Systematically analyze the key technical points in LLC transformer design

LLC resonant converters are widely used in modern switching power supplies due to their high efficiency, high power density, and soft-switching characteristics. Among them, the transformer (more accurately referred to as an 'integrated component of resonant inductor + transformer') is the core and a key challenge in the design process.

This article systematically analyzes the key technical points in LLC transformer design through 23 Questions and 23 Answers about LLC transformer design technology.

Part 1: Basic Concepts and Core Principles

1. Q: What is the core difference between an LLC transformer and a transformer used in ordinary PWM converters?

A: The core difference lies in functional integration and operating mode.

Ordinary PWM transformers (e.g., flyback, forward transformers): Their main functions are electrical isolation and energy transfer. Their magnetizing inductance is usually designed to be as large as possible to reduce magnetizing current loss.
LLC 'transformers': They integrate three functions: 1) Transformer (turn ratio conversion); 2) Resonant inductor (Lr); 3) Magnetizing inductor (Lm). Lm is a crucial parameter involved in resonance and requires precise design and control. LLC transformers operate in a sinusoidal resonant state rather than a square-wave pulse state.

2. Q: Why can LLC converters achieve Zero-Voltage Switching (ZVS) for primary-side switches and Zero-Current Switching (ZCS) for secondary-side rectifiers?

ZVS (Primary-side): During the dead time of the switches, the resonant current (Ir) charges and discharges the junction capacitance (Coss) of the switches. The switch voltage is pulled down to zero before the switch is turned on, thus realizing ZVS. This process requires sufficient energy, i.e., a sufficiently large amplitude of the resonant current.
ZCS (Secondary-side): When the magnetizing inductor (Lm) participates in resonance, the magnetizing current rises to match the resonant current (Ir). At this point, the secondary-side current naturally drops to zero, enabling the rectifier to turn off under ZCS conditions and eliminating reverse recovery issues.

3. Q: What is the gain characteristic of LLC converters? Why can they operate within a wide input voltage range?

A: The voltage gain of an LLC converter is a curve related to the normalized frequency (Fn = fsw / fr) and inductance ratio (Ln = Lm / Lr). The curve has a 'peak' characteristic, with a gain of approximately 1 near the resonant point (Fn = 1).

When the input voltage is high, the converter operates near Fn ≈ 1 (gain ≈ 1), where efficiency is maximized.
When the input voltage is low, a higher gain is required. The gain is increased by reducing the switching frequency (Fn < 1) to stabilize the output voltage. This frequency-modulated voltage regulation method is the basis for the LLC converter’s wide input voltage operation.

Part 2: Design Steps and Parameter Calculation

4. Q: What initial specifications are required to design an LLC transformer?

A: The essential initial conditions include:

Input voltage range (Vin_min, Vin_nom, Vin_max)
Rated output voltage (Vo) and current (Io)
Rated output power (Po)
Resonant frequency (fr) or target switching frequency range (usually selected based on trade-offs between efficiency and size, e.g., 100kHz–200kHz)
Maximum operating frequency (fmax, typically limited by the controller)

5. Q: How to determine the transformer turn ratio (n = Np : Ns)?

A: The turn ratio n is determined by the minimum input voltage (Vin_min) and the resonant point (Fn = 1). At the resonant point, the circuit gain M = 1. Therefore:
n = (Vin_min / 2) / (Vo + Vf)
where Vf is the forward voltage drop of the output diode. The term 'Vin_min / 2' arises because the LLC converter adopts a half-bridge topology, and the amplitude of the square wave under maximum duty cycle is Vin / 2.

6. Q: How to select the inductance ratio (Ln = Lm / Lr)? What does it affect?

A: Ln is a critical design parameter, typically ranging from 3 to 7.

Small Ln (e.g., < 3): A small magnetizing inductor (Lm) leads to large magnetizing current, resulting in high circulating energy and increased conduction losses. However, it facilitates ZVS implementation.
Large Ln (e.g., > 10): A small magnetizing current reduces conduction losses, but narrows the gain range. A lower frequency is required to achieve the same gain, which may increase core losses. Additionally, the energy required for ZVS may be insufficient.
Empirical value: A value of 5 or 6 is usually chosen as a good starting point, balancing loss reduction and gain range.

7. Q: How to calculate the resonant inductor (Lr) and resonant capacitor (Cr)?

A: Once Ln and the resonant frequency (fr) are determined, the characteristic impedance (Z0) of the resonant tank and its parameters can be calculated.

Calculate the characteristic impedance:
Z0 = sqrt(Lr / Cr) = (8 × Ln² × R_load) / π²
(where R_load = Vo² / Po)
Calculate the resonant angular frequency:
ωr = 2 × π × fr = 1 / sqrt(Lr × Cr)
Solve the above two equations simultaneously to obtain:
Lr = Z0 / ωr
Cr = 1 / (ωr × Z0)
Finally, calculate the magnetizing inductor:
Lm = Ln × Lr

8. Q: How to calculate the number of turns for the primary and secondary windings?

A: The AP Method (Area Product Method) is used to initially estimate the core size. After determining the core, calculate the number of primary turns (Np) as follows:

According to Faraday’s Law, the minimum number of turns to prevent core saturation is given by:
Np_min ≥ (Vin_max × 10⁸) / (4 × fmin × B_max × Ae)
- Vin_max: Maximum input voltage (use Vin_max / 2 for half-bridge topologies)
- fmin: Minimum operating frequency (frequency at maximum gain)
- B_max: Maximum allowable magnetic flux density (in mT), depending on the core material (e.g., ~300mT for PC95, with a safety margin)
- Ae: Effective cross-sectional area of the core (in cm²)
Fine-tune Np based on the calculated Lm value: Lm ∝ Np². If the Lm value derived from the calculated Np does not match the target, adjust Np.
Calculate the number of secondary turns: Ns = Np / n

Part 3: Refined Design and Practical Techniques

9. Q: How to select the resonant capacitor (Cr)?

A: High-frequency, low-ESR, and non-polar capacitors must be used.

Type: C0G (NP0) ceramic capacitors are preferred due to their extremely low ESR and excellent temperature stability. Film capacitors (e.g., PPN) are a secondary option.
Avoid: Ceramic capacitors such as X7R/Y5V (with significant capacitance variation under DC bias and temperature) and electrolytic capacitors (high ESR and polar characteristics).
Voltage stress: The peak voltage of Cr can be estimated as π × Io × n × Z0 / 2, and a sufficient voltage margin must be reserved.

10. Q: How to arrange the primary and secondary winding order during transformer winding to reduce leakage inductance?

A: The resonant inductor (Lr) is essentially the leakage inductance of the transformer. To precisely control the Lr value, the sandwich winding method is typically used.

Standard sandwich: Primary (half) → Secondary → Primary (half). This method ensures good coupling and low leakage inductance.
Increasing leakage inductance: If the design requires a larger Lr, separate winding (primary and secondary windings wound separately) or intentionally adding insulation between the primary and secondary windings can be used to increase leakage inductance.

11. Q: How to accurately measure the parameters (Lm, Lr) of an LLC transformer?

Magnetizing inductance (Lm) measurement: Short-circuit all secondary windings and measure the inductance at the primary side. At this point, the leakage inductance (Lr) is short-circuited, and the measured value is Lm.
Resonant inductor/leakage inductance (Lr) measurement: Open-circuit all secondary windings and measure the inductance at the primary side. The measured value is (Lm + Lr). Since Lm is much larger than Lr, this value is approximately equal to Lm. For greater accuracy, first measure Lm, then subtract Lm from the open-circuit measurement result to obtain Lr (Lr = L(open_sec) - L(short_sec)).

12. Q: What effect does the air gap have on an LLC transformer?

A: The main functions of the air gap are to prevent core saturation and adjust inductance.

In LLC transformers, Lm is subject to DC bias (the average voltage of the half-bridge is Vin / 2). An air gap must be added to prevent core saturation.
A larger air gap reduces Lm and consequently decreases Ln. Adjusting the air gap is a key method to control Lm and Lr.

13. Q: What are the main losses of an LLC transformer? How to optimize them?

Core loss (Pcore): Related to frequency, flux swing (ΔB), and temperature. Using low-loss core materials (e.g., PC95, PC200) and reducing ΔB (by increasing the number of turns) can minimize core loss.
Winding loss (Pcu):
- Skin effect: High-frequency current tends to concentrate on the conductor surface, reducing the effective current-carrying area. Using multi-strand Litz wire or flat copper wire is an effective solution.
- Proximity effect: Eddy current loss caused by magnetic fields from adjacent wires. Methods such as using parallel thin wires and interleaved winding can significantly reduce this loss. For example, the sandwich winding method (placing the secondary winding between two primary winding layers) can greatly optimize the AC resistance of the primary and secondary windings.

14. Q: Why does the efficiency of LLC converters decrease under light load? How to improve it?

Reason: Under light load, the amplitude of the resonant current (Ir) decreases, which may be insufficient to charge and discharge the junction capacitance of the switches during dead time. This causes ZVS loss, leading to a sharp increase in switching loss.
Improvement methods:
1. Frequency control: Significantly increase the switching frequency (entering the inductive region) under light load, but this method has limited effectiveness.
2. Burst Mode: Under extremely light load, the converter operates for several cycles and then enters a sleep state. This is currently the most mainstream high-efficiency solution for light-load conditions.
3. Optimize dead time to vary with load.

Part 4: Common Issues and Debugging

15. Q: After design completion, what should be done if the gain is insufficient (output voltage drops under low input voltage)?

Root cause: The actual circuit gain is lower than the theoretical value.
Solutions:
1. Check parameters: Verify whether the Lm and Lr values are accurate, especially if Lr is larger than the designed value (excessive leakage inductance).
2. Reduce Ln: Appropriately reduce Lm (by increasing the air gap) to expand the gain range, making it easier to stabilize the voltage under low input conditions.
3. Reduce fr: If permitted by the controller, reduce the resonant frequency, but parameters must be recalculated.

16. Q: How to select core materials?

A: High-frequency, low-loss soft magnetic materials must be selected.

PC95, PC200: The most commonly used Mn-Zn power ferrites, suitable for frequencies from tens of kHz to hundreds of kHz.
Ni-Zn ferrites: Suitable for ultra-high frequencies above MHz, but with lower saturation flux density.
Amorphous and nanocrystalline materials: Offer excellent performance but are costly, and are mostly used in high-end applications.

17. Q: How to reduce the AC loss of windings?

A: The skin effect and proximity effect at high frequencies are the main causes.

Skin effect: Use multi-strand Litz wire or copper foil.
Proximity effect: Adopt interleaved winding (e.g., P-S-P-S structure). This structure can greatly offset magnetic fields, reduce proximity effect loss, and is the most effective process method.

18. Q: During power-on testing, why does the converter fail to start or have unstable output voltage under low input voltage?

A: Insufficient gain. Possible causes:

The actual Lr of the transformer is larger than the designed value (excessive leakage inductance), or Lm is smaller than the designed value.
The load is heavier than the designed value.
The actual capacitance of the resonant capacitor (Cr) decreases due to DC bias or temperature (avoid using X7R capacitors!).
The actual input voltage is lower than the designed minimum input voltage.

19. Q: What may cause severe heating of the switches?

ZVS failure: Insufficient dead time or insufficient resonant current energy (excessively large Ln or too light a load). Check the Vds waveform of the switches to see if the voltage drops to zero before turn-on.
Conduction loss: Excessively large loop resistance (including MOSFET Rds(on) and transformer winding resistance).
Switching loss: Even if ZVS is achieved, turn-off loss still exists. Excessively large turn-off current can also cause heating.

20. Q: What should be done if the transformer emits a 'squeaking' sound under light load?

A: This is usually caused by core or winding vibration during Burst Mode (periodic start-stop operation). Ensure that the frequency of Burst Mode is outside the human audible range (>20kHz), or optimize the Burst Mode modulation strategy to smooth the oscillation frequency.

21. Q: What should be done if the voltage stress spike of the secondary-side rectifier diode is too high?

A: The secondary-side rectifier diodes of LLC converters turn off under ZCS conditions, so there is theoretically no reverse recovery issue. However, parasitic inductance in the PCB layout and diode junction capacitance can form resonance, generating voltage spikes.

Solution: Connect an RC snubber circuit in parallel across the rectifier diodes. Carefully adjust the R and C values to suppress spikes without significantly affecting efficiency.

22. Q: Why is there a large gap between simulation and actual measurement results?

Inaccurate models: The simulation model fails to account for PCB parasitic parameters (especially parasitic inductance in the resonant loop), MOSFET Coss nonlinearity, transformer nonlinearity, etc.
Measurement errors: At high frequencies, the ground loop of the measurement probe introduces significant interference, causing waveform distortion. A probe with a short ground loop or a differential probe must be used for accurate measurement.
Parameter deviations: The actual parameters (Lm, Lr) of the wound transformer deviate from the designed values.

23. Q: What is the final step in LLC design?

A: Iterative optimization (Tuning). LLC design is a highly integrated engineering process that combines electromagnetic theory, core materials, winding technology, and practical debugging experience. It is almost impossible to achieve a perfect design on the first attempt. The following steps must be performed:

Fabricate a prototype.
Accurately measure key waveforms (primary-side current, switch Vds, secondary-side current).
Compare the measured results with theoretical calculations and simulations.
Fine-tune parameters (e.g., air gap, number of turns, Cr value) or even reselect the core until performance meets requirements.

Conclusion

LLC transformer design is a systematic engineering task that integrates in-depth knowledge of electromagnetic theory, core materials, winding processes, and practical debugging experience. A successful LLC design starts with rigorous theoretical calculations, is refined through detailed model simulations, and ultimately relies on patient debugging and optimization on the test bench.