ENGINEERING CALCULATOR · FORMULAS INCLUDED
RLC Q Factor & Bandwidth Calculator
Calculate series RLC resonant frequency, quality factor Q, half-power bandwidth and lower/upper band edges. Use the total resistance of the complete series loop.
Input parameters
Calculated results
Inputs changed. Calculate again to refresh the result.
| Natural resonant frequency f₀ | 159.154943 kHz |
|---|---|
| Quality factor Q | 5 |
| Half-power bandwidth BW | 31.8309886 kHz |
| Lower half-power frequency fL | 144.033244 kHz |
| Upper half-power frequency fH | 175.864233 kHz |
| Damping ratio ζ | 0.1 |
Half-power edges are where loop current falls to 1/√2 of its resonant maximum. R includes source resistance, load and component series losses.
Series RLC equations
f₀ = 1 / (2π√LC) · Q = √(L/C) / R · BW = R / (2πL) = f₀/Q
fL = [√(BW² + 4f₀²) − BW] / 2 · fH = [√(BW² + 4f₀²) + BW] / 2
ζ = 1/(2Q) · fH − fL = BW · √(fL × fH) = f₀
Use L in H, C in F, R in Ω and frequency in Hz. Bandwidth refers to series current, or voltage across a fixed series resistor. It is not the bandwidth of the voltage across L or C.
Example: 10 μH, 100 nF and 2 Ω
The result is f₀ = 159.155 kHz, Q = 5 and BW = 31.831 kHz. Doubling resistance to 4 Ω halves Q to 2.5 and doubles bandwidth to 63.662 kHz. The resonance frequency stays fixed because L and C are unchanged.
How to use the results
Which resistance belongs in R?
Enter total effective series resistance: the real part of source impedance, series load, inductor winding loss and capacitor ESR. If losses vary significantly with frequency, use values near the operating frequency and verify with an AC simulation.
Does this calculate a parallel RLC circuit?
Not directly. A parallel resistor uses a different Q equation. This calculator covers the series loop shown. At high frequencies, parasitics and component self-resonance can invalidate a lumped-element model.
Is a higher Q always better?
Higher Q narrows bandwidth but can increase reactive-component voltages and ringing near resonance. Balance selectivity, settling time and component limits.