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LLC Coupled Transformer (with Inductor)

An LLC transformer and its series resonant inductor on one stack of PQ cores, simulated at 150 kHz with 120 V on the primary and a 10 Ω load, with steady-state heat transfer: losses per winding, core and heatsink, and the hotspot temperature.

  • Component: a PQ core pair, Btm, in Ferroxcube 3C95 with a 20 µm virtual gap, and a third PQ half, Top, on a 0.4 mm epoxy spacer; primary and secondary of 8 turns each of 1.5 mm × 0.5 mm flat copper, interleaved; inductor of 12 turns of 1 mm litz, 50 strands of 0.1 mm; aluminum heatsink and epoxy encapsulation.
  • Simulation: Harmonic at 150 kHz with 120 V RMS on the primary, and Steady-state heat transfer; half model (Symmetric).
  • Winding model: Massive (solid) for the transformer; Stranded & Litz with Homogenization for the inductor.
  • You get: losses of the primary, secondary, inductor, core and heatsink, the primary current and the hotspot temperature.
  • Files: none; every part comes from the Geometry Builder.
  • In TRAFOLO: Welcome screen › Examples › Transformer with Inductor is this model with its results.
  • Run time: about 2 min on 6 CPU cores, meshing included.

Model Description

The transformer sits in Btm, a PQ core pair. The resonant inductor sits in Top, a third PQ half placed upside down on Btm with a 0.4 mm spacer in between, so the inductor flux closes through the upper plate of Btm. Primary and secondary are interleaved layers of flat solid copper around the centre leg of Btm; the litz inductor is wound around the centre leg of Top. An aluminum heatsink frame and an epoxy encapsulation enclose the parts; the bottom faces of the core and the heatsink are held at 50 °C.

Core Shape Material Gap
Btm PQ pair, y −8.1 to 8.1 mm Ferroxcube 3C95 100C 20 µm virtual gap at y = 0
Top PQ half, upside down, y 8.5 to 16.6 mm Ferroxcube 3C95 100C 0.4 mm epoxy spacer to Btm
Winding Coil groups Wire Turns Conductor
Primary Group3coil, Group5coil Massive (solid) 8 1.5 mm × 0.5 mm copper
Secondary Group2coil, Group4coil Massive (solid) 8 1.5 mm × 0.5 mm copper
Inductor (Additional_Coil1) Group1coil Stranded & Litz 12 1 mm litz, 50 strands of 0.1 mm
Material Used for Key properties
Ferroxcube 3C95 100C Btm, Top ferrite, µr 3880, σ 0.2 S/m, k 4.25 W/(m·K)
Copper windings σ 5.96·10⁷ S/m, k 401 W/(m·K)
Aluminum heatsink σ 3.77·10⁷ S/m, k 239 W/(m·K)
Epoxy encapsulation, spacer insulator, k 0.2 W/(m·K)

Air domain, sized by TRAFOLO: x −40.95 to 40.95 mm, y −36.2 to 45.7 mm, z 0 to 40.95 mm (the half above z = 0).

LLC Transformer, Trafolo
Model of LLC Coupled Transformer

Video (20 min): this transformer with its integrated resonant inductor, from set-up to losses and temperature (recorded in an earlier TRAFOLO version).

Modelling Instructions

Setup

  1. Under DOMAIN TYPE, select Symmetric. TRAFOLO models the half above z = 0 and scales the results to the whole component.
  2. Under ELECTROMAGNETICS, select Harmonic: the excitation is a 150 kHz sine.
  3. Under HEAT TRANSFER, select Steady-state and keep Temperature Iterations at 1.
Setup tab with Symmetric, Harmonic and Steady-state selected
Symmetric (1), Harmonic (2), Steady-state (3).

Materials

  1. Under Global Materials, select Ferroxcube 3C95 100C and click Copy.
  2. Copy Copper, Aluminum, Epoxy and Fiberglass Reinforced Epoxy (FR4) the same way. All five appear under Project Materials.
  3. Under Project Materials, select Ferroxcube 3C95 100C and click Edit Material.

  4. On General, select Relative Permeability, keep its value, 3.88e3, and click Save.

    The library copy comes with Complex Permeability, which takes the core loss from its imaginary part instead of from the Core Loss tab. The example uses a constant permeability.

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

Core Coil Other Bobbin Gaps
Ferroxcube 3C95 100C Copper Aluminum Epoxy Fiberglass Reinforced Epoxy (FR4)
Materials tab with 3C95 found in Global Materials, Copy, Project Materials and Default Materials
Ferroxcube 3C95 100C in Global Materials (4), Copy (5), Project Materials (6), Default Materials (7).

Core

  1. On Core, click New Group. Group1core appears: Btm in the example.
  2. Click Configure next to Group1core.
  3. Set Source to Template, Scale to mm, Gap Type to Virtual and Virtual Gap to 20 µm: the contact gap between the two halves, not meshed.

  4. In Geometry Builder, set Type to PQ, enter the dimensions in mm, keep Mirror ticked and click Apply:

    A B C D E F G
    21.3 8.1 14 5.15 18 8.8 12

    Btm core group with Template, Virtual gap and PQ dimensions, and the core pair in an angled view
    Btm: Source, Scale, Gap Type, Virtual Gap (8); PQ dimensions, Mirror, Apply (9).

  5. Back on Core, click New Group again, then Configure next to Group2core: Top in the example.

  6. Set Source to Template, Scale to mm and Gap Type to None.
  7. In Geometry Builder, set Type to PQ with the same dimensions, untick Mirror and click Apply. This builds one half.
  8. Under Translation and Rotation, set y to −8.5 mm and the x rotation to 180 deg and click Apply. The half now sits upside down above Btm, from y = 8.5 to 16.6 mm, 0.4 mm clear of it.

Coil

  1. On Coil, click New Group. Group1coil, the inductor, appears.
  2. Click Configure next to Group1coil.
  3. Set Source to Template, Scale to mm, Wire Type to Stranded & Litz and Turns per solid to 1: each of the 12 bodies is one turn.

  4. In Geometry Builder, set Type to Matrix, enter the dimensions in mm and click Apply: 3 turns per layer in 4 layers, round wire of 1 mm.

    A B C D R H N r M W
    0 0 1 1 5 4.75 4 0.5 3 3.5

  5. Under Translation and Rotation, set y to 11 mm and click Apply. The inductor then sits in the window of Top, y = 8.6 to 13.4 mm.

    Inductor coil group with Stranded and Litz wire, y 11 mm and Matrix dimensions, and the 12 turns in an angled view
    Group1coil, the inductor: wire (10), y 11 mm (11), Matrix dimensions (12), Configure Wire (13).

  6. Click Configure Wire. In the Group1coil_2D tab (named after the group, so Inductor_2D in the example), select Homogenization and set:

    Setting Value
    Packing Hexagonal
    Strand Thickness 0.1 mm
    Max Frequency ≤ 1MHz
    Fill Factor 0.5

  7. Next to Fill Factor, click Calculate, keep Strand Type Round and Strand thickness 0.1, set N strands to 50 and click Accept. Fill Factor becomes 0.5: 50 strands of 0.1 mm fill half of the 1 mm wire. Max Frequency ≤ 1MHz covers the 150 kHz excitation.

  8. Click Generate Mesh: TRAFOLO builds the 2D model of the strand bundle; without it the run stops.

    Inductor_2D tab with Homogenization settings, the Fill Factor Calculator with 50 strands and the strand mesh
    Homogenization (14), wire settings (15), calculator with 50 strands (16), Generate Mesh (17); right, the strand mesh.

  9. Back on Coil, click New Group, then Configure next to Group2coil.

  10. Set Source to Template, Scale to mm and Wire Type to Massive (solid).

  11. In Geometry Builder, set Type to Matrix, enter the dimensions in mm and click Apply: 2 turns per layer in 2 layers of 1.5 mm × 0.5 mm.

    A B C D R H N r M W
    0 0 1.5 0.5 5 1.5 2 0 2 3.5

  12. Under Translation and Rotation, set y to 3 mm and click Apply.

  13. Build Group3coil, Group4coil and Group5coil the same way, or copy Group2coil with ⋮ and change only y. Primary and secondary layers alternate:
Coil group Name in the example Winding y (mm)
Group2coil Sec1 Secondary 3
Group3coil Pri1 Primary 1
Group4coil Sec2 Secondary −1
Group5coil Pri2 Primary −3
Coil tab with the five coil groups, the inductor above the interleaved transformer windings
New Group (18), Configure (19); the inductor above the four interleaved transformer groups.

Other

  1. On Other, click New Group. Group1othergeometry, the heatsink, appears.
  2. Click Configure next to Group1othergeometry.
  3. Set Source to Template and Scale to mm.

  4. In Geometry Builder, set Type to HeatSink, enter the dimensions in mm and click Apply:

    A B C D E
    21.3 8.8 1 2 24.7

  5. Under Translation and Rotation, set y to 4.25 mm and click Apply.

Heatsink group with HeatSink dimensions and y 4.25 mm, and the aluminum frame in an angled view
Heatsink: HeatSink dimensions and Apply (20), y 4.25 mm (21).

Bobbin

  1. On Bobbin, click New Group. Group1bobbin, the encapsulation, appears.
  2. Click Configure next to Group1bobbin.
  3. Set Source to Template and Scale to mm.

  4. In Geometry Builder, set Type to Cylinder, enter the dimensions in mm and click Apply:

    H Rin Rout
    18.8 0 9.1

  5. Under Translation and Rotation, set y to 4.25 mm and click Apply.

  6. Back on Bobbin, click New Group again, then Configure next to Group2bobbin: the spacer between Btm and Top.
  7. Set Source to Template and Scale to mm. In Geometry Builder, set Type to Box with X 21.3, Y 0.4 and Z 14 mm, and click Apply.
  8. Under Translation and Rotation, set y to 8.3 mm and click Apply. The spacer fills y = 8.1 to 8.5 mm and takes the Bobbin material, Epoxy.
Spacer bobbin group with Box 21.3 by 0.4 by 14 mm at y 8.3 mm
Group2bobbin, the spacer (FR4 in the example): Box dimensions (22), y 8.3 mm (23).

Assembly

  1. On Assembly, click Assemble Geometry. Each body takes the default material of its component.
Assembly tab with the bodies and their materials, and the assembled half model
The assembled half model: material of each body (24); after assembly the button reads Reset Geometry (25).

ElMag

  1. Under Primary Winding, set Excitation to Urms [V] and Coil group connection type to Series.
  2. Tick Secondary Winding, set Excitation to Circuits and Coil group connection type to Series: the secondary has no source of its own and drives the load resistor.
  3. Leave 2nd Secondary Winding unticked.
  4. Under Additional Coils, click New Coil and set the drop-down next to Additional_Coil1 to Primary: the inductor is then in series with the primary.
  5. In the coil group table, set the groups:
Coil Group Winding Connection
Group1coil Additional_Coil1 Series
Group2coil Secondary Series
Group3coil Primary Series
Group4coil Secondary Series
Group5coil Primary Series
ElMag tab with the windings, Additional_Coil1 on Primary and the coil group table
Primary Winding (26), Secondary Winding (27), Additional Coils (28), coil groups (29).

Circuits

TRAFOLO builds one circuit per winding and places Additional_Coil1 in the primary circuit. Elements with the same node number are connected; node 0 is ground.

  1. In the secondary circuit, click New Element, choose Resistor and set its value to 10 Ω.

  2. Set or check the node numbers. The source then drives the inductor and the primary in series:

    Circuit Element Positive node Negative node
    Primary Pri_Ph1, the source 10 0
    Primary Additional_Coil1, Group1coil 5 10
    Primary Pri_Winding1, Group3coil and Group5coil 5 0
    Secondary Sec_Winding1, Group2coil and Group4coil 100 0
    Secondary Sec_R1, the load 0 100

  3. Click Draw and Save: TRAFOLO saves the circuits and redraws the diagram.

Circuits tab with the primary and secondary circuits, the 10 ohm load and the diagram
New Element (30) adds the 10 Ω load Sec_R1 (31); Draw and Save (32).

Waveform

  1. In the Harmonics table, column Fundamental, set F [Hz] to 150000 and Primary Urms [V] to 120.
Waveform tab Harmonics table with 150000 Hz and 120 V in the Fundamental column
F [Hz] and Primary Urms [V] in the Fundamental column (33).

Heat

  1. Under GLOBAL SETTINGS, set Predicted Steady-State Temperature to 65 °C: TRAFOLO evaluates the copper resistance at this temperature. Ferroxcube 3C95 100C has no Thermal Coefficients, so its core loss comes from the 100 °C data whatever this value is.
  2. Under FACES, select Geometry: settings made there apply to every face. Under SURFACE SETTINGS, keep Type Convection, set External temperature to 50 °C and tick Auto next to Heat transfer coefficient. TRAFOLO then estimates the coefficient of each face for free convection in still air.
  3. Under FACES, select the three bottom faces Group1core1Face5, Group1othergeometry1Face10 and Group1othergeometry1Face18, set Type to Fixed Temperature and Temperature to 50 °C. They stand for the mounting surface, which acts as a heat sink.
Heat tab with the predicted temperature and a fixed temperature face of the heatsink selected
Predicted Steady-State Temperature (34), a fixed face selected (35, blue), Fixed Temperature 50 °C (36).

Mesh

  1. Open GLOBAL SETTINGS (+) and set Mesh Algorithm to Netgen and Mesh Refinement to Very Coarse.
  2. Click Compute Mesh. On a new model TRAFOLO first evaluates the mesh parameters when the tab opens (status Mesh evaluated successfully); until then the button reads Evaluate Mesh, so click that first if it does. The mesh has 95,561 elements, with an aspect ratio of 37.3.
Mesh tab with Netgen, Very Coarse, Compute Mesh and the mesh information
Mesh Algorithm, Mesh Refinement (37), Compute Mesh (38), 95,561 elements (39).

Solve

  1. Set Parallel cores to the number of performance cores of your CPU (TRAFOLO shows a Recommended value next to it) and keep Solver Preset Fast.
  2. Click Simulation Setup, then Run Simulation. The run takes about 1.5 min on 6 cores and ends with Solved successfully.
Solve tab with Parallel cores, Solver Preset, Simulation Setup and Run Simulation
Parallel cores (40), Solver Preset (41), Simulation Setup, Run Simulation (42).

Results

At 120 V RMS and 150 kHz with the 10 Ω load (Results › Summary):

Primary winding Secondary winding Inductor Windings Core Heatsink (Other) Total
1.353 W 1.371 W 1.073 W 3.796 W 1.651 W 1.041 W 6.49 W

The primary draws 5.1 A RMS at −65.1°. With its R AC source of 9.889 Ω the component takes 5.1² × 9.889 Ω = 257 W; 6.49 W of it, 2.5 %, are losses and the rest reaches the 10 Ω load.

Results Summary with the losses per winding, core and heatsink, the primary current 5.1 A and the hotspot 83.8 degrees
Summary: losses (43), primary current (44), hotspot (45).

Flux density is mostly 0.1 to 0.2 T and peaks at 0.56 T at the inner corners of the windows (Magnetic Flux).

Magnetic flux density in the Btm and Top cores, mostly 0.1 to 0.2 T
Flux density in the cores, up to 0.56 T at the inner corners of the windows (Magnetic Flux).

The aluminum heatsink loses 1.04 W, 16 % of the total: the fringing field of the gaps induces eddy currents in it, mostly in the legs at the height of the spacer (Other Losses).

Eddy current loss density in the aluminum heatsink frame
Eddy-current loss density in the aluminum heatsink, highest in the legs near the spacer (Other Losses).

The hotspot is 83.8 °C, in the transformer windings; the parts near the 50 °C mounting faces stay close to 50 °C (Temperature). TRAFOLO evaluated the copper resistance at the predicted 65 °C, 19 K below the hotspot; the core loss comes from the 100 °C data of 3C95 100C at any temperature. For a design check, set Predicted Steady-State Temperature to 84 °C and run again, or raise Temperature Iterations on Setup.

Steady state temperature of the half model from 50 to 83.8 degrees
Temperature, 50 to 83.8 °C, highest in the transformer windings (Temperature).

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

ParaView Analysis
Temperature and loss distribution on the LLC Coupled transformer surface using ParaView for detailed analysis