capacitance, or layer pressure |
| Reduce conductor AC loss | Lower winding heating | Higher-cost litz/foil optimization or more complex winding |
| Use larger core | Lower flux density and greater thermal area | Larger size and cost |
| Use lower-loss ferrite | Lower core heating | Material availability or cost |
| Increase primary turns | Lower flux excursion | More copper length and winding layers |
| Adjust switching frequency | Can reduce core or copper loss | Changes component size and control behavior |
| Reduce leakage/fringing exposure | Lower parasitic winding/clamp loss | May increase capacitance or require winding changes |
| Improve airflow / thermal conduction | Lower temperature rise | System-level mechanical changes |
The best correction is the one that improves total converter performance without causing a larger problem elsewhere.
16. Loss and Thermal Design Checklist
- Primary, secondary, and auxiliary RMS currents are known.
- DCR is corrected to expected operating temperature.
- Skin, proximity, and fringing effects are included in AC winding loss.
- Core-loss data match the selected material, waveform, frequency, flux, and temperature.
- Peak flux and temperature-adjusted saturation margin remain acceptable.
- Lead, pin, shield, and termination losses are considered.
- Leakage-related clamp loss is included in the converter thermal budget where relevant.
- Thermal analysis uses realistic ambient and cooling conditions.
- Winding hot spot and core hot spot are distinguished from surface temperature.
- Loss and temperature are iterated to convergence.
- Worst-case line, load, frequency, inductance, and ambient corners are checked.
- Prototype temperature is verified by appropriate measurement methods.
- Final temperature remains below all material, insulation, safety, magnetic, and lifetime limits with margin.
17. Design Handoff to Manufacturing, Testing, and Validation
At the end of Chapter 13, the transformer has a coherent electrical, magnetic, winding, parasitic, loss, and thermal design. The next question is whether that design can be built repeatedly and verified in production.
Chapter 14 will develop:
- Production drawing and winding specification
- Incoming core and bobbin controls
- Turns, polarity, and pin verification
- Magnetizing-inductance acceptance limits
- Leakage-inductance limits
- DCR limits
- Hi-pot and dielectric testing
- Insulation-resistance testing
- Mechanical inspection
- Thermal and converter validation
- Production traceability and revision control
SOLIDMAG ENGINEERING INSIGHT
A Design Is Not Finished Until It Can Be Verified
The transformer model produces targets; manufacturing turns those targets into a physical component; testing proves that the component actually meets them.
Chapter 14 converts the engineering design into reproducible production controls and validation evidence.
Technical References for This Chapter
Use the selected ferrite manufacturer’s core-loss data, conductor data, approved insulation-system ratings, and thermal information for the production design. Final transformer temperature should be verified in the actual converter and mechanical environment.
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