Engineering
RLC Resonant Frequency (f0), Quality Factor (Q) & -3 dB Bandwidth
Calculate LC tank resonant frequency f_0 = 1 / (2 * PI() * SQRT(L * C)) (Hz), Series RLC Quality Factor Q = (1 / R) * SQRT(L / C), and half-power -3 dB Bandwidth BW = f_0 / Q.
Tune RF bandpass filters, NFC antennas, and wireless-charging coils!
At resonance inside any Inductor-Capacitor (LC) circuit, inductive reactance X_L = 2 * PI() * f * L exactly cancels capacitive reactance X_C = 1 / (2 * PI() * f * C)—leaving pure real resistance and locking Resonant Frequency to Thomson's formula: f_0 = 1 / (2 * PI() * SQRT(L * C)) (in Hz)!
How sharply selective is the resonance peak? Characteristic impedance Z_0 = SQRT(L / C) divided by series resistance R defines the Series Quality Factor Q = (1 / R) * SQRT(L / C) (for a parallel tank resistor R_p, Q_p = R_p / SQRT(L / C))! Dividing f_0 by Q immediately gives the -3 dB Half-Power Passband Bandwidth: Delta_f = f_0 / Q = R / (2 * PI() * L)!
| RLC Tank Metric (L = 100 uH = 0.0001 H, C = 10 nF = 1e-8 F) | Formula | Low-Loss R = 5 Ohm | Damped R = 25 Ohm |
|---|---|---|---|
| Resonant Frequency f_0 (Hz) | 1 / (2 * PI() * SQRT(L * C)) | 159,154.94 Hz (159.15 kHz) | 159,154.94 Hz (Unchanged!) |
| Series Quality Factor Q | (1 / R) * SQRT(L / C) | (1/5) * 100 = 20.00 | (1/25) * 100 = 4.00 |
| -3 dB Passband Bandwidth BW | f_0 / Q | 7,957.75 Hz (~8 kHz) | 39,788.74 Hz (5x wider!) |
LC Tank Resonant Frequency f_0 = 1 / (2 * PI() * SQRT(L * C)) (Hz)
Computes natural resonant frequency in Hz from inductance B2 (Henries) and capacitance B3 (Farads).
=IF(OR(B2 <= 0, B3 <= 0), "L and C Must Be > 0", ROUND(1 / (2 * PI() * SQRT(B2 * B3)), 2))Series RLC Quality Factor Q & -3 dB Half-Power Bandwidth (Hz)
Evaluates Series Q = (1 / R) * SQRT(L / C) using series resistance B4 (Ohms).
=IF(B4 <= 0, "Resistance R Must Be > 0", ROUND((1 / B4) * SQRT(B2 / B3), 2))Try the example
Use the original values or change them to test your understanding.