Resonant Frequency
f = 1 / (2π√(LC))
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Formula
Description
The resonant frequency of an LC tank circuit is where the inductive reactance exactly equals the capacitive reactance, causing them to cancel out. At this frequency the circuit impedance is purely resistive (determined only by parasitic resistance), and energy oscillates back and forth between the inductor's magnetic field and the capacitor's electric field. This principle is the foundation of radio tuning, oscillator circuits, and bandpass/bandstop filters. The formula shows that resonant frequency depends on the geometric mean of L and C, so halving one and doubling the other keeps the same frequency.
Variables
- f — Resonant frequency in hertz (Hz)
- L — Inductance in henries (H)
- C — Capacitance in farads (F)
Practical Notes
In series RLC circuits, resonance produces minimum impedance and maximum current. In parallel RLC circuits, resonance produces maximum impedance and minimum current. Crystal oscillators exploit the extremely high Q factor of piezoelectric resonance for precise frequency generation.
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