LC Resonant Frequency Calculator

LC resonant frequency: f₀ = 1 / (2π √(LC)). At resonance the inductive and capacitive reactances are equal and cancel. Used for LC filter design, resonant converters, and tank circuit selection.

LC Resonant Frequency

ParameterValue
Resonant Frequency f₀--
Angular Frequency ω₀--
XL = XC at f₀--

Formula & Theory

  • Resonant frequency: f₀ = 1 / (2π × √(L × C))
  • Angular frequency: ω₀ = 2π × f₀ = 1 / √(L × C)
  • Reactance at resonance: X = ω₀ × L = 1 / (ω₀ × C) = √(L/C)

The characteristic impedance Z₀ = √(L/C) determines the peak voltage in a parallel tank circuit: Vpeak = I × Q × Z₀. Minimizing Z₀ reduces voltage stress in resonant converter designs.

Worked Example

Buck converter output LC filter (12 µH, 100 µF MLCC):

  • f₀ = 1 / (2π × √(12×10⁻⁶ × 100×10⁻⁶)) = 1 / (2π × √(1.2×10⁻⁹)) = 4,547 Hz ≈ 4.55 kHz
  • ω₀ = 2π × 4547 = 28,568 rad/s
  • X at resonance = √(12×10⁻⁶ / 100×10⁻⁶) = √0.12 = 0.346 Ω
  • Loop crossover target: < 4547/5 ≈ 900 Hz for stable control

Assumptions & Limitations

  • Ideal lossless components — real inductors have DCR and real capacitors have ESR that damp resonance
  • Single resonance — no parasitic self-resonances from component leads or PCB traces
  • Series resonance model — for parallel tank circuit, same f₀ but impedance at resonance is maximum (not minimum)

Common Mistakes

  • Ignoring the inductor's self-resonant frequency (SRF): An inductor ceases to behave inductively above its SRF — it looks capacitive. Verify the LC resonant frequency is well below both the inductor's SRF and the capacitor's SRF.
  • Not accounting for MLCC capacitance derating: A 100 µF ceramic capacitor at its rated voltage may actually be 40–60 µF due to DC bias derating. Use the effective capacitance at operating voltage to calculate f₀.

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Frequently Asked Questions

What is the resonant frequency of an LC circuit?

At resonance, the inductive reactance XL = 2πfL equals the capacitive reactance XC = 1/(2πfC). The two cancel, leaving only the series or parallel resistance of the circuit. Resonant frequency f₀ = 1/(2π√(LC)).

How does LC resonance relate to buck converter design?

In a buck converter, the LC output filter (inductor + output capacitor) forms a second-order low-pass filter with resonant frequency f₀. The converter's control loop crossover frequency must be set below f₀ to maintain stability. Typical designs place crossover at 1/5 to 1/10 of f₀.

What is the Q factor of an LC circuit?

Q = (1/R) × √(L/C) for a parallel circuit. Higher Q means a sharper resonance peak and lower bandwidth. For RF tank circuits, Q should be as high as possible. For converter output filters, high Q causes peaking near resonance — usually damped with a series resistor across the capacitor.