LC Resonant Frequency Calculator — with Q and bandwidth
Resonant frequency, Q factor and bandwidth for LC tank circuits.
Example: 100 µH with 1 nF resonates at 503.3 kHz, with a characteristic impedance of 316.2 Ω.
Formula
f₀ = 1 / (2π√(LC)) Z₀ = √(L/C)Worked example
100 µH with 1 nF resonates at 503.3 kHz, with a characteristic impedance of 316.2 Ω.
f₀ = 1 / (2π√(LC))
1 / (2π√(100 µH × 1 nF))
503.3 kHz
At this frequency X_L equals X_C and the two cancel.
Z₀ = √(L/C)
√(100 µH / 1 nF)
316.2 Ω
Q = Z₀ / R
316.2 Ω / 10 Ω
31.62
In a series circuit, resistance lowers Q — you want it small.
BW = f₀ / Q
503.3 kHz / 31.62
15.92 kHz
Frequently asked questions
How do I calculate LC resonant frequency?
f₀ = 1 / (2π√(LC)). A 100 µH inductor with a 1 nF capacitor resonates at about 503 kHz. Note the square root: to halve the frequency you must quadruple L or C.
What is Q factor?
How sharp the resonance is — the ratio of resonant frequency to bandwidth. High Q means a narrow, tall peak; low Q a broad, shallow one. For a series circuit Q is Z₀/R, for a parallel tank it is R/Z₀, so resistance helps one and hurts the other.
Why does resistance raise Q in a parallel circuit but lower it in series?
Because the loss path differs. In series, current flows through the resistor, so more resistance means more loss. In a parallel tank the resistor shunts the circulating current away, so a larger resistance steals less of it and Q goes up.
How much does component tolerance move the resonant frequency?
Roughly half the component error, because frequency depends on the square root of the product. A 5% error in either L or C shifts f₀ by about 2.5%. If both are 5% out in the same direction you get about 5%.
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