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The LLC resonant converter is the workhorse of modern high-efficiency, isolated DC-DC power supplies — laptop adapters, LED drivers, server and telecom rectifiers, and EV on-board chargers. A half-bridge drives a resonant tank made of three reactive elements: a resonant inductor Lr, a resonant capacitor Cr, and the transformer magnetizing inductance Lm. By varying the switching frequency around the tank's resonance, the converter regulates the output while keeping the switches in soft-switching (ZVS), which is why LLC reaches efficiencies above 95%.
Two resonant frequencies matter. The series resonant frequency fr is set by Lr and Cr alone — at this point the voltage gain is exactly 1 for any load, and the converter is normally designed to run near here. The lower resonant frequency fr2 involves Lr+Lm and marks the boundary below which the tank can no longer boost the output.
| Quantity | Formula |
|---|---|
| Series resonant frequency | fr = 1 / (2π√(LrCr)) |
| Lower resonant frequency | fr2 = 1 / (2π√((Lr+Lm)Cr)) |
| Characteristic impedance | Zo = √(Lr/Cr) |
| Inductance ratio | Ln = Lm/Lr |
| Turns ratio (unity gain) | n = Vin / (2×Vout) |
| AC-equivalent load | Rac = (8/π²)×n²×(Vout/Iout) |
| Quality factor | Q = Zo / Rac |
The inductance ratio Ln (typically 3–8) and quality factor Q (typically 0.2–0.5) together define the gain curve. A lower Ln and lower Q give a wider gain range (good for a wide input range) at the cost of higher circulating current. These are the two knobs a designer tunes on the LLC gain plot.
An isolated DC-DC converter that uses a resonant tank (two inductors Lr and Lm plus a capacitor Cr) driven by a half- or full-bridge. Frequency control around resonance regulates the output while the switches turn on at zero voltage (ZVS), giving very high efficiency.
The series resonant frequency is fr = 1/(2π√(LrCr)), set only by the resonant inductor and capacitor. The converter is usually designed to operate at or near this point, where the voltage gain equals 1.
fr = 1/(2π√(LrCr)) is the series resonance (gain = 1). The lower resonance fr2 = 1/(2π√((Lr+Lm)Cr)) occurs when the magnetizing inductance joins the tank at no load, and marks the lower edge of the operating range.
Zo = √(Lr/Cr). It sets the scale of the tank current and appears in the quality factor Q = Zo/Rac. Typical LLC designs land around 20–80 Ω.
Ln = Lm/Lr, the ratio of magnetizing to resonant inductance. A smaller Ln (3–5) gives a wider gain range for a wide input voltage; a larger Ln (6–10) lowers circulating current and conduction loss but narrows the gain.
At the resonant point the gain is 1, so for a half-bridge LLC n = Vin/(2×Vout). The factor of 2 comes from the half-bridge applying half the bus voltage to the tank. Design n at the nominal input so resonance sits in the middle of your frequency range.
Q = √(Lr/Cr)/Rac, where Rac is the reflected AC load. Q measures loading of the tank: low Q (light load) gives a high peak gain, high Q (heavy load) flattens and lowers the gain curve. Full-load Q is usually kept around 0.3–0.5.
Rac is the load resistance seen by the tank after the rectifier and transformer. Because the tank works with the fundamental of a square wave (first harmonic approximation), the DC load RL=Vout/Iout is scaled by 8/π² and by the square of the turns ratio: Rac=(8/π²)×n²×RL.
The resonant tank lets the primary switches turn on at zero voltage (ZVS) and the secondary diodes turn off at zero current (ZCS) near resonance. This nearly eliminates switching losses and EMI, so well-designed LLC stages exceed 95–97% efficiency.
Zero-Voltage Switching means a MOSFET turns on after its drain-source voltage has already fallen to zero. The magnetizing current keeps flowing during the dead time and discharges the switch node, so the body diode conducts first and the FET turns on losslessly. Running slightly above fr guarantees the inductive (ZVS) region.
Above fr the tank is inductive and gives ZVS with gain below 1 (buck). Below fr (but above fr2) the gain rises above 1 (boost) while still keeping ZVS. Designs sweep across fr to cover the input and load range, but stay in the inductive region to preserve ZVS.
Together they define the LLC gain plot M(fn, Ln, Q). Lower Ln and lower Q raise the peak gain (wider regulation range) but increase circulating current; higher values reduce loss but shrink the usable gain. Designers pick Ln and full-load Q to just cover the required min/max gain.
Most LLC converters run between about 50 kHz and 500 kHz, with the resonant frequency fr often in the 80–150 kHz range for mains-connected supplies. Higher frequencies shrink the magnetics but raise core and gate-drive losses.
Half-bridge LLC is standard up to several hundred watts and applies Vin/2 to the tank (hence n = Vin/(2Vout)). Full-bridge LLC applies the full Vin and doubles the effective turns ratio, used at higher power such as EV chargers and telecom rectifiers.
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