1. Introduction — Why the LLC Is the Topology of Choice at 90% Efficiency

The LLC resonant converter has become the default topology for isolated medium-to-high power supplies — server power, on-board chargers, TV and LED backlight power stages, and high-efficiency AC-DC adapters above roughly 100 W. Its appeal is simple to state: by exploiting the resonant tank formed by a series inductor (often the transformer leakage inductance), a series capacitor, and the magnetizing inductance, the LLC can operate the primary switches with zero-voltage switching (ZVS) across the entire load range while the secondary rectifiers operate with zero-current switching (ZCS) at light load. The result is peak efficiency well above 90% and very low switching loss, allowing higher switching frequencies and therefore a smaller magnetic transformer than a hard-switched forward or flyback of the same power. This guide walks through the half-bridge LLC: the operating principle, the fundamental harmonic approximation (FHA) used for design, the gain (M vs f) curves, the step-by-step design of Lr, Cr and Lm, the transformer design, the coupling to a resonant current calculator, the common failures (ZVS loss, excessive magnetizing current, burst-mode oscillation), and an FAQ section.

2. Topology and Operating Principle

2.1 Circuit structure

The half-bridge LLC consists of two primary MOSFETs (Q1, Q2) driven by complementary 50% duty signals plus a small dead time, a resonant tank composed of a series resonant capacitor Cr, a series resonant inductor Lr (or the transformer leakage Lk plus a discrete Lr), and the transformer magnetizing inductance Lm in parallel with the ideal transformer. The secondary is a center-tapped or full-bridge rectifier followed by the output capacitor. The input is a DC bus, typically the output of a power-factor-correction (PFC) stage (390 V for universal mains).

• Q1/Q2: switches at 50% duty with dead time; current commutates so the output capacitance discharges before turn-on (ZVS).
• Cr: series capacitor blocks DC and resonates with (Lr + Lm) in the light-load region.
• Lr: either a discrete resonant inductor or the transformer leakage; together with Cr it defines the series resonance f0.
• Lm: the transformer magnetizing inductance; it defines the second, lower resonance frequency and carries the magnetizing current that helps charge/discharge the MOSFET capacitance for ZVS.

The load is connected to the transformer secondary; the effective AC load resistance reflected to the primary is Ra = 8 n^2 RL / π² for a full-bridge rectifier, where n = Np/Ns is the turns ratio and RL is the load resistance. Two resonance frequencies exist:

Series resonance (Lr, Cr): f0 = 1 / (2π √(Lr·Cr))

Series + magnetizing resonance: fp = 1 / (2π √((Lr + Lm)·Cr))

The converter normally operates between fp and f0 (below-resonance region at heavier load), at f0 (the ideal point, ZCS on the secondary), or above f0 (above-resonance, used at light load). The switching frequency is the single control variable; regulation is achieved by moving fsw.

3. The Fundamental Harmonic Approximation (FHA)

A rigorous analysis of the LLC uses the state-plane approach; for practical design the fundamental harmonic approximation is the standard tool. The idea: the resonant tank is a band-pass filter driven by the square wave at the switching frequency, so only the fundamental component of the switch-node voltage meaningfully contributes to power transfer. The input square wave Vab has a fundamental amplitude of 4·Vin/π; the effective AC input voltage is treated as a sinusoidal source, and the output rectifier plus load becomes an equivalent AC resistance. Under FHA the gain of the tank is computed from the voltage divider formed by the series impedance (jωLr − j/(ωCr)) and the parallel combination of jωLm with the reflected load Ra:

M = |G(jω)| = | (jωLm || Ra) / ( jωLr − j/(ωCr) + (jωLm || Ra) ) |

Where A = Lm/Lr is the inductance ratio and Q = (1/Ra)·√(Lr/Cr) is the load quality factor, the gain can be written in normalized form:

M(fn) = 1 / √( (1 + 1/A·(1 − 1/fn²))² + Q²·(fn − 1/fn)² )

with normalized frequency fn = f/f0. When fn = 1 (switching at f0), M = 1 exactly: the tank cancels and the converter behaves like a transformer with gain fixed by n. Below f0 the gain rises above 1 (boost region, used during startup, hold-up, or wide input range), above f0 the gain falls below 1 (buck region, light load). The maximum gain before ZVS is lost at light load is bounded by the capacitance ratio and is a key design constraint.

4. Design Flow — Step by Step

4.1 Choose Vin range, Vo, Po, f0 and fp

• Input: bulk voltage Vin_nom = 390 V (from PFC), Vin_min = 350 V (hold-up), Vin_max = 410 V.
• Output: Vo, Po. Example: 12 V, 600 W, f0 = 100 kHz.
• Required gain range: M_max at Vin_min (e.g. 1.15), M_min at Vin_max (e.g. 0.95); the operating curve must stay inside the ZVS region.

4.2 Transformer turns ratio and equivalent load

Turns ratio from the f0 operating point where M = 1: n = Vin_nom / (2·Vo) for a center-tapped secondary (each half conducts half the period). With n computed, the reflected primary AC resistance is:

Ra = 8·n²·Vo² / (π²·Po)

4.3 Choose the inductance ratio A and select Lr, Cr

Pick A = Lm/Lr typically between 3 and 7. Higher A gives wider gain range but lower peak gain and worse light-load ZVS margin. Compute the required maximum gain curve to find the minimum A that still delivers M_max at the lightest load (largest Q). With A and f0 fixed, and choosing a target Q (0.3–0.6 at full load):

Lr = Q·Ra / (2π·f0),   Cr = 1 / ((2π·f0)²·Lr),   Lm = A·Lr

Always sanity-check with a resonant tank calculator: enter the target f0 and the desired Q, then verify that the resulting peak gain on the FHA curve with your Lm/Lr ratio covers the required M_max by the selected margin (typically ≥ 1.1×). A quick frequency-planning helper is the switching frequency calculator, which converts between period and frequency so the f0/fp targets and the dead-time window can be double-checked against the controller’s oscillator accuracy. For the magnetic core, flux density and saturation headroom are tied to the inductance; the inductor saturation calculator helps confirm that the peak tank current never drives Lm into saturation at the minimum switching frequency.

4.4 Verify ZVS and dead time

ZVS requires that, during the dead time, the magnetizing current (plus any reflected secondary current) fully discharges the two MOSFET output capacitances Coss. The condition is I_m ≥ (2·Coss_eff·Vin) / t_dead. As load lightens the magnetizing current becomes the dominant charging source through the rising region of the gain curve; if Lm is too large, ZVS margin at light load disappears and the converter reverts to hard switching, destroying efficiency. Tune Lm so the magnetizing current is roughly 10–15% of the full-load primary current.

5. Transformer Design for the LLC

Because Lm and the leakage inductance are resonant elements, they must be controlled — the transformer is an engineered part, not a commodity. Use a ferrite core (e.g. N27/N87 class) and interleave windings (primary between two secondary halves) to control leakage Lk; if Lk is too low compared to the target Lr, add a small external resonant inductor. Design the turns count from the core area-product method with the peak flux density at the lowest frequency where the magnetizing current is highest:

Np = Lm·I_m_peak / (B_max·Ae)

with B_max typically 0.25–0.35 T for PFC-fed LLC at high frequency. Follow skin-effect and proximity-effect rules: use Litz or multiple strands when the ratio of wire diameter to skin depth exceeds ~1.6. The secondary rectifier sees a high-frequency AC current with a DC component; choose Schottky or synchronous-rectification MOSFETs sized for the resonant current waveform rather than the DC average.

6. Worked Example — 390 V to 12 V, 600 W LLC

Specifications: Vin_nom = 390 V, Vin_min = 350 V, Vo = 12 V, Po = 600 W, f0 = 100 kHz, desired M_range = 0.95…1.15.

• Turns ratio: n = 390 / (2·12) = 16.25 → choose n = 16 (Vo_eff slightly above 12 V, regulator trims).
• Ra = 8·16²·12² / (π²·600) = 8·256·144 / 5921.7 ≈ 49.8 Ω.
• Choose A = 5, Q = 0.45: Lr = 0.45·49.8 / (2π·100k) = 35.7 µH; Cr = 1/((2π·100k)²·35.7µ) ≈ 71 nF → use two 33 nF + 4.7 nF (70.7 nF); Lm = 178 µH.
• Peak gain check: with A=5 and this Q the FHA curve reaches M_max ≈ 1.2 at fn ≈ 0.72, covering the 1.15 requirement with margin.
• ZVS: 2·Coss_eff·Vin / I_m = dead time; with I_m = Vin/(2π·f0·Lm) ≈ 3.5 A and a 150 ns dead time, required Coss_eff = I_m·t_dead/(2·390) ≈ 67 pF — comfortable with most 500 V MOSFETs.
• Now verify with the calculators: at f0 = 100 kHz each tank element is 1/Q scaled; a saturation check on the 178 µH Lm at 3.5 A peak must show B below 0.3 T for the chosen core.

7. Common Design Mistakes

• Wrong Lm/ZVS trade-off: oversized Lm kills light-load ZVS; undersized Lm raises circulating current and ruins full-load efficiency.
• Ignoring the dead time: too short a dead time prevents complete Coss discharge; too long creates asymmetric currents and transformer saturation.
• Designing for Q too high: gain curve collapses and the required M_max moves into the capacitive region where ZVS is lost and the MOSFETs hard-switch with body-diode recovery.
• Magnetizing overlap with leakage: assuming zero or wrong leakage; leakage inductance is part of Lr and must be measured with a shorted-secondary test, not guessed.
• Operating far above f0 at heavy load: loses the ZCS advantage, secondary diode reverse recovery appears and efficiency drops sharply.
• Ignoring burst-mode at no load: without a light-load burst strategy the converter oscillates between pulses and audible noise / output ripple appear.

8. FAQ

Q: Why does the LLC need a PFC stage? A: The gain curve is nearly flat and the output is regulated by frequency over a narrow range; a wide mains variation (90–264 V) would require an impractically wide frequency span, so a PFC bus is standard.

Q: What is the difference between the load-independent point and maximum gain? A: At f0 the gain is exactly 1 regardless of load (the load-independent point); moving below f0 the gain rises but only up to the peak of the curve, after which the operation becomes capacitive (fails ZVS).

Q: Can I use a flyback-grade transformer? A: No — the LLC transformer’s leakage and magnetizing inductance are resonant elements with tolerances that directly shift f0 and fp; uncontrolled leakage causes production spread in gain and worst case loss of ZVS.

Q: What happens with a short circuit? A: The tank current is limited by the series element; short-circuit control typically frequency-folds to fp or stops switching. The Cr voltage must be rated for the DC bus plus the AC swing.

9. Conclusion

The LLC resonant converter is the workhorse of high-efficiency isolated power. The design discipline is: fix the operating window, size the tank with FHA gain curves, verify ZVS at light load, engineer the transformer as a resonant component, and validate the results against measurements — including the resonant tank calculators on this site for the frequency and saturation sanity checks. Done correctly, the LLC delivers efficiency and density that hard-switched topologies cannot match.