Series RLC frequency response

RLC Bandwidth Calculator

Calculate bandwidth, resonant frequency, or quality factor for a resonant RLC circuit. Review estimated lower and upper half-power frequencies with each result.

Series RLC resonance

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Result

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Resonance frequency range

What is bandwidth in an RLC circuit?

Bandwidth is the frequency interval between the lower and upper half-power points of a resonant circuit.

It describes how wide the circuit's useful resonance response is around its center or resonant frequency.

Main equation

RLC bandwidth formula

BandwidthBW = f₀ ÷ Q

  • BW is bandwidth in hertz.
  • f₀ is the resonant frequency in hertz.
  • Q is the dimensionless quality factor.

Worked calculation

Calculate RLC bandwidth

Suppose a resonant circuit has a resonant frequency of 1,000 Hz and a quality factor of 20.

  1. Use BW = f₀ ÷ Q.
  2. Substitute BW = 1,000 ÷ 20.
  3. The bandwidth is 50 Hz.

Solve related variables

Rearranged bandwidth equations

Resonant frequencyf₀ = BW × Q

Quality factorQ = f₀ ÷ BW

Frequency limits

Lower and upper half-power frequencies

For a simple centered estimate, half of the bandwidth is subtracted from and added to the resonant frequency.

Lower frequencyf₁ ≈ f₀ − BW ÷ 2

Upper frequencyf₂ ≈ f₀ + BW ÷ 2

These values show the approximate frequency range across which the resonant response remains within its half-power limits.

Resonance selectivity

How quality factor affects bandwidth

  • A higher quality factor produces a narrower bandwidth.
  • A lower quality factor produces a broader bandwidth.
  • Narrow-band circuits provide greater frequency selectivity.
  • Broad-band circuits respond over a wider frequency range.

Related calculators

Common questions

RLC bandwidth calculator FAQ

What formula does the RLC bandwidth calculator use?

The calculator uses BW = f₀ ÷ Q, where BW is bandwidth, f₀ is resonant frequency, and Q is the circuit quality factor.

How do you calculate resonant frequency from bandwidth?

Multiply bandwidth by quality factor using f₀ = BW × Q.

How do you calculate quality factor from bandwidth?

Divide resonant frequency by bandwidth using Q = f₀ ÷ BW.

What does a narrow RLC bandwidth mean?

A narrow bandwidth normally indicates a higher quality factor, sharper resonance, and greater frequency selectivity.

What are half-power frequencies?

Half-power frequencies are the lower and upper cutoff frequencies that define the circuit bandwidth around resonance.