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Flyback Transformer

A flyback transformer on an RM8 core at 150 kHz, simulated in the time domain with the converter's current waveforms: losses, temperature and interwinding capacitance.

  • Component: RM8/I core, Ferroxcube 3C97, 0.3 mm centre gap; primary of 24 turns of litz, 45 strands of 0.05 mm; secondary of 4 turns of litz, 120 strands of 0.1 mm.
  • Simulation: Transient over 2 switching periods of imported currents, with Steady-state heat transfer and Capacitance; half model (Symmetric).
  • Winding model: Homogenization.
  • You get: average core and winding losses, the hotspot temperature, the interwinding capacitance, and flux and loss density at each time step.
  • Files: the converter currents, flyback-transformer-waveforms-150kHz.csv (CSV, 42 kB). The same file is waveform_dump.csv in the cached folder of the example project.
  • In TRAFOLO: Welcome screen › Examples › Flyback Transformer is this model with its results.
  • Run time: about 1.5 min on 8 CPU cores.

Model description

The windings carry the currents of a flyback converter switching at 150 kHz: the primary current ramps up to 2.3 A while the switch is on, then the secondary takes over at 13.8 A and ramps down to zero before the next period.

Core Core material Air gap Gap material
RM8/I Ferroxcube 3C97 0.3 mm, centre limb FR4
Winding Wire Turns Layers Strands Strand diameter Wire diameter
Primary Litz 24 2 45 0.05 mm 0.555 mm
Secondary Litz 4 1 120 0.1 mm 2.0 mm

Modelling instructions

Setup

  1. Under DOMAIN TYPE, select Symmetric (1). TRAFOLO models the half above z = 0 and scales the results to the whole transformer.
  2. Under ELECTROMAGNETICS, select Transient (2), because the currents are not sinusoidal, and tick Capacitance (3).
  3. Under HEAT TRANSFER, select Steady-state (4).
Setup tab with Symmetric, Transient, Capacitance and Steady-state selected
Symmetric (1), Transient (2) with Capacitance (3), Steady-state (4).

Materials

  1. Under Global Materials, select Ferroxcube 3C97 100C and click Copy (5).
  2. Copy Copper, Epoxy and Fiberglass Reinforced Epoxy (FR4) the same way. All four appear under Project Materials (6).
  3. Under Project Materials, select Ferroxcube 3C97 100C and click Edit Material.

  4. On General, select Relative Permeability, keep its value, 3.65e3, and set Core Loss Model to iGSE. Click Save.

    The library copy comes with Complex Permeability, and a Transient run does not start with it. The example uses a constant permeability and iGSE.

  5. Under Default Materials (7), set the material of each component:

Core Coil Other Bobbin Gaps
Ferroxcube 3C97 100C Copper Not set Epoxy Fiberglass Reinforced Epoxy (FR4)
Materials tab with Copy, the four project materials and the default material per component
Copy (5), Project Materials (6), Default Materials (7).

Core

  1. On Core, click New Group. Group1core appears.
  2. Click Configure next to Group1core.
  3. Set Source to Template, Scale to mm and Gap Type to Physical (8).

  4. In Geometry Builder, set Type to RM and subtype to 3, enter the dimensions in mm (9) and keep Mirror ticked:

    A B C D E F G H J R
    23.2 8.2 11 5.4 17 8.55 9.5 0 19.7 0

  5. Click New Gap, enter gMin −0.15 and gMax 0.15 (a 0.3 mm gap), and set Limb to Central limb (10).

  6. Click Apply (11).
  7. Under Translation and Rotation, set the y rotation to 90 deg and click Apply (12).
Group1core settings with Source, Scale, Gap Type, the RM dimensions, Apply and the 90 degree rotation about y
Group1core: Source, Scale and Gap Type (8), RM dimensions (9), Apply (11), rotation about y (12).
RM core in an angled 3D view with the dimension sketch and the gap table
The RM core with the dimension sketch, and the 0.3 mm centre gap (10).

Coil

  1. On Coil, click New Group (13). Group1coil, the primary, appears.

  2. Click Configure (14) next to Group1coil.

    Coil tab with New Group and Configure for Group1coil and Group2coilPrimary and secondary windings in an angled 3D view

  3. Set Source to Template, Scale to mm, Wire Type to Stranded & Litz and Turns per solid to 24 (15): one solid body carries all 24 turns.

  4. In Geometry Builder, set Type to Filled, enter the dimensions in mm and click Apply (16):

    A B C R H
    0 0 1.1 4.8 8

    Group1coil settings with Stranded and Litz wire, 24 turns per solid, the Filled Geometry Builder and Configure Wire
    Group1coil: wire settings (15), Filled dimensions and Apply (16), Configure Wire (17).

    Filled primary winding in an angled 3D view with the dimension sketch
    The primary: one Filled body carries all 24 turns.

  5. Click Configure Wire (17). In the Group1coil_2D tab, select Homogenization and set Packing to Hexagonal, Strand Thickness to 0.05 mm and Max Frequency to ≤ 1MHz (18).

    Group1coil_2D settings with Homogenization, Hexagonal packing, 0.05 mm strands, Max Frequency 1 MHz, Fill Factor and Generate Mesh
    Group1coil_2D: Homogenization settings (18), Fill Factor and Calculate (19), Generate Mesh (22).

  6. Next to Fill Factor, click Calculate (19), keep Strand Type Round and Strand thickness 0.05, set N strands to 45 (20) and click Accept (21). Fill Factor becomes 0.241. Then click Generate Mesh (22): TRAFOLO builds the 2D model of the strand bundle; without it the run stops.

    Fill Factor Calculator with 24 turns per solid, 0.05 mm round strands, 45 strands and fill factor 0.242D mesh of the hexagonal strand model of the primary

  7. Back on Coil, click New Group again, then Configure (23) next to Group2coil, the secondary. Set Source, Scale and Wire Type as for the primary and Turns per solid to 1 (24).

  8. In Geometry Builder, set Type to Massive, which builds the 4 round turns, enter the dimensions in mm and click Apply (25):

    A B C D R H N r
    0 0 2 2 6.1 8.3 4 1

    Group2coil settings with Stranded and Litz wire, 1 turn per solid, the Massive Geometry Builder and Configure Wire
    Group2coil: wire settings (24), Massive dimensions and Apply (25), Configure Wire (26).

    Four round secondary turns in an angled 3D view with the dimension sketch
    The secondary: 4 Massive turns.

  9. Click Configure Wire (26) and set Group2coil_2D like the primary, with Strand Thickness 0.1 mm (27). In Calculate (28), set N strands to 120 (29) and click Accept (30). Fill Factor becomes 0.3. Click Generate Mesh (31).

    Group2coil_2D settings with Homogenization, 0.1 mm strands, Fill Factor 0.3 and Generate MeshFill Factor Calculator with 0.1 mm round strands, 120 strands and fill factor 0.3

Bobbin

  1. On Bobbin, click New Group. Group1bobbin appears.
  2. Click Configure next to Group1bobbin.
  3. Set Source to Template and Scale to mm (32).
  4. In Geometry Builder, set Type to Default, enter the dimensions in mm and click Apply (33):
A B R H r h Gx Gz
0 0 7.1 8.5 1.4 1.15 0 0
Group1bobbin settings with Source, Scale and the Default bobbin dimensions
Group1bobbin: Source and Scale (32), Default dimensions and Apply (33).
Bobbin in an angled 3D view with the dimension sketch
The bobbin with the dimension sketch.

Assembly

  1. On Assembly, click Assemble Geometry.
Assembly table with air, both coils, core, bobbin and gap and their materials
Assembly: the bodies and their materials after Assemble Geometry.
Assembled half model in an angled 3D view
The assembled half model: core, gap, bobbin and both windings.

ElMag

  1. Under Primary Winding, set Excitation to Irms [A] and Coil group connection type to Series (34).

  2. Tick Secondary Winding and set the same (35).

    Primary and Secondary Winding with Irms excitation and Series connection
    Primary Winding (34) and Secondary Winding (35): Irms [A] and Series.

  3. In the coil group table (36), set both groups:

Coil Group Winding Connection
Group1coil Primary Series
Group2coil Secondary Series
Coil group table with Group1coil Primary and Group2coil Secondary
Coil groups (36): Group1coil Primary, Group2coil Secondary, both Series.
Front view of the half model with the windings coloured by winding
ElMag 3D view: the windings coloured as Primary and Secondary.

Circuits

Nothing to change: TRAFOLO builds the primary and secondary circuits from the ElMag settings.

Circuits tab with the primary and secondary circuit tables
The automatic circuits: ground, FEM coil and current source for each winding.
Circuit schematic with the transformer and a current source on each side
Schematic of the automatic circuits: each winding is driven by its current source.

Waveform

  1. Under General, set Frequency [Hz] to 150000 and Periods to 2 (37).
  2. Select Load (38).
  3. Under Import, click Import and open flyback-transformer-waveforms-150kHz.csv, downloaded under Files above, or waveform_dump.csv from the cached folder of the Flyback Transformer example. Set Time to SW1 - Current - Time [s], Primary Source to SW1 - Current and Secondary Source to TX1 - W2 - Current (39). TRAFOLO uses the last 2 periods of the file.

  4. Tick Optimize Timesteps, set #Points per period to 37 and Algorithm to 4 (40). Algorithm 4 places short time steps at the switching edges: 55 steps from 2.5 ns to 0.64 µs.

    Waveform settings with 150000 Hz, 2 periods, Load, the imported columns and Optimize TimestepsWaveform plot of the imported and simulated primary and secondary currents with the time step statistics

  5. Under Discrete Fourier Transform, set Number of harmonics to 7.

Heat

  1. Under GLOBAL SETTINGS, set Predicted Steady-State Temperature to 80 °C and Velocity Vector to (2.0; 0.0; 0.0) m/s (41): forced air at 2 m/s along x.

    Heat global settings with 80 degrees and 2 m per s air, and surface settings with convection at 70 degrees and automatic coefficient
    GLOBAL SETTINGS (41); SURFACE SETTINGS (43): Convection, 70 °C, Auto.

  2. Under FACES, select Geometry (42): settings made there apply to every face. Under SURFACE SETTINGS, keep Type Convection, set External temperature to 70 °C and tick Auto next to Heat transfer coefficient (43). TRAFOLO then estimates the coefficient of each face from the air velocity.

    Faces tree with Geometry selectedHalf model with all outer faces highlighted in blue

Mesh

  1. Under GLOBAL SETTINGS, set Mesh Algorithm to Netgen and Mesh Refinement to Normal (44).

    Mesh global settings with Netgen and Normal
    Mesh Algorithm Netgen and Mesh Refinement Normal (44).

  2. Click Compute Mesh (45). The mesh has about 31,000 elements.

    Compute Mesh buttonMesh of the half model with the mesh information

Solve

  1. Set Parallel cores (46) to the number of performance cores of your CPU and keep Solver Preset Fast (47).

    Solve tab with Parallel cores and Solver Preset Fast
    Parallel cores (46) and Solver Preset Fast (47).

  2. Click Simulation Setup, then Run Simulation (48).

    Simulation Setup and Run Simulation buttons
    Simulation Setup, then Run Simulation (48).

Results

Averages over the 2 simulated periods, with the copper resistance at the predicted 80 °C (Results › Summary):

Primary winding Secondary winding Windings Core Total
0.211 W 0.194 W 0.405 W 0.302 W 0.708 W
Results Summary with the average losses and the DC resistance of primary and secondary
Summary: average losses and the DC resistance of each winding.

Winding losses: AC against DC

The RMS currents of the imported waveforms and the DC resistances from Summary give the loss each winding would have with a DC current of the same RMS value:

Winding IRMS Ipeak Rdc at 80 °C IRMS²·Rdc Simulated loss AC/DC
Primary 0.85 A 2.3 A 0.191 Ω 0.139 W 0.211 W 1.52
Secondary 5.63 A 13.8 A 3.95 mΩ 0.125 W 0.194 W 1.55

A third of the winding loss comes from skin and proximity effects: the triangular currents carry harmonics into the MHz range, and each harmonic induces eddy currents in the strands. Homogenization computes this per harmonic; an estimate from the RMS current and Rdc alone would miss it.

Core loss and flux density

The core loses 0.30 W, 43 % of the total. The flux rises while the switch is on (2.5 µs) and falls back while the secondary conducts. Faraday's law gives the swing in the 8.55 mm centre pole: ΔB = V·ton/(N·A) = 130 V × 2.5 µs/(24 × 57 mm²) ≈ 0.24 T, and the field view shows 0.25 to 0.3 T there at the end of the on-time. More primary turns lower the swing, and the core loss with it, at the cost of more copper loss.

The field views step through the 2 periods; in the loss views, frame 1 is the period average.

Magnetic flux density in the core at the end of the on-time
Flux density at the end of the on-time, when the primary current peaks: about 0.3 T in the centre limb (Magnetic Flux, frame 36).
Coil loss density at the end of the on-time, in the primary winding only
Coil loss density at the end of the on-time: only the primary carries current (Coil Losses, frame 36).
Coil loss density after turn-off, in the secondary turns only
Coil loss density after turn-off: the secondary carries the current (frame 43).

Temperature

The hotspot is 79.1 °C, in the primary: the inner winding, whose heat has to pass the secondary, the bobbin or the core to reach the air. The transformer runs 3 to 9 K above the 70 °C air for 0.71 W of loss, about 13 K/W with 2 m/s forced air.

Temperature panel with the hotspot of 79.1 degrees
Summary, Temperature: hotspot 79.1 °C.

TRAFOLO evaluated the copper resistance at the predicted 80 °C, within 1 K of the computed hotspot, so one temperature iteration is enough. When the two differ by more than a few kelvin, set Predicted Steady-State Temperature to the computed hotspot and run again, or raise Temperature Iterations on Setup. Ferroxcube 3C97 100C has no Thermal Coefficients, so its core loss comes from the 100 °C data whatever this temperature is.

Steady-state temperature of core, windings and bobbin, highest in the primary winding
Steady-state temperature, 73 to 79 °C, highest in the primary winding (Temperature).

Interwinding capacitance

37.3 pF between primary and secondary (Capacitance Matrix on Summary). It carries common-mode current from the primary's switching edges into the secondary, i = C·dv/dt: a 10 V/ns edge drives 0.37 A. More distance between the windings, or a grounded screen between them, lowers it.

The example ships with these views but without 3D field data: run it before Open in ParaView (ParaView (post-processing).

Background

Why homogenization in a transient run

The flyback currents contain many harmonics, and each one adds proximity loss in the litz strands. Homogenization replaces each winding with an equivalent material that TRAFOLO computes from a 2D model of the strand bundle at harmonics of the switching frequency (DC to 1.95 MHz here), so the 3D mesh treats each winding as a solid and needs no strand-level elements. Max Frequency ≤ 1MHz sizes the strand mesh for the skin depth at 1 MHz; the harmonics above it carry 6 % of the primary current's I² and 5 % of the secondary's, so the coarser mesh there changes the winding loss little.

Method details: Homogenization of Litz and Stranded Windings; transient set-up: Transient Waveforms & Simulations; capacitance: Parasitic Extraction.

Further reading