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Soft-Switching Power Electronics & EV Chargers

LLC Resonant Converter Tank Frequency, Ln & Q Formula

Calculate Half-Bridge LLC Series Resonant Frequency f_r = 1000 / (2*PI()*SQRT(L_r_uH * C_r_uF)) (kHz), Characteristic Impedance Z_0 = SQRT(L_r / C_r), Inductance Ratio L_n = L_m / L_r, and Loaded Quality Factor Q_e = Z_0 / R_ac.

Balance LLC resonant ZVS soft-switching against hold-up voltage gain via L_n and Q_e!

High-efficiency 80-Plus Titanium server PSUs and EV onboard chargers achieve Zero-Voltage Switching (ZVS) on primary MOSFETs and Zero-Current Switching (ZCS) on secondary rectifiers using the three-element LLC Resonant Tank: series resonant inductor L_r, series resonant capacitor C_r, and parallel transformer magnetizing inductance L_m! Expressing L_r in microhenries (uH) and C_r in microfarads (uF) makes SQRT(L_r_uH * C_r_uF) microseconds and SQRT(L_r_uH / C_r_uF) exact Ohms! Three dimensionless/tank ratios govern the First Harmonic Approximation (FHA) gain curve: (1) Series Resonant Frequency f_r_kHz = 1000 / (2 * PI() * SQRT(L_r_uH * C_r_uF)); (2) Characteristic Tank Impedance Z_0 = SQRT(L_r_uH / C_r_uF); (3) Inductance Ratio L_n = L_m / L_r (typically 4–8: smaller L_n boosts peak buck-boost gain but raises circulating magnetizing current!); and (4) Loaded Quality Factor Q_e = Z_0 / R_ac (where R_ac is reflected AC load resistance)!

Verify on a 160 kHz LLC Tank—Series_Inductance L_r = 25.0 uH (B2), Resonant_Capacitance C_r = 0.04 uF (40 nF, B3 -> SQRT(25 * 0.04) = 1.00 us exact!), Magnetizing_Inductance L_m = 150.0 uH (B4), and Reflected_AC_Load R_ac = 50.0 Ohm (B5): Series Resonant Frequency f_r is 1000 / (2 * PI()) = 159.15 kHz (E2); Characteristic Impedance Z_0 is SQRT(25 / 0.04) = 25.00 Ohm (E3); Inductance Ratio L_n is 150 / 25 = 6.00 (E4); and Loaded Quality Factor Q_e is 25 / 50 = 0.5000 (E5)!

LLC Resonant Tank Metric (L_r=25 uH, C_r=0.04 uF, L_m=150 uH, R_ac=50 Ohm)FormulaVerified Output
Series Resonant Freq f_r (kHz)1000 / (2 * PI() * SQRT(L_r_uH * C_r_uF))159.15 kHz
Characteristic Impedance Z_0SQRT(L_r_uH / C_r_uF)25.00 Ohm
Magnetizing Ratio L_nL_m_uH / L_r_uH6.00
Loaded Quality Factor Q_eZ_0_Ohm / R_ac_Ohm0.5000 (2.0000 @ R_ac=12.5 Ohm)

LLC Tank Characteristic Impedance & Loaded Quality Factor Formula

Validate strictly positive tank components L_r > 0, C_r > 0, L_m > 0, and reflected AC load resistance R_ac > 0!

=LET(l_ru, B2, c_ru, B3, l_mu, B4, r_ac, B5, IF(OR(l_ru <= 0, c_ru <= 0, l_mu <= 0, r_ac <= 0), "Invalid LLC Tank Component", LET(z_0, SQRT(l_ru / c_ru), ROUND(z_0 / r_ac, 4))))

4x Overload Peak-Gain Compression Check (Set R_ac = 12.5 Ohm)

Drop Reflected_AC_Load B5 from 50 Ohm to 12.5 Ohm (4x heavy current surge): Quality Factor Q_e E5 jumps 4x to 2.0000—warning designers to verify that peak LLC tank gain still exceeds V_min hold-up requirements!

=IF(ISTEXT(E5), E5, ROUND(1000 / (2 * PI() * SQRT(B2 * B3)), 2))

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