How to Calculate Switching Power Supply Transformers: A Complete Method from Parameter Determination to Core Selection
2026-08-28
Switching power supply transformers are the core magnetic components in high-frequency switching power supplies, mainly responsible for power transmission, electrical isolation, voltage conversion, and energy storage. Compared with traditional power frequency transformers, switching power supply transformers typically operate at frequencies ranging from several kilohertz to several hundred kilohertz, thus having smaller size, lighter weight, and higher efficiency. However, at the same time, their design process is also more complex, requiring comprehensive consideration of input voltage, output power, topology, operating frequency, core material, number of turns in the winding, wire diameter, temperature rise, and leakage inductance, among other factors.
- What parameters need to be determined before calculating the switching power supply transformer?
Before starting the calculation, the following basic design conditions must be clarified:
1.Input voltage range
For example: 85 - 265V AC, or 18 - 36V DC.
2.Output voltage and output current
For example: 12V/3A, with an output power of 36W.
3. Switching power supply topology
Common topologies include:Flyback (reverse charging), Forward (positive charging), Push-Pull, Half-Bridge, Full-Bridge, LLC resonant
3. Switching power supply topology
Common topologies include:Flyback (reverse charging), Forward (positive charging), Push-Pull, Half-Bridge, Full-Bridge, LLC resonant
4. Working frequency
For example, 65kHz, 100kHz, 200kHz, etc. The higher the frequency, the usually smaller the core volume can be, but the switching loss, iron loss and EMI issues will become more prominent.
5. Estimated efficiency
It can usually be estimated at 80% to 92%. The efficiency of small power flyback power supplies may be 75% to 88%, while that of larger power half-bridge or full-bridge power supplies can reach above 90%.
6. Maximum duty cycle
The maximum duty cycle will affect the input voltage, output voltage and the number of primary windings. Flyback power supplies usually take the maximum duty cycle of 0.4 to 0.5, while forward and half-bridge types are determined according to the specific control method.
For example, 65kHz, 100kHz, 200kHz, etc. The higher the frequency, the usually smaller the core volume can be, but the switching loss, iron loss and EMI issues will become more prominent.
5. Estimated efficiency
It can usually be estimated at 80% to 92%. The efficiency of small power flyback power supplies may be 75% to 88%, while that of larger power half-bridge or full-bridge power supplies can reach above 90%.
6. Maximum duty cycle
The maximum duty cycle will affect the input voltage, output voltage and the number of primary windings. Flyback power supplies usually take the maximum duty cycle of 0.4 to 0.5, while forward and half-bridge types are determined according to the specific control method.
- Calculating Input Power
The first step in transformer design is to calculate the input power. The input power is equal to the output power divided by the efficiency:
4. Calculate the number of secondary turns
The number of secondary turns is generally determined based on the reflected voltage or the input-output relationship:
The calculation methods for different topologies differ significantly. For flyback transformers, the focus is on energy storage, inductance and air gap design; for forward, half-bridge and full-bridge transformers, more attention is paid to flux reset, volt-ampere balance, leakage inductance and power transmission capacity. Theoretical calculation can only serve as an initial design basis. Ultimately, it must be confirmed through prototype testing regarding waveforms, temperature rise, efficiency, standby power consumption and safety performance.
For power supplies with AC input, there are risks of high-voltage electric shock, fire and device explosion. During debugging, use isolation transformers, current-limiting bulbs or adjustable AC power supplies, and equip with appropriate oscilloscope probes. Do not use ordinary ground oscilloscopes to measure high-voltage switch nodes.
If you plan to design a specific switching power supply, you can further provide the input voltage, output voltage, output current, topology structure and switching frequency. CXWON can create a more detailed transformer calculation example based on these parameters.
Pin=ηPout
(Note:Pin: Input power; Pout: Output power; η：Estimated power supply efficiency)
(Note:Pin: Input power; Pout: Output power; η：Estimated power supply efficiency)
For example, with an output of 12V/3A:
Pout=12×3=36W
Assuming an efficiency of 85%:
Pin=0.8536≈42.4W
Therefore, the transformer needs to be designed with an input power of at least 42W or more, and some margin should also be reserved.
Pout=12×3=36W
Assuming an efficiency of 85%:
Pin=0.8536≈42.4W
Therefore, the transformer needs to be designed with an input power of at least 42W or more, and some margin should also be reserved.
- Determine the core type and effective cross-sectional area
Switching power supply transformers usually use ferrite cores, such as the EE, EF, EFD, ETD, PQ and RM series.
When choosing a magnetic core, the following factors need to be considered:
Effective cross-sectional area of the magnetic core Ae
Window area of the magnetic core Aw
Volume of the magnetic core
Operating frequency of the magnetic core material
Transformer power and temperature rise requirements
Effective cross-sectional area of the magnetic core Ae
Window area of the magnetic core Aw
Volume of the magnetic core
Operating frequency of the magnetic core material
Transformer power and temperature rise requirements
In actual design, the magnetic core can be selected based on experience first, and then verified through calculation to see if it meets the requirements.
For example:
For power supplies under 10W, EE16 and EE19 type small magnetic cores can be used;
For power supplies ranging from 20W to 50W, EE25, EE28, and EF25 can be considered;
For power supplies from 50W to 100W, EE30, ETD29, and PQ2625 are commonly used;
For higher power levels, ETD, EER, PQ, or larger-sized magnetic cores need to be adopted.
It should be noted that the size of the magnetic core is not necessarily the larger the better. An overly large magnetic core will increase costs and volume, while an overly small magnetic core is prone to problems such as excessive magnetic flux density, excessive temperature rise, and insufficient window.
For example:
For power supplies under 10W, EE16 and EE19 type small magnetic cores can be used;
For power supplies ranging from 20W to 50W, EE25, EE28, and EF25 can be considered;
For power supplies from 50W to 100W, EE30, ETD29, and PQ2625 are commonly used;
For higher power levels, ETD, EER, PQ, or larger-sized magnetic cores need to be adopted.
It should be noted that the size of the magnetic core is not necessarily the larger the better. An overly large magnetic core will increase costs and volume, while an overly small magnetic core is prone to problems such as excessive magnetic flux density, excessive temperature rise, and insufficient window.
- Calculation Method for Flyback Transformers
The transformer in a flyback switching power supply is actually more like a "storage inductor". During the conduction period of the switching transistor, the energy is stored in the primary inductor; after the switching transistor is turned off, the energy is released to the load through the secondary winding.
1. Estimating the primary inductance
The primary inductance of the flyback can be estimated using the following formula:
1. Estimating the primary inductance
The primary inductance of the flyback can be estimated using the following formula:
Lp=2PinfsVin(min)2Dmax2
(Note: Lp: Primary inductance; Vin(min): Minimum DC input voltage; Dmax:Maximum duty cycle; Pin:Input power; fs:Switching frequency)
Taking an input of 85 to 265 V AC as an example, the lowest DC bus voltage after rectification and filtering is approximately:
Vdc(min)≈85×1.414−Pressure drop
During actual design, it can be estimated at about 100 V to 110 V. Assuming:
Vin(min)=100V
Dmax=0.45
Pin=42.4W
fs=65kHz
Substitute into the formula:
Lp=2×42.4×650001002×0.452
The calculation result is approximately:
Lp≈3.7mH
This value is only an initial estimate. In practice, it needs to be adjusted in combination with the peak current of the control chip, the working mode, and the air gap of the transformer.
2. Calculate the primary peak current
The primary peak current can be calculated based on the slope of the inductor current:
Ipk=LpfsVin(min)Dmax
The primary peak current can be calculated based on the slope of the inductor current:
Ipk=LpfsVin(min)Dmax
Excessive peak current will lead to increased current stress on the MOSFET, rising copper loss, and susceptibility of the magnetic core to saturation. Therefore, during the design process, it is necessary to reasonably select the primary inductance value and working mode.
3. Calculate the primary turns
According to the volt-second balance relationship, the primary turns can be calculated using the following formula:
Np=BmaxAefsVin(max)Dmax
(Note: Np:Primary turns; Bmax：Maximum operating magnetic flux density; Ae:Effective cross-sectional area of the magnetic core; fs：Switching frequency)
For common power ferrite cores, it is recommended to limit the maximum flux density to approximately 0.18T to 0.25T during design. At high frequencies, one should not blindly pursue excessively high flux densities, as this will significantly increase iron loss and temperature rise.
4. Calculate the number of secondary turns
The number of secondary turns is generally determined based on the reflected voltage or the input-output relationship:
NpNs=VRVo+VD
(Note: Ns:Secondary turns; VoVo: Output voltage; VD: Rectifier diode drop; VR: Secondary voltage reflected to the primary
Therefore:Ns=NpVRVo+VD
If the reflection voltage is too high, it will increase the drain voltage stress of the MOSFET; if the reflection voltage is too low, it will cause the primary peak current to increase. During the design process, a compromise needs to be made among the device's withstand voltage, duty cycle and efficiency.
5. Calculate the auxiliary winding
If the control chip requires auxiliary power supply, the number of turns of the auxiliary winding also needs to be calculated:
Na=NpVRVa+VD
Here, VaVa represents the output voltage required for the auxiliary winding. The voltage of the auxiliary winding must take into account the voltage drop of the rectifier diodes, variations in the load, and the peak of leakage inductance.
If the control chip requires auxiliary power supply, the number of turns of the auxiliary winding also needs to be calculated:
Na=NpVRVa+VD
Here, VaVa represents the output voltage required for the auxiliary winding. The voltage of the auxiliary winding must take into account the voltage drop of the rectifier diodes, variations in the load, and the peak of leakage inductance.
- How to calculate the air gap of a transformer?
The flyback transformer must have an air gap to store energy and avoid magnetic core saturation. The air gap mainly affects the primary inductance and the maximum energy storage capacity.
When the air gap accounts for the main magnetic resistance, an approximate formula can be used:
g≈Lpμ0Np2Ae
(Note: g: Total air gap length; μ0: Vacuum permeability; Np: Primary turns; Ae: Effective cross-sectional area of the magnetic core; Lp: Primary inductance)
During actual production, the air gap is usually achieved by padding insulation paper, polyester film, or special pads in the magnetic core. If the air gap is too small, it is prone to saturation; if the air gap is too large, it will lead to increased leakage flux, decreased efficiency and worse EMI.
For forward-connection, half-bridge and full-bridge transformers, energy storage is not usually their main purpose, and the magnetic core generally does not need to have a significant air gap like that of the flyback transformer.
When the air gap accounts for the main magnetic resistance, an approximate formula can be used:
g≈Lpμ0Np2Ae
(Note: g: Total air gap length; μ0: Vacuum permeability; Np: Primary turns; Ae: Effective cross-sectional area of the magnetic core; Lp: Primary inductance)
During actual production, the air gap is usually achieved by padding insulation paper, polyester film, or special pads in the magnetic core. If the air gap is too small, it is prone to saturation; if the air gap is too large, it will lead to increased leakage flux, decreased efficiency and worse EMI.
For forward-connection, half-bridge and full-bridge transformers, energy storage is not usually their main purpose, and the magnetic core generally does not need to have a significant air gap like that of the flyback transformer.
- Calculation of Winding Wire Diameter and Current Density
The wire diameter of the transformer winding should be selected based on the effective current. The commonly used current density is approximately:
J=2～5A/mm2
For naturally cooled small switching power supplies, it is recommended to take 2.5 - 4 A/mm²; if forced air cooling is used, it can be appropriately increased.
The formula for calculating the cross-sectional area of the wire:
S=JI
For example, if the effective current of a certain winding is 2A, and calculated based on 4A/mm²:
S=42=0.5mm2
Under high-frequency conditions, the wire will also be affected by the skin effect. Ordinary thick enameled wires may not be able to fully utilize the cross-sectional area of the conductor, so the primary winding often uses multiple strands wound together, or uses Litz wire. The higher the frequency, the more attention should be paid to the skin effect and proximity effect.
J=2～5A/mm2
For naturally cooled small switching power supplies, it is recommended to take 2.5 - 4 A/mm²; if forced air cooling is used, it can be appropriately increased.
The formula for calculating the cross-sectional area of the wire:
S=JI
For example, if the effective current of a certain winding is 2A, and calculated based on 4A/mm²:
S=42=0.5mm2
Under high-frequency conditions, the wire will also be affected by the skin effect. Ordinary thick enameled wires may not be able to fully utilize the cross-sectional area of the conductor, so the primary winding often uses multiple strands wound together, or uses Litz wire. The higher the frequency, the more attention should be paid to the skin effect and proximity effect.
- Winding Structure and Insulation Design
The winding arrangement has a significant impact on leakage inductance, distributed capacitance, and EMI. Common winding methods include:
1.Primary - Secondary - Primary
2.Primary - Auxiliary - Secondary
3.Layered winding of primary and secondary
4.Sandwich winding method
If you want to reduce leakage inductance, you can use the sandwich structure where the primary is segmented and clamped to the secondary. However, this structure will increase the distributed capacitance between the primary and secondary, so a balance must be struck between leakage inductance and common-mode interference.
High-voltage input power supplies must pay attention to insulation distance and creepage distance. Usually, multi-layer insulating tape, triple insulation wires, or insulating barriers are used between the primary and secondary. The specific distances should be determined based on the input voltage, working environment, pollution level, and relevant safety regulations, and cannot be handled merely based on experience.
1.Primary - Secondary - Primary
2.Primary - Auxiliary - Secondary
3.Layered winding of primary and secondary
4.Sandwich winding method
If you want to reduce leakage inductance, you can use the sandwich structure where the primary is segmented and clamped to the secondary. However, this structure will increase the distributed capacitance between the primary and secondary, so a balance must be struck between leakage inductance and common-mode interference.
High-voltage input power supplies must pay attention to insulation distance and creepage distance. Usually, multi-layer insulating tape, triple insulation wires, or insulating barriers are used between the primary and secondary. The specific distances should be determined based on the input voltage, working environment, pollution level, and relevant safety regulations, and cannot be handled merely based on experience.
- Magnetic Core Loss and Temperature Rise Inspection
After completing the calculation of the number of turns and wire diameter, it is also necessary to check the magnetic core loss and temperature rise. The magnetic core loss is related to the following factors:
1.Working frequency
2.Range of flux density variation
3.Core material
4.Operating temperature
5.Waveform shape
If the core temperature is too high, the following methods can be adopted to optimize:
1.Increase the core size;
2.Reduce the operating flux density;
3.Reduce the operating frequency or choose a more suitable core material;
4.Reduce the copper loss of the winding;
5.Improve the winding filling rate and heat dissipation conditions;
6.Optimize the switching speed of the switch tube and the absorption circuit.
During the prototype testing stage, it is recommended to measure the core temperature, winding temperature, MOSFET temperature and rectifier temperature simultaneously. Generally, any abnormal temperature rise of a key component may indicate problems with the magnetic component parameters or the switching waveform.
2.Range of flux density variation
3.Core material
4.Operating temperature
5.Waveform shape
If the core temperature is too high, the following methods can be adopted to optimize:
1.Increase the core size;
2.Reduce the operating flux density;
3.Reduce the operating frequency or choose a more suitable core material;
4.Reduce the copper loss of the winding;
5.Improve the winding filling rate and heat dissipation conditions;
6.Optimize the switching speed of the switch tube and the absorption circuit.
During the prototype testing stage, it is recommended to measure the core temperature, winding temperature, MOSFET temperature and rectifier temperature simultaneously. Generally, any abnormal temperature rise of a key component may indicate problems with the magnetic component parameters or the switching waveform.
- Common Mistakes in Designing Switching Power Supply Transformers
1. Selecting the core only based on output power
Selecting the core based solely on power is not sufficient. It is also necessary to consider the input range, topology, frequency, duty cycle and temperature rise.
2. Ignoring the minimum input voltage
For wide-range input power supplies, the minimum input voltage usually determines the maximum duty cycle and the primary peak current, which is a key condition in the design.
3. Setting the flux density too high
Too high flux density will cause the core to heat up, efficiency to decrease, and in severe cases, saturation of the core and damage to the switch tube.
4. Ignoring leakage inductance
Leakage inductance will generate switching spikes, causing the MOSFET to withstand higher voltages and increasing EMI problems. Usually, it needs to be handled in combination with RCD absorption, TVS or active clamping circuits.
5. Calculating only the average current without considering the peak current
The peak current of the flyback power supply may be significantly higher than the average current. The wire diameter, MOSFET and rectifier components must be verified according to peak and effective values.
Selecting the core based solely on power is not sufficient. It is also necessary to consider the input range, topology, frequency, duty cycle and temperature rise.
2. Ignoring the minimum input voltage
For wide-range input power supplies, the minimum input voltage usually determines the maximum duty cycle and the primary peak current, which is a key condition in the design.
3. Setting the flux density too high
Too high flux density will cause the core to heat up, efficiency to decrease, and in severe cases, saturation of the core and damage to the switch tube.
4. Ignoring leakage inductance
Leakage inductance will generate switching spikes, causing the MOSFET to withstand higher voltages and increasing EMI problems. Usually, it needs to be handled in combination with RCD absorption, TVS or active clamping circuits.
5. Calculating only the average current without considering the peak current
The peak current of the flyback power supply may be significantly higher than the average current. The wire diameter, MOSFET and rectifier components must be verified according to peak and effective values.
- Summary
The calculation of switching power supply transformers usually includes input power calculation, core selection, determination of operating frequency, calculation of primary turns, secondary turns, primary inductance, air gap design, wire diameter selection, insulation and temperature rise verification.
The calculation methods for different topologies differ significantly. For flyback transformers, the focus is on energy storage, inductance and air gap design; for forward, half-bridge and full-bridge transformers, more attention is paid to flux reset, volt-ampere balance, leakage inductance and power transmission capacity. Theoretical calculation can only serve as an initial design basis. Ultimately, it must be confirmed through prototype testing regarding waveforms, temperature rise, efficiency, standby power consumption and safety performance.
For power supplies with AC input, there are risks of high-voltage electric shock, fire and device explosion. During debugging, use isolation transformers, current-limiting bulbs or adjustable AC power supplies, and equip with appropriate oscilloscope probes. Do not use ordinary ground oscilloscopes to measure high-voltage switch nodes.
If you plan to design a specific switching power supply, you can further provide the input voltage, output voltage, output current, topology structure and switching frequency. CXWON can create a more detailed transformer calculation example based on these parameters.
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