Flyback Transformer

Introduction

Flyback converters, isolated buck-boost-derived converters, are highly popular for their efficiency, simplicity, and cost-effectiveness, making them integral to numerous electronic applications. The most important part of the converter is a coupled inductor, often referred to as a transformer, making its design the pivotal aspect of the flyback architecture. The term “flyback” in this context originates from the operation of the transformer within the circuit. Unlike conventional converters, where the transformer operates continuously, in a flyback converter, energy is stored in the transformer during the on-time of the switching cycle and then released, or “flyback,” during the off-time. So, the need to properly design the air gap for energy storage, estimate core and winding losses, and accurately estimate parasitic capacitance, particularly at high switching frequencies, makes designing a flyback transformer challenging. Using finite element numerical simulations, we can account for non-homogeneous temperature distributions within different parts of the transformer. By accurately modeling these temperature variations, the simulations ensure precise estimation of core and copper losses. Moreover, the rise in temperature due to these losses can also be studied using a coupled electro-thermal analysis to ensure that the flyback transformer works below the critical temperature to prevent the degradation of dielectric materials.

Model description

A flyback transformer with an RM8/I-3C97 core being modeled is operated at 150 kHz, as described in the Frenetic & Omicron Lab webinar. Both the primary and the secondary winding utilize stranded Litz wire. The detailed specifications of the core and the windings have been provided below.

Core Specification

Core	Core material	Air gap (mm)	Gap material
RM8/I-3C97	Ferroxcube 3C97	0.3	Fiberglass Reinforced Epoxy (FR4)

Winding Specification

Winding	Wire type	No. of turns	No. of layers	No. of strands	Strand diameter (mm)	Wire diameter (mm)
Primary	Litz	24	2	45	0.05	0.555
Secondary	Litz	4	1	120	0.1	2.0

The simulation encompasses the computation of various parameters crucial to the design of a flyback transformer, including core and copper losses, temperature rise, and interwinding capacitance.

Modelling Instructions

Setup

1. From the Model Builder, click on the Setup tab.
2. Locate the General section and set the Domain type as Symmetric due to its symmetry along the z-axis. This setting is beneficial for models with a plane of symmetry that divides the core and coil into symmetrical segments. This method ensures that the computed values reflect the complete system despite only modeling a symmetrical section. Subsequently, parameters such as voltage, resistance, losses, inductance, and other related values are appropriately scaled to represent the entire geometry accurately.
3. In the Simulation Type section, set Electromagnetics to Transient to account for the time-dependent nature of non-sinusoidal waveforms in a flyback transformer. These waveforms exhibit rapid changes and non-linearities that steady-state or harmonic analysis cannot accurately capture. Transient analysis divides the waveform into small time steps, allowing for precise modeling of the system’s dynamic behavior.
4. Additionally, set Heat transfer to Steady-state.
5. Check the Capacitance box to calculate interwinding capacitance between primary and secondary windings.

Materials

1. From the Model Builder, select the Materials tab.
2. From the Global Material section, select Copper and click the Copy button.
3. Copy Epoxy, 3C97 Ferroxcube 100C, and Fiberglass Reinforced Epoxy (FR4) from the Global Materials section to the Local Materials section in a similar manner.
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	Others	Bobbin	Gaps
   Material type	3C97 Ferroxcube 100C	Copper	Not set	Epoxy	Fiberglass Reinforced Epoxy (FR4)

Core

1. From the Model Builder, click on the Core tab.
2. Click the New Group button. The Group1core will open.
3. Click the Open in new tab icon.
4. From the Source dropdown list, select Template.
5. From the Scale dropdown list, select mm.
6. From the Gap Type dropdown list, select Physical.

7. In the Rotation and Translation section, set the rotation to 90 deg.
8. In the Geometry Builder section, select RM from the Type dropdown list, and set the dimensions (mm) as per the table below:
   

   A	B	C	D1	D2	E	F	G
   23.2	11.0	9.5	8.55	17.0	16.4	10.8	19.7

9. Click the Apply button.
10. Click the New Gap button.
11. In the gMin and gMax text fields, enter -0.15 and 0.15, respectively.
12. From the Limb dropdown list, select the Central Limb.

Coil

1. Click on the Coil tab from the Model Builder.
2. Click the New Group tab. Group1coil will show up. This will represent our primary winding.
3. Click the Open in new tab icon. The Group1coil tab will be added.
4. From the Source dropdown list, select Template.
5. From the Scale dropdown list, select mm.
6. From the Wire Type dropdown list, select Stranded & Litz wire.
7. Set the Turns per solid to 24.

8. In the Geometry Builder section, set the Type to Filled and the Linked Core to None. Enter the dimensions (mm) according to the table below:
   

   a	b	c	R	h
   0.0	0.0	1.1	4.8	8.0

9. Click the Apply button.

• Click the Configure Wire button.

• To calculate the proximity factor using in-build Dowell’s method, select Dowell’s Equation from Rac computation methods.

From the Strand Type dropdown list, select Litz.

In the Strand thickness text field, enter 0.05 mm.

• In the Number of Layers text field, enter 13.

• To calculate the Fill Factor, click the Calculator button. Enter the data as per the table below:
  

  Strand type	Strand thickness (mm)	N Strand
  Litz	0.05	45

The calculated Fill Factor will be displayed. Click the Accept button to update the Fill Factor values in the coil.

Click the Apply button.
The calculated proximity factors will be available in the results section.

 

For the secondary winding, create Group2Coil by clicking the New Group button.

Set the Source as Template, Scale as mm, and Wire Type as Stranded & Litz from the dropdown list.

• Set the Turns per solid to 1.

• Navigate to the Geometry Builder section.

• From the Type dropdown list, select Massive.

Set the Linked Core to None.

Set the dimensions (mm) according to the table below:

a	b	c	R	h	N	r
0.0	0.0	1.1	4.8	8.0	4	1.0

Click the Apply button.

Click the Configure Wire button.

From Rac computation methods, select Dowell’s Equation.

From the Strand Type dropdown list, select Litz.

In the Strand thickness text field, enter 0.1.

• In the Number of Layers text field, enter 11.

• To calculate the Fill Factor, click the Calculator button. Enter the data as per the table below:
  

  Strand type	Strand thickness (mm)	N Strand
  Litz	0.1	120

• The calculated Fill Factor will be displayed. Click the Accept button to update the Fill Factor values in the coil.

• Click the Apply button.
  

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. From the Model Builder, click on the Bobbin tab.
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. Locate the Geometry Builder section.
7. Enter the details as per the below table.
   

   Type	Linked Coil	H	Rin	Rout
   Cylinder	Group2coil	8.5	0.0	7.1

8. Click the Apply button.

Similarly, create Group2bobbin.

Set the Source as Template and Scale as mm.

In the Rotation and Translation section, in the y text field, enter 4.825 mm for translation. Click the Apply button.

Enter the details in the Geometry Builder section according to the table below and click the Apply button.

Type	Linked Coil	H	Rin	Rout
Cylinder	None	1.15	0.0	8.5

Click the Bobbin tab.

Click the Copy button associated with Group2bobbin. The Group3bobbin will be added.

Click the Open in new tab associated with Group3bobbin.

• In the Rotation and Translation section, modify the y text field to -4.825 mm for translation. Click the Apply button.

Assembly

1. In the Model Builder, click the Assembly tab
2. Click the Assemble Geometry button. The assembled geometry will be displayed.

EIMag

1. From the Model Builder, open the EIMag tab.
2. Locate the Primary Winding section.
3. Set the Excitation to Irms [A] and the Coil group connection type to Series from the dropdown list.
4. Enable the Secondary Winding by checking the box.
5. Set the Excitation to Irms [A] and the Coil group connection type to Series from the dropdown list.
6. Set the Winding and Connection as per the table below:
   

   Coil Group	Winding	Connection
   Group1coil	Primary	Series
   Group2coil	Secondary	Series

Circuits

1. From the Model Builder, select the Circuits tab.

2. Click the Apply button.

Waveform

1. From the Model Builder, select the Waveform tab.
2. Mark the Load From File button.
3. In the Frequency [Hz] text field, enter 150000.
4. In the Periods text field, enter 2.
5. In the #Points per period text field, enter 37.
6. Check the Optimize Timesteps checkbox.

7. From the Algorithm dropdown list, select 4.

8. Check the Skip 1st period from the averaged losses checkbox, as the first few timesteps in transient simulation typically have high errors.
9. Click the Import button to import the waveform file.
10. From the Time dropdown list, select SW1-Current-Time [s].
11. From the Primary Source dropdown list, select SW1-Current.
12. From the Secondary Source dropdown list, select TX1-W2-Current.
13. In the Discrete Fourier Transform section, set the Number of harmonics as 7. It is evident from DFT graphs that these harmonics have significant amplitude and hence will be used to calculate the effective proximity effect.

Heat

1. From the Model Builder, click on the Heat tab.
2. In the Settings section, enter 115.0 as the Initial Temperature in deg C.

3. In the Temperature Iteration text field, enter 1.
4. Locate the Boundary Conditions section.
5. Click on Group1bobbin.
6. In the Type dropdown list, select Convection.
7. In the External temperature text field, type 26.
8. In the Heat transfer coefficient text field, type 5.0.

9. Set the Boundary conditions for other components in a similar manner.

Mesh

1. From the Model Builder, click on the Mesh tab.
2. In the Settings section, from the Mesh Refinement dropdown list, select Coarse.
3. Click the Evaluate Mesh button.
4. Click the Compute Mesh button.

Solve

1. From the Model Builder, click on the Solve tab.
2. Click on the Simulation Setup button, followed by the Run Simulation button.

Results

1. From the Model Builder, click on the Results tab.
2. Click on the Summary tab to get the average values of various parameters.
3. Further, the user can switch between the Results tabs to visualize the processed results.
4. Click the Open in ParaView button to open simulation results in post-processing software.

The peak magnetic flux density is observed using the timesteps at time = 3 µs, as shown in the figure above. The figure indicates that the central limb has a maximum flux density of approximately 0.3 T, well below the saturation threshold. The core loss, governed by flux density, also shows maximum losses at time = 3 µs.

Due to the switching operation in the flyback converter, coil losses occur in the primary winding during the first half, and in the secondary winding during the second half of the switching cycle, as the current flows through the coils. These losses can be observed in the Coil Losses tab from the timesteps.

The figure above shows an instance of coil loss in the primary winding while charging the coupled inductor during the first half of the switching cycle.

The figure above shows an instance of coil loss in the secondary winding while discharging the coupled inductor during the second half of the switching cycle.

The temperature distribution plot indicates that the highest temperature occurs in the central limb, followed by primary and secondary windings. The hotspot temperature, approximately 112 °C, is below the critical temperature of the transformer.

Conclusion

The core and winding losses of 0.735 W and 0.345 W, respectively, have been estimated in the present analysis using TRAFOLO. It is also observed that the core losses are nearly double the winding losses. Frenetic, on the other hand, has estimated core losses that are lower than copper losses, at 0.41 W and 0.97 W, respectively. For TRAFOLO and Frenetic, the overall losses are 1.08 W and 1.38 W, respectively.