LLC Resonant Half-Bridge Gain Calculator

Q: What happens in the below-resonance region (fn < 1.0)?

When fn 1.0). The resonant current hits the magnetizing current before the half-cycle ends, allowing secondary diodes to turn off softly with zero reverse recovery (ZCS). However, operating too far below resonance risks entering the capacitive region (ZCS for primary switches), causing severe reverse-recovery shoot-through.

Model First Harmonic Approximation (FHA) voltage gain curves, evaluate ZVS boundaries, and optimize resonant tank components (Lr, Cr, Lm) for high-efficiency PSUs.

Input Voltage V_in (V)

Output Voltage V_out (V)

Output Power P_out (W)

Resonant Freq f_r (kHz)

Resonant Tank Parameters

Inductance Ratio k = L_m / L_r:

Quality Factor Q:

Transformer Ratio n = N_p / N_s:

Switching Freq f_sw (kHz):

MOSFET Coss & Dead Time

MOSFET C_oss (pF):

Dead Time t_dead (ns):

Resonant Tank & Voltage Gain Results

Voltage Gain M(f_n) -

Normalized Freq (f_n) -

Resonant Inductor L_r: -

Resonant Capacitor C_r: -

Magnetizing Inductance L_m: -

Parallel Resonant Freq (f_p): -

Equivalent AC Load (R_ac): -

Peak Magnetizing Current (I_m,pk): -

ZVS Soft-Switching Verification

Primary ZVS State: -

Min Dead Time for Coss Discharge: -

Operating Region: -

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Principles of the LLC Resonant Half-Bridge Converter

The LLC resonant converter is the industry standard topology for high-efficiency, high-density isolated DC-DC power conversion in server PSUs, telecommunications rectifiers, and electric vehicle on-board chargers. By combining a series resonant inductor ($L_r$), a resonant capacitor ($C_r$), and the transformer magnetizing inductance ($L_m$), the LLC topology achieves Zero Voltage Switching (ZVS) for primary switches across the entire load range, and Zero Current Switching (ZCS) for secondary rectifiers.

First Harmonic Approximation (FHA) Voltage Gain

Using First Harmonic Approximation (FHA), the normalized DC voltage conversion ratio $M$ is expressed as:

\[ M(f_n, k, Q) = \frac{1}{\sqrt{ \left(1 + \frac{1}{k} - \frac{1}{k f_n^2}\right)^2 + Q^2 \left(f_n - \frac{1}{f_n}\right)^2 }} \]

Where:

$f_r = \frac{1}{2\pi \sqrt{L_r C_r}}$: Series resonant frequency where gain $M = 1.0$ regardless of load.
$f_p = \frac{1}{2\pi \sqrt{(L_r + L_m) C_r}} = \frac{f_r}{\sqrt{k + 1}}$: Parallel resonant frequency.
$f_n = f_{sw} / f_r$: Normalized operating switching frequency.
$k = L_m / L_r$: Inductance ratio (typically 4 to 7). Lower $k$ increases peak gain capability at the expense of higher circulating magnetizing current.
$R_{ac} = \frac{8 n^2}{\pi^2} R_o$: Reflected primary AC load resistance.

ZVS Soft-Switching Criteria

For the primary MOSFETs to turn on with zero voltage, the magnetizing current $I_{mag,pk}$ during the dead time must fully discharge the drain-source capacitance ($C_{oss}$) of the incoming MOSFET and charge the outgoing MOSFET:

\[ t_{dead} \ge 16 \cdot C_{oss} \cdot f_{sw} \cdot L_m \quad \text{and} \quad \frac{1}{2} L_m I_{mag,pk}^2 > 2 \cdot \left(\frac{1}{2} C_{oss} V_{in}^2\right) \]

Frequently Asked Questions

Why should LLC converters operate near fn = 1.0 (at resonance)?

At fn = 1.0, the series tank impedance cancels to zero, primary current is purely sinusoidal, secondary rectifiers switch at natural zero current (ZCS), and conduction losses reach an absolute minimum. Operating within 0.9 ≤ fn ≤ 1.1 delivers peak 97%+ power supply efficiencies.

What happens in the below-resonance region (fn < 1.0)?

When fn < 1.0, the LLC operates in boost mode (gain M > 1.0). The resonant current hits the magnetizing current before the half-cycle ends, allowing secondary diodes to turn off softly with zero reverse recovery (ZCS). However, operating too far below resonance risks entering the capacitive region (ZCS for primary switches), causing severe reverse-recovery shoot-through.

What is the trade-off of choosing a small inductance ratio k?

A smaller k (e.g. k = 3 or 4) provides a steeper gain curve with high boost capability for wide input voltage holdup. However, a small Lm increases peak magnetizing current, leading to higher primary conduction losses and core losses.