Calculators
Series RLC Circuit Calculator
Calculate series RLC resonance, Q, bandwidth, and damping.
Analyze an ideal passive series RLC circuit from resistance, inductance, and capacitance. Calculate resonance, Q, -3 dB bandwidth, half-power frequencies, and damping locally in your browser.
Series RLC results
- Resonant frequency
- 1.5915494 kHz
- Quality factor (Q)
- 10
- Bandwidth
- 159.15494 Hz
- Lower half-power frequency
- 1.5139602 kHz
- Upper half-power frequency
- 1.6731151 kHz
- Damping ratio (ζ)
- 0.05
- Envelope time constant
- 0.002 s
- Angular resonant frequency
- 10000 rad/s
This tool models an ideal lumped series RLC circuit. Real inductors and capacitors have loss, parasitics, tolerance, self-resonance, and frequency-dependent behavior, while source and load impedances can change the effective resistance and measured response.
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
- Enter the effective series resistance, including relevant source or winding resistance when your model requires it.
- Enter inductance and capacitance and choose the appropriate engineering units.
- Read resonance, Q, bandwidth, exact lower and upper half-power frequencies, damping ratio, and the decay-envelope time constant.
- 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). The natural-response envelope decays with e^(−Rt/(2L)), giving an envelope time constant 2L/R. A larger R therefore increases damping and makes the natural transient decay faster.
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.
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