How it works
An LLC resonant converter regulates its output by changing the switching frequency around the resonance of a series inductor Lr, series capacitor Cr and the transformer's magnetizing inductance Lm. Operating near resonance gives zero-voltage switching on the primary MOSFETs and low switching loss, which is why LLC is popular in server, telecom and EV charger power supplies.
This tool follows the first harmonic approximation (FHA) design flow described in Infineon's application note on LLC resonant converters. It starts from your input voltage range, output voltage and power, picks a transformer turns ratio, and then chooses the inductance ratio m = (Lr + Lm) / Lr and the maximum quality factor Qmax so the converter can still reach the required gain at minimum input voltage and full load.
The gain plot shows the normalized voltage gain versus normalized frequency for several load conditions. The peak of the Qmax curve sets the minimum switching frequency and the maximum gain available; designs should stay to the right of that peak to keep ZVS.
FHA is an approximation: it is most accurate near resonance and becomes less accurate far below it. Always confirm the final design with simulation and measurement.
Design procedure
- 1Set the turns ratio so that the converter runs at resonance (gain 1) at the nominal input voltage: n = Np/Ns ≈ V_in,nom / V_out for a full-bridge input and full-bridge rectifier. Operation at resonance gives the best efficiency.
- 2Compute the required gain range. The maximum gain is needed at minimum input voltage, K_max = V_in,nom / V_in,min, and the minimum gain at maximum input voltage.
- 3Pick the maximum quality factor Qmax for full load and the inductance ratio m = (Lr + Lm) / Lr so that the peak of the Qmax gain curve exceeds K_max with some margin. Lower m gives more gain but more magnetizing current.
- 4Calculate the equivalent AC load R_ac = (8 n² / π²) · R_load and then Lr, Cr and Lm from fr, Qmax and m.
- 5Check that the minimum switching frequency stays above the gain peak (inductive region) at minimum input voltage and full load, so that zero-voltage switching is kept, and verify with a circuit simulation.
Formulas
- Resonant frequency
- f_r = 1 / (2π · √(Lr · Cr))
- Inductance ratio
- m = (Lr + Lm) / Lr
- Quality factor
- Q = √(Lr / Cr) / R_ac
- Equivalent AC load (full-bridge rectifier)
- R_ac = (8 · n²) / π² · R_load
- Normalized frequency
- F_x = f_s / f_r
Worked example
For a 33 V nominal input (18–36 V), 400 V / 250 W output, the tool picks a turns ratio from the nominal gain point, then sizes m and Qmax so the gain at 18 V and full load stays below the peak of the Qmax curve. The resulting Lr, Cr and Lm can be read off directly and checked on the gain plot.
Common mistakes
- Designing for a gain peak exactly equal to the requirement. Component tolerances move fr and the peak, so keep a margin of about 10% or more.
- Choosing a very large m for efficiency and then not reaching the required gain at low input voltage.
- Trusting FHA far below resonance. The first-harmonic model loses accuracy there, especially at light load, so confirm the corner cases in simulation.
- Forgetting that Lm must also deliver enough current to discharge the switch capacitances during the dead time; otherwise ZVS can be lost at light load even in the inductive region.
Frequently asked questions
What value of m should I choose?
Smaller m gives more gain range and a narrower frequency range but higher circulating current. Values between about 4 and 10 are common; the tool can optimize m automatically for your input range. Auto mode picks the largest m that still gives 10% more gain than the minimum input voltage needs, so a wide input range such as 2:1 can push m below 4.
Why must I stay above the gain peak frequency?
To the right of the peak the resonant tank looks inductive, which is what enables zero-voltage switching. Left of the peak the tank becomes capacitive and ZVS is lost.
Is the FHA method accurate?
It is a good first design step and is accurate near resonance. Below resonance and at light load the real gain differs, so verify with a circuit simulator.
Results are engineering estimates. Verify your design with datasheets, simulation and measurement.