LC Resonance Calculator
Calculate resonant frequency, angular frequency and characteristic impedance for LC tank circuits.
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f₀ = 1 / (2π√(LC))
How does LC resonance work?
An LC circuit — also called a tank circuit — consists of an inductor and capacitor connected together. Energy oscillates between the magnetic field of the inductor and the electric field of the capacitor at a natural frequency determined by f₀ = 1/(2π√(LC)). At this frequency the inductive and capacitive reactances are equal and opposite, so they cancel.
In a series LC circuit, impedance is minimum at resonance — the circuit passes maximum current at f₀ and acts as a bandpass element. In a parallel LC circuit, impedance is maximum at resonance — it blocks current at f₀ and acts as a notch or trap. Both configurations resonate at the same frequency; the difference is how they interact with the rest of the circuit.
The characteristic impedance Z₀ = √(L/C) determines the Q factor when combined with circuit resistance: Q = Z₀/R for series, Q = R/Z₀ for parallel. Higher Q means a narrower bandwidth and a sharper resonance peak. In radio receivers, LC tanks with Q > 50 can select a single station from a crowded band.
Resonant Frequency (f₀)
f₀ = 1 / (2π√(L·C))Angular Frequency (ω₀)
ω₀ = 1 / √(L·C)Characteristic Impedance (Z₀)
Z₀ = √(L/C)Key Points
- At resonance: inductive reactance XL = capacitive reactance XC
- Series LC: minimum impedance at f₀ (passes current)
- Parallel LC: maximum impedance at f₀ (blocks current)
- Q factor determines bandwidth: BW = f₀ / Q
Applications
- Radio frequency tuning and channel selection
- Bandpass and notch filter design
- Oscillator circuits (Colpitts, Hartley)
- Impedance matching networks