Planar Inductor

Introduction

The demand for compact and efficient DC-DC converters across industries like aerospace, telecommunications, and electric vehicles is driving significant advancements in modern-day power electronics. A key innovation in this area is the transition from mid-frequency to high-frequency magnetics, largely enabled with the help of wide-bandgap (WBG) semiconductor devices. Among these developments, planar magnetic components have become increasingly prominent due to their low profile and compatibility with PCB technology, which utilizes copper tracks. This shift has led to their widespread adoption in industry and academia in recent years.

Planar inductors offer numerous advantages over traditional wire-wound components, such as higher power density, improved thermal performance, low leakage inductance in transformers using interleaving, and greater ease of manufacturing and repeatability. However, designing these components for high-frequency applications—often in the hundreds of kHz—introduces unique challenges. The skin and proximity effects become more pronounced, which results in increasing AC resistance in the windings. Additionally, the proximity of windings with large surface area results in parasitic capacitance, which becomes more significant at high frequencies, potentially causing electromagnetic interference, waveform distortion, and reduced overall efficiency. Also, the fixed geometry of copper traces on PCBs limits post-manufacturing adjustments, making accurate initial design crucial.

When designing these components, key considerations include core material selection, air gap configuration, efficiency, and size constraints. Precisely estimating critical parameters like inductance, parasitic capacitance, and resistance is essential, as these factors are often interdependent, making manual calculations prone to erroneous results. Nevertheless, accurately pre-determining core and copper losses becomes increasingly complex at high frequencies due to skin and proximity effects as well as the non-sinusoidal behavior of the core fluxes.
Given these challenges, FEM-based software tools have become indispensable, allowing for precise numerical simulations that enable accurate pre-determination of performance and losses. TRAFOLO excels at modeling transformers and inductors with complex PCB copper trace geometries, accurately simulating intricate layouts. It can calculate key parameters such as inductance, capacitance, and resistance—while also evaluating core and copper losses. This ensures that the PCB and core operate efficiently and within safe thermal limits, leading to a more reliable and effective design process for high-frequency planar magnetic components.

Model Description

The planar inductor is modeled with an EE ferrite core, featuring a two-layer copper winding on a PCB plate. The planar inductor is evaluated over a frequency range of 10 kHz to 100 kHz through an inductance sweep, measuring electrical parameters and losses in the system. The model incorporates electromagnetic behavior under steady-state thermal conditions to ensure an accurate assessment of the inductor’s performance.

Planar inductor with an E/El ferrite core and two-layer copper trace winding on a PCB.

Modeling Instructions

Setup

1. From the Model Builder, click the Setup tab.
2. Locate the General section and set the Domain Type as Full since the geometry is unsymmetric.
3. In the Simulation Type section, set Electromagnetics to Inductance.
4. Check the Without Circuits box. As we measure inductance for a planar model at very high frequencies, the current distribution within the conductors becomes increasingly complex due to phenomena like the skin effect, proximity effect, and parasitic capacitance. This complexity can make it difficult for the solver to converge to a solution.
   To address this issue, the ‘Without Circuits’ option can be utilized. This option allows the solver to bypass the circuit elements and directly apply a voltage to the terminals. By simplifying the problem in this way—focusing solely on the electromagnetic behavior of the model without the additional constraints of circuit components—the solver is more likely to converge to a solution efficiently, even at high frequencies.
5. Heat transfer is disabled by default as the Without circuits setting is being used.
   

   Domain type and Simulation type settings for planar inductor analysis.

Materials

1. Select the Materials tab from the Model Builder.
2. From the Global Material section, select Copper and click the Copy button.
3. Similarly, copy 3C90 Ferroxcube 100C and Fiberglass Reinforced Epoxy (FR4) from the Global Materials section to the Local Materials section.
4. In the Default Materials section, select the material type for each component from the dropdown list as per the table below:
   

   Component	Core	Coil	Other	Bobbin	Gaps
   Material type	3C90 Ferroxcube 100C	Copper	Not set	Fiberglass Reinforced Epoxy (FR4)	Not set

   

   Interface for material selection for different components of the model.

Core

1. From the Model Builder, click on the Core tab.
2. Click the New Group button. The Group1core will be added.
3. Click the Open in new tab icon. The Group1core tab will open.
4. From the Source dropdown list, select Template.
5. From the Scale dropdown list, select mm.
6. From the Gap Type dropdown list, select None.
7. In the Rotation and Translation section, set the translation (mm) according to the table below to align the core with the CAD-imported coil geometry while assembling.
   

   x	y	z
   -0.7685	0.9	33.0

8. In the Geometry Builder section, set the Type to E / EL and enter the dimensions (mm) as per the table below:
   

   A	B	C	D1	D2	E	F	R
   32.0	20.5	24.9	20.5	6.4	10.5	4.4	0.0

9. Click the Apply button.
   

   3D model configuration and visualization of core geometry.

Coil

1. From the Model Builder, click on the Coil tab.
2. Click the New Coil tab. The Group1coil will be added.
3. Click Open in new tab icon. The Group1coil tab will open.
4. From the Source dropdown list, select CAD.
5. Click the Import button. The Import CAD geometry dialog box will show up.
   

   Importing CAD geometry with unmodified geometry handling algorithm.

6. Import the coil geometry file.
7. From the Scale dropdown list, select mm.
8. Select Unmodified from the Geometry Handling Algorithm dropdown list to avoid cutting the coil by other geometries and to detect overlapping while assembling the geometry.
9. Click the Ok button.
10. From the Wire Type dropdown list, select Massive (solid).
    

    3D configuration and visualization of winding geometry.

Other

1. If there is any additional body type like clamp, dielectric, or shield, it can be included in Other. Here, this step can be skipped.

Bobbin

1. Click on the Bobbin tab from the Model Builder.
2. Click the New Group button. The Group1bobbin will be added.
3. Click the Open in new tab icon. The Group1bobbin tab will open.
4. From the Source dropdown list, select Template.
5. From the Scale dropdown list, select mm.
6. In the Rotation and Translation section, set the translation (mm) according to the table below to align the bobbin geometry with the CAD-imported coil geometry.
   

   x	y	z
   -0.5	0.9	30.0

7. Click the Apply button.
8. Locate the Geometry Builder section.
9. Enter the details as per the below table.
   

   Type	Linked Coil	xb	yb	zb
   Box	None	28.0	1.6	60.0

10. Click the Apply button.
    

    Geometry configuration and 3D visualization of PCB layout.

Assembly

1. Click the Assembly tab from the Model Builder.
2. For unsymmetrical geometries, the terminals must be extended to the outer boundary, which requires cutting the air domain. To achieve this, change the Z Min value to 0.0.
3. Click the Assemble Geometry button. The assembled geometry will be displayed.
   

   Assembled geometry with component details.

EIMag

1. Open the EIMag tab from the Model Builder.
2. Locate the Primary Winding section.
3. Since “Without Circuits” was enabled in the Setup tab, the Excitation is automatically set to Urms [V].
4. Set the Coil group connection type to Series.
5. Under Coil Group, set the Winding to Primary and Connection to Series for Group1coil.
   

   Connections and excitation for the winding in EIMag.

Circuits

1. Select the Circuits tab from the Model Builder.
2. The software sets up circuits automatically, connecting FEM components and sources in series. Equal indexes for positive/negative nodes indicate that elements are connected. Nodes that are not connected should have different indexes.
3. Click the Apply button.
   

   Electrical circuit indices to build the planar inductor.

Waveform

1. Select the Waveform tab from the Model Builder.
2. Select the Frequency option to perform the inductance sweep across different frequencies.
3. Set the Fixed Urms value to 1.0 [V].
4. Enter 10000.0 100000.0 in the Primary Frequency [Hz] List text field to define the frequency range for the sweep.

Note: The impedance of an inductor changes with frequency, which impacts the current even if the voltage remains constant. When dealing with core materials that exhibit a B-H curve, it’s crucial to interpret frequency-dependent impedance from voltage-excited simulations with extra caution. This is because the impedance is influenced not only by the frequency but also by the B-H characteristics of the material.

Waveform generator configuration for frequency-dependent inductance sweep.

Heat

1. Select the Heat tab from the Model Builder.
   Although the heat simulation is disabled in the Setup, setting the temperature is still necessary to define material properties, such as the temperature-dependent electrical conductivity of copper.
2. In the Settings section, enter 80.0 °C as the Steady-State Temperature.
   

   Steady-state temperature setting in the Heat tab.

Mesh

1. From the Model Builder, click on the Mesh tab.
2. Under the Settings section, from the Mesh Refinement dropdown list, select Coarse.
3. Click the mesh corresponding to each geometry group and adjust the mesh refinement by specifying the All Max Element Edge Size (mm) value according to the table below:
   

   Coil group	Group1coil	Group1core	Group1bobbin
   All Max Element Edge Size (mm)	52.1	1.0	60.0

4. Uncheck the Sub-Mesh option.
5. Click the Evaluate Mesh button followed by the Compute Mesh button.
   

   Generated mesh for the simulation.

Solve

1. From the Model Builder, click on the Solve tab.
2. To solve such complex geometries involving solid wires and high frequencies accurately, the solver must account for skin and proximity effects. These effects create a highly non-uniform current distribution within the wire, requiring a substantial number of iterations to achieve convergence. To address this, increase the solver’s iteration limit by setting the Solver Preset to Custom and entering 20 in the Nonlinear Max Iterations field to ensure reliable results.
3. Click on the Simulation Setup button followed by the Run Simulation button.
   

   Solver settings to run the simulation.

Results and Discussion

1. From the Model Builder, click on the Results tab.
2. Click on the Summary tab to get the average values of various parameters.
   

   The Results Summary tab provides the average values of the evaluated losses for the various components across various frequencies.

   With the increase in frequency from 10 kHz to 100 kHz while keeping voltage fixed, copper losses increase, but the drop in core losses is more substantial. As a result, total losses decrease, demonstrating the superior performance of the planar inductor in minimizing losses at higher frequencies.

3. Additionally, you can switch between the Results tabs to visualize the processed results.
   As frequency increases, the magnetic flux density in an inductor decreases primarily due to the rise in impedance. When the applied voltage is held constant, the higher impedance results in a lower current through the inductor, consequently reducing the magnetic flux density. The reduced flux density subsequently results in lower core losses.
   

   Magnetic flux distribution on the core surface.

   An increase in frequency also intensifies skin and proximity effects, causing most of the current to flow along the surface of the winding. This results in higher resistance and increased coil losses.

   

   Significant losses in the coil due to intensified skin and proximity effects at high frequency.

   TRAFOLO calculates inductance using the Circuit Method and the Energy Method. The Circuit Method determines inductance by dividing the complex voltage by the complex current, reflecting the overall electrical behavior. In contrast, the Energy Method calculates inductance based on the magnetic field energy within the domain. This method often yields slightly lower values, as it accounts for eddy currents induced in the core or other conductors, which reduce the magnetic field’s amplitude and energy. Despite these differences, the results from both methods are close as shown in the table below.

   Frequency (kHz)	10	100
   Circuit inductance (µH)	165.6	163.7
   Energy inductance (µH)	165.1	162.1

   It must be noted that with the voltage kept constant in this scenario, changes in circuit impedance will lead to corresponding changes in the current flowing through the inductor.
   The increase in the Q factor with frequency rise from 2.02 × 10³ to 1.30 × 10⁴ is primarily due to the increased inductive reactance, which outweighs the effects of rising resistance and other losses. The reduced core losses also contribute to this improvement in performance, resulting in better energy efficiency at higher frequencies.
   Furthermore, the parasitic capacitance decreases from 39.676 pF to 31.089 pF as frequency increases due to the skin effect confining current to conductor surfaces, reducing the effective area for charge storage. Additionally, more localized electric fields and the overall dominance of inductive effects at higher frequencies further reduce the capacitance.
   

   

   Comparison of inductance variation with frequency using circuit and energy methods, along with key electrical parameters.

4. Click the Open in ParaView button to open simulation results in post-processing software. It allows manipulation with results, changing color schemes, making slices, and doing any other manipulations with results.
   ParaView has been used for detailed visualization and analysis of the flux density, and loss distribution, as shown in the accompanying figures.
   
   

   Detailed analysis of coil and copper loss and flux density distribution in ParaView.

   The figure below shows the detailed distribution of current using a logarithmic scale indicating the effect of skin and proximity effects on current distribution leading it to concentrate along edges.
   

   

   Detailed current distribution in planar winding using a logarithmic scale, highlighting the effects of skin and proximity phenomena.