Resonant Frequency Calculator
Calculate resonant frequency for LC and RLC circuits, plus Q-factor, bandwidth, and reactance. Includes series and parallel RLC analysis.
Circuit Type
Common LC Resonant Frequencies
| L | C | f₀ | Application |
|---|---|---|---|
| 1 mH | 1 nF | 159.2 kHz | AM radio tuning |
| 10 µH | 100 pF | 5.03 MHz | Shortwave radio |
| 1 µH | 1 pF | 159.2 MHz | FM / VHF circuits |
| 10 mH | 10 µF | 503 Hz | Audio filter |
| 100 µH | 220 pF | 1.07 MHz | Medium wave receiver |
Frequently Asked Questions
The resonant frequency of an LC circuit is: f = 1 ÷ (2π × √(L × C)), where L is inductance in Henries and C is capacitance in Farads. At resonance, the inductive reactance XL = 2πfL equals the capacitive reactance XC = 1/(2πfC), making them cancel out.
Q-factor (quality factor) measures how sharp the resonance peak is. For a series RLC circuit: Q = (1/R) × √(L/C) = ω₀L/R. For a parallel RLC circuit: Q = R × √(C/L). Higher Q means narrower bandwidth and sharper resonance. Q > 10 is considered high-Q (sharp resonance).
Bandwidth (BW) is the range of frequencies over which power is at least half the peak value (−3 dB points): BW = f₀ ÷ Q = R ÷ (2πL) for series RLC. The two −3 dB frequencies are f₁ = f₀ − BW/2 and f₂ = f₀ + BW/2 (approximately, for high Q).
At resonance: (1) Inductive and capacitive reactances cancel (XL = XC). (2) Impedance is purely resistive — minimum for series RLC, maximum for parallel RLC. (3) Current is maximum in series circuits. (4) Voltage across L and C can be Q times larger than the source voltage (voltage magnification). (5) The circuit absorbs maximum power from the source.
LC vs RLC Resonance
An ideal LC circuit has zero resistance and oscillates indefinitely at f₀ = 1/(2π√LC). Real circuits always have resistance, forming an RLC circuit. Resistance causes damping, broadening the resonance peak. The quality of resonance is quantified by the Q-factor: higher Q = sharper peak = more selective filtering.
Reactances at Resonance
At resonance: X_L = ω₀L = √(L/C) and X_C = 1/(ω₀C) = √(L/C). Both reactances are equal and cancel, leaving only R in the impedance. The characteristic impedance Z₀ = √(L/C) is a useful design parameter.
- Series RLC: minimum impedance at resonance (current maximum)
- Parallel RLC: maximum impedance at resonance (current minimum from source)
- Applications: radio tuners, notch filters, oscillators, power factor correction