LC Resonant Frequency
Resonant frequency of an LC tank — solve for f, L or C — plus the characteristic impedance Z₀.
Pick what to solve for; enter the other two. f₀ = 1/(2π√(LC)), Z₀ = √(L/C).
Resonance of an LC tank
At resonance the inductive and capacitive reactances cancel, leaving the natural frequency
Rearranging lets you size a component for a target frequency:
The ratio of voltage to current swing at resonance is the characteristic (surge) impedance
For example, a 10 µH inductor with a 1 nF capacitor resonates at 1.5915 MHz and has . Use this for tuned tank circuits, oscillators, matching networks and snubber design.
Frequently asked questions
How do you calculate LC resonant frequency?
Use f0 = 1 / (2π√(L·C)). Convert L and C to henries and farads first. For L = 10 µH and C = 1 nF, √(L·C) = √(1e-5 × 1e-9) = 1e-7, so f0 = 1 / (2π × 1e-7) = 1.5915 MHz.
What is the resonant frequency formula?
The resonant (or natural) frequency of an LC tank is f0 = 1 / (2π√(L·C)) in hertz, with L in henries and C in farads. At this frequency the inductive and capacitive reactances are equal and cancel, so the tank's impedance peaks (parallel) or dips (series).
How do I find the inductor or capacitor for a target frequency?
Rearrange the formula: L = 1 / ((2πf)²·C) and C = 1 / ((2πf)²·L). To resonate at 1.5915 MHz with C = 1 nF, you need L = 1 / ((2π × 1.5915e6)² × 1e-9) ≈ 10 µH.
What is the characteristic impedance of an LC tank?
The characteristic (surge) impedance is Z0 = √(L/C) in ohms. It sets the ratio of voltage to current swing at resonance. For L = 10 µH and C = 1 nF, Z0 = √(1e-5 / 1e-9) = √(1e4) = 100 Ω.