Copper Loss, Core Loss, and Thermal Design — Chapter 13

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.

In This Chapter — Click to Expand

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.

PTR=PWIND+PCORE+POTHERP_{TR}=P_{WIND}+P_{CORE}+P_{OTHER}

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:

PCU,DC=IRMS2RDC(T)P_{CU,DC}=I_{RMS}^2R_{DC}(T)

Copper resistance increases approximately linearly with temperature over the normal transformer operating range:

RT=RREF[1+αCU(T−TREF)]R_T=R_{REF}\left[1+\alpha_{CU}(T-T_{REF})\right]
VariableMeaning
RTWinding resistance at temperature T
RREFMeasured or calculated resistance at reference temperature
αCUCopper temperature coefficient near the reference temperature
TWinding operating temperature
TREFReference 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:

PCU=∑n=0∞In,RMS2RAC,nP_{CU}=\sum_{n=0}^{\infty} I_{n,RMS}^2R_{AC,n}

For simplified early estimates, an AC-resistance factor can be applied to the temperature-corrected DCR:

FR=RACRDCF_R=\frac{R_{AC}}{R_{DC}}
PCU≈IRMS2RDC(T)FRP_{CU}\approx I_{RMS}^2R_{DC}(T)F_R

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.

PWIND=PP+PS+∑PAP_{WIND}=P_P+P_S+\sum P_A

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.

WindingTypical Loss Driver
PrimaryTurns count, RMS current, multilayer proximity loss, temperature-corrected DCR
Main secondaryHigh RMS current, foil/parallel-conductor AC effects, tabs and terminations
AuxiliaryLoad level, conductor size, regulation-driven placement
ShieldEddy-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.

PCORE=PvVeP_{CORE}=P_vV_e
VariableMeaning
PCORETotal ferrite core loss
PvCore-loss density for the material and operating condition
VeEffective core volume

A Steinmetz-type approximation is often expressed as:

Pv≈kfαBβP_v\approx kf^\alpha B^\beta

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.

Flyback transformer loss map showing how copper loss, AC winding loss, core loss, switching frequency, flux-density excursion, and primary turns count interact to determine total transformer loss.

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.


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:

ΔT=PLOSSθTH\Delta T=P_{LOSS}\theta_{TH}
THOT≈TAMB+PLOSSθTHT_{HOT}\approx T_{AMB}+P_{LOSS}\theta_{TH}

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.

PartPossible Limiting Mechanism
Copper windingInsulation life, conductor temperature, solder/termination temperature
Ferrite coreMaterial loss, saturation margin, adhesive or coating temperature
BobbinPolymer temperature rating, mechanical stability, safety approval
Tape / sleevingInsulation-system temperature class and dielectric aging
Adhesive / varnish / pottingThermal rating, expansion, mechanical stress
Pins / solder jointsLocal 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:

  1. Assume initial winding and core temperatures.
  2. Calculate temperature-corrected DCR.
  3. Calculate AC winding loss.
  4. Calculate core loss at the assumed material temperature.
  5. Calculate or estimate temperature rise.
  6. Update winding and core temperatures.
  7. Repeat until the temperatures and losses converge.

The iterative nature is important because copper and ferrite loss both depend on temperature.

T(n+1)=TAMB+PLOSS(T(n))θTHT^{(n+1)}=T_{AMB}+P_{LOSS}\!\left(T^{(n)}\right)\theta_{TH}

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:

TH=TC+RH/RC−1αCUT_H=T_C+\frac{R_H/R_C-1}{\alpha_{CU}}

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.

Cross-sectional flyback transformer thermal network showing heat generation in primary and secondary windings, ferrite core, and terminations, with conduction, convection, radiation, and PCB heat-flow paths.

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.

ParameterIllustrative Value
Primary RMS current1.18 A
Secondary RMS current9.44 A
Primary DCR at 25°C98.7 mΩ
Secondary DCR at 25°C1.54 mΩ
Assumed winding temperature100°C
Copper temperature coefficient0.00393 /°C
Primary AC-resistance factor1.35
Secondary AC-resistance factor1.60
Auxiliary / lead winding loss allowance0.05 W
Candidate core volume6.3 cm³
Illustrative core-loss density95 mW/cm³
Illustrative transformer thermal resistance32 °C/W
Maximum ambient for example50°C

Step 1 — Correct DCR to 100°C

FT=1+0.00393(100−25)≈1.2948F_T=1+0.00393(100-25)\approx1.2948
RP,100≈98.7 mΩ(1.2948)≈127.8 mΩR_{P,100}\approx98.7\ \mathrm{m\Omega}(1.2948)\approx127.8\ \mathrm{m\Omega}
RS,100≈1.54 mΩ(1.2948)≈1.99 mΩR_{S,100}\approx1.54\ \mathrm{m\Omega}(1.2948)\approx1.99\ \mathrm{m\Omega}

Step 2 — Calculate Hot DC Copper Loss

PP,DC≈(1.18)2(0.1278)≈0.178 WP_{P,DC}\approx(1.18)^2(0.1278)\approx0.178\ \mathrm{W}
PS,DC≈(9.44)2(0.00199)≈0.178 WP_{S,DC}\approx(9.44)^2(0.00199)\approx0.178\ \mathrm{W}

Step 3 — Apply Illustrative AC-Resistance Factors

PP≈0.178(1.35)≈0.240 WP_P\approx0.178(1.35)\approx0.240\ \mathrm{W}
PS≈0.178(1.60)≈0.285 WP_S\approx0.178(1.60)\approx0.285\ \mathrm{W}
PWIND≈0.240+0.285+0.050≈0.575 WP_{WIND}\approx0.240+0.285+0.050\approx0.575\ \mathrm{W}

Step 4 — Estimate Core Loss

PCORE=PvVeP_{CORE}=P_vV_e
PCORE≈(0.095 W/cm3)(6.3 cm3)≈0.599 WP_{CORE}\approx(0.095\ \mathrm{W/cm^3})(6.3\ \mathrm{cm^3})\approx0.599\ \mathrm{W}

Step 5 — Estimate Total Transformer Loss

PTR≈0.575+0.599≈1.174 WP_{TR}\approx0.575+0.599\approx1.174\ \mathrm{W}

Step 6 — Estimate Temperature Rise

ΔT≈1.174(32)≈37.6∘C\Delta T\approx1.174(32)\approx37.6^\circ\mathrm{C}
TEST≈50+37.6≈87.6∘CT_{EST}\approx50+37.6\approx87.6^\circ\mathrm{C}

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:

ηTR,APPROX=60.560.5+1.174≈98.1%\eta_{TR,APPROX}=\frac{60.5}{60.5+1.174}\approx98.1\%

This is only a transformer loss ratio. It does not include MOSFET, rectifier, clamp, gate-drive, control, capacitor, PCB, or other converter losses.

Calculated QuantityResult
Primary resistance at 100°C127.8 mΩ
Secondary resistance at 100°C1.99 mΩ
Primary winding loss with AC factor0.240 W
Secondary winding loss with AC factor0.285 W
Total winding loss incl. allowance0.575 W
Illustrative core loss0.599 W
Total transformer loss1.174 W
Estimated rise with 32°C/W37.6°C
Estimated temperature at 50°C ambient87.6°C
Approximate transformer-only efficiency98.1%

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.

Worked flyback transformer loss budget showing temperature-corrected primary and secondary copper loss, AC winding factors, ferrite core loss, total transformer loss, and estimated temperature rise.

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 ChangeLikely BenefitPossible Tradeoff
Increase copper areaLower DCRMore window fill, capacitance, or layer pressure
Reduce conductor AC lossLower winding heatingHigher-cost litz/foil optimization or more complex winding
Use larger coreLower flux density and greater thermal areaLarger size and cost
Use lower-loss ferriteLower core heatingMaterial availability or cost
Increase primary turnsLower flux excursionMore copper length and winding layers
Adjust switching frequencyCan reduce core or copper lossChanges component size and control behavior
Reduce leakage/fringing exposureLower parasitic winding/clamp lossMay increase capacitance or require winding changes
Improve airflow / thermal conductionLower temperature riseSystem-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.

Ready to Design a Flyback Transformer?

Move from design theory to an automated magnetic design. Enter the converter requirements and evaluate a coordinated transformer candidate, winding geometry, loss estimates, thermal performance, and CAD output.

ABOUT THE AUTHOR

Stan Gibson

Electrical Engineer & Founder, SolidMagnetics

Stan Gibson is an electrical engineer and founder of SolidMagnetics, an engineering platform focused on magnetic-component design automation. His work includes power electronics, inductor and transformer design, magnetic-core selection, winding design, thermal analysis, and manufacturable CAD development. Through SolidMagnetics, he develops technical guides, calculators, and automated design tools intended to help engineers move from electrical requirements to practical magnetic-component designs.

View Full Author Profile