Circuit Analysis & FundamentalsDesign workbench
RLC Resonance Calculator
Resonant frequency, quality factor Q, bandwidth, and damping for a series or parallel RLC circuit — with the resonance curve and half-power points drawn.
About this calculator
At one special frequency an RLC circuit's inductive and capacitive reactances cancel, and the circuit resonates. This calculator finds that resonant frequency and the numbers that describe how sharply the circuit responds around it: the quality factor Q, the −3 dB bandwidth, the damping ratio, and the two half-power frequencies that bound the passband.
The resonant frequency depends only on L and C: f0 = 1 / (2π·√(LC)). What R controls is the sharpness. In a series RLC circuit a smaller resistance gives a higher Q and a narrower, taller response; in a parallel (tank) circuit the roles reverse, and a larger parallel resistance gives the higher Q. The tool applies the correct Q relationship for the topology you pick and plots the universal resonance curve so you can see the peak at f0 and the 0.707 (−3 dB) crossings at the band edges.
Resonance is the mechanism behind tuned filters, oscillator tanks, antenna matching, and the ringing that R is often added to damp. Q ties the pieces together: it is the ratio of the resonant frequency to the bandwidth, and it also equals the reactance at resonance divided by R. A high-Q circuit is selective but rings; a low-Q circuit is broad but well damped. The worked steps show f0, then Q, then the bandwidth and half-power frequencies derived from them, so the relationship between selectivity and damping is explicit rather than assumed.
Design notes & common mistakes
- f0 = 1/(2π√(LC)) — R does not move the resonant frequency, only the sharpness (Q) and bandwidth around it.
- Series and parallel Q are RECIPROCAL in R: series Q = (1/R)√(L/C), parallel Q = R√(C/L). Using the wrong one inverts the trend with R.
- Q = f0/BW = (reactance at resonance)/R. High Q is selective but rings; low Q is broad but damped.
- Damping ratio ζ = 1/(2Q). ζ < 1 rings (underdamped), ζ = 1 is the fastest non-ringing response, ζ > 1 is sluggish (overdamped).
- The half-power (−3 dB) points are where the response falls to 0.707 of the peak, i.e. half the power — not half the amplitude.
Assumptions
- Ideal lossless inductor and capacitor; all loss is lumped into the single resistor R.
- Linear, time-invariant elements with values independent of frequency and amplitude.
- Angular frequency ω = 2πf; the half-power bandwidth uses the 0.707 (−3 dB) definition.
When to use this calculator
Appropriate for
- Finding the resonant frequency, Q, and bandwidth of a tuned LC circuit
- Choosing R to set the selectivity or damping of a series or parallel RLC stage
- Teaching the relationship between Q, bandwidth, and damping
Not suitable for
- Coupled resonators, multi-pole filters, or crystal/ceramic resonators
- Circuits where inductor and capacitor losses must be modelled separately
- Large-signal, saturating, or nonlinear tank circuits
What this calculator does not cover
- Single-resonance R-L-C only; multi-resonant, coupled, or higher-order networks are out of scope.
- All loss is modelled as one lumped resistor — real inductor ESR, capacitor ESR/leakage, and radiation are not separated out.
- Component values are treated as constant; core saturation, dielectric change, and skin effect with frequency are ignored.
- Reports the small-signal linear resonance only, not large-signal or nonlinear tank behaviour.
- As with every calculator on this site: results are preliminary and educational, are not verified for any specific installation, and must be reviewed against the applicable code edition and stamped by a licensed Professional Engineer before real-world use.
Frequently asked questions
What is the resonant frequency of an RLC circuit?
f0 = 1 / (2π·√(LC)). It depends only on the inductance and capacitance, not on the resistance. The resistance sets how sharp the resonance is (the quality factor Q and the bandwidth), but it does not shift the frequency at which the circuit resonates.
What is the quality factor Q, and how does it differ for series and parallel RLC?
Q measures how selective and lightly damped the resonance is; it equals the resonant frequency divided by the −3 dB bandwidth. For a series RLC circuit Q = (1/R)·√(L/C), so a smaller resistance gives a higher Q. For a parallel (tank) circuit the relationship inverts to Q = R·√(C/L), so a larger parallel resistance gives a higher Q.
What are the half-power frequencies?
They are the two frequencies either side of resonance where the response falls to 0.707 of its peak — half the power. The distance between them is the −3 dB bandwidth, and their ratio to the resonant frequency is set by Q.
References
- Nilsson, J. & Riedel, S., Electric Circuits, 11th ed. (series and parallel resonance)
- Sadiku, M., Fundamentals of Electric Circuits, 6th ed. (quality factor and bandwidth)
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