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Series RLC Circuit Calculator

Calculate series RLC resonance, Q, bandwidth, impedance, and damping.

Series RLC Circuit Calculator tool

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About This Tool

A series RLC circuit combines resistance, inductance, and capacitance in one current path. Its response is shaped not only by the LC natural frequency but also by resistance, which determines damping, selectivity, and bandwidth. This calculator brings those related quantities together on one page: resonant frequency, quality factor, exact half-power frequencies, -3 dB bandwidth, damping ratio, and the natural-response envelope time constant. It is useful for electronics study, passive filter analysis, resonance experiments, and first-pass component evaluation. Calculations stay in your browser.

How To Use It

  1. Enter the effective series resistance, including relevant source or winding resistance when your model requires it.
  2. Enter inductance and capacitance and choose the appropriate engineering units.
  3. Read resonance, Q, bandwidth, exact half-power frequencies, resonance impedance and reactance, damping regime, damped natural frequency, and decay time constant.
  4. Treat the result as an ideal lumped-component model and compare it with component tolerances, parasitics, loading, and datasheet limits before applying it to a physical circuit.

Examples

10 Ω, 10 mH, and 1 µF

This ideal series RLC has f₀ ≈ 1.592 kHz, Q = 10, and bandwidth ≈ 159.15 Hz. Its half-power frequencies are about 1.514 kHz and 1.673 kHz.

Effect of more resistance

Keeping L and C fixed while increasing series resistance lowers Q and increases bandwidth. Resonant frequency from ideal L and C stays the same, but the response becomes less selective.

Changing inductance

Increasing L with R and C fixed lowers the natural resonant frequency and, for the series model, changes both Q and bandwidth. This is why resonance and damping should be considered together rather than tuning only f₀.

Useful Notes

Series RLC resonant frequency

The ideal natural resonant angular frequency is ω₀ = 1/√(LC), and f₀ = 1/(2π√(LC)). At this frequency XL and XC have equal magnitude, so their reactive terms cancel in the series impedance and the remaining ideal impedance is R.

Quality factor

For an ideal series RLC circuit, Q = ω₀L/R = 1/(ω₀CR). Higher Q corresponds to lower damping and a narrower frequency response around resonance. The formula uses the effective series resistance in the modeled loop.

Bandwidth and half-power frequencies

The exact -3 dB bandwidth for the ideal series RLC current response is Δf = R/(2πL). The half-power frequencies satisfy |XL − XC| = R. Their exact angular forms are (√(R² + 4L/C) ∓ R)/(2L), and their frequency difference equals the bandwidth.

Damping ratio and transient decay

The series RLC damping ratio is ζ = (R/2)√(C/L). A value below 1 is underdamped, 1 is critically damped, and above 1 is overdamped. For an underdamped circuit, the oscillation frequency is fd = f₀√(1 − ζ²). The natural-response envelope decays with e^(−Rt/(2L)), giving a time constant of 2L/R.

Impedance and reactance at resonance

At resonance, inductive and capacitive reactance have equal magnitude X₀ = √(L/C) and cancel in the series sum. The ideal circuit impedance is therefore purely resistive with |Z| = R. The same √(L/C) value is the circuit's characteristic impedance and equals QR for this series model.

Resonance versus damped natural frequency

The LC natural frequency f₀ used here is not always the same as the oscillation frequency of an underdamped transient, which is ωd = ω₀√(1 − ζ²). Strong damping can eliminate oscillatory natural response even though the ideal frequency-domain reactance-cancellation condition still exists.

Real circuit limitations

Physical inductors have winding resistance, core loss, parasitic capacitance, tolerance, saturation, and self-resonance. Capacitors have ESR, ESL, leakage, and tolerance. Source and load impedances also affect the effective circuit, so measured Q, bandwidth, and resonance can differ from this ideal model.

FAQ

How is this different from the LC Resonance Calculator?

The LC tool focuses on the ideal L-C natural frequency and reactance. This series RLC tool adds resistance so it can calculate damping, Q, bandwidth, and exact half-power frequencies as one coherent series-circuit analysis.

Is bandwidth always f₀ divided by Q?

For this ideal series RLC model, yes: Δf = R/(2πL) and Q = ω₀L/R, so Δf = f₀/Q. The exact half-power frequencies are not generally symmetric around f₀ on a linear frequency axis, although their difference is exactly Δf.

What resistance should I enter?

Use the effective series resistance represented by your model. Depending on the circuit, that can include an explicit resistor plus meaningful source resistance and inductor winding resistance.

Does a low Q mean there is no resonant frequency?

The ideal series impedance still has reactance cancellation at ω₀ = 1/√(LC). However, low Q means a broad, heavily damped response, and a strongly damped natural transient may not oscillate.

Can this predict a real inductor near self-resonance?

Not reliably. Near an inductor's self-resonant frequency, parasitic capacitance and frequency-dependent losses invalidate the simple lumped ideal-inductor model.