numvana

Series RLC Circuit Resonance Calculator

Calculate a series RLC circuit's resonant frequency, quality factor (Q), -3dB bandwidth, and damping ratio from its resistance, inductance, and capacitance.

Resonant frequency (f₀)
159.15 Hz
Quality factor (Q)
10
Bandwidth (-3dB)
15.92 Hz
Half-power points
151.2 Hz – 167.11 Hz
Damping ratio (ζ)
0.05 (Underdamped)

How it works

A series RLC circuit resonates at f₀ = 1 ÷ (2π√(LC)) — the same formula this site's LC Circuit Resonant Frequency calculator uses for an ideal, resistance-free tank circuit. Adding the resistor's effect shows how sharp that resonance actually is: the quality factor Q = (1/R)·√(L/C) measures it directly, with a high Q meaning a tall, narrow resonance peak that rings for many cycles, and a low Q meaning a short, broad one that damps out quickly.

The -3dB bandwidth — the width of the frequency band around resonance where the circuit still responds at half power or more — is Δf = f₀ ÷ Q, and the (symmetric) half-power points are f₀ ± Δf/2. The damping ratio ζ = 1 ÷ (2Q) comes from matching the circuit's governing differential equation to the standard damped-oscillator form, and classifies its behavior: underdamped (ζ < 1, the usual case for anything worth calling 'resonant') rings before settling; critically damped (ζ = 1) settles fastest without ringing; overdamped (ζ > 1) settles slower still with no ringing at all.

FAQ

How is this different from the LC Circuit Resonant Frequency calculator?

That calculator models an idealized LC tank with no resistance, so it can solve for resonant frequency, inductance, or capacitance, but it has nothing to say about how sharp the resonance is — a real circuit always has some resistance, which is exactly what sets its Q factor and bandwidth. This calculator adds that resistance back in to answer the 'how sharp' question the ideal LC model can't.

Why is a high Q factor usually considered desirable in a radio tuner, but not in a car's suspension?

It depends on whether ringing helps or hurts. A radio tuner's resonant circuit needs a high Q (low damping) to sharply pick out one frequency and reject nearby ones — that narrow bandwidth is the whole point. A car's suspension is a mechanical analog of an RLC circuit, and there you want it closer to critically damped: enough damping that the car doesn't keep bouncing (ringing) after a bump, without being so overdamped that it responds sluggishly.

Related calculators