How this calculator works
An RLC resonator combines electric and magnetic storage with resistive loss. Quality factor compares stored energy with energy dissipated each cycle. A larger series resistance lowers Q, whereas a larger parallel resistance reduces leakage and raises Q. Bandwidth describes the series current or parallel impedance resonance response. The damping ratio classifies unforced motion; undamped natural resonance is distinct from the damped oscillation frequency.
Formula
omega0 = 1/sqrt(LC); f0 = omega0/(2 pi). Qseries = omega0 L/R; Qparallel = R/(omega0 L); bandwidth = f0/Q; damping ratio = 1/(2Q).
Worked example
A series circuit with L = 1 H, C = 1 F and R = 0.5 ohm has f0 = 0.15915494 Hz, Q = 2 and bandwidth 0.07957747 Hz. With L = 4 H and C = 1 F, Q = 4 requires R = 0.5 ohm.
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Frequently asked questions
Does a damped circuit oscillate at f0?
Its free oscillation frequency is lower when damping is nonzero. Critical and overdamped responses do not oscillate.
Can I substitute coil winding resistance as parallel R?
No. Series coil loss needs its own model or a frequency-dependent equivalent transformation.
Why does increasing parallel resistance improve Q?
It reduces shunt current loss while leaving the ideal energy-storage elements unchanged.