Series RLC Bandpass Filter Calculator | Resonance, Q & Bandwidth

Calculate an ideal series RLC bandpass response with output measured across the resistor. Compare resonance, Q, half-power bandwidth, gain and phase at the observation frequency.

Parameters

Resistance R

Inductance L

Capacitance C

μF

Observation frequency f

Results

—

Resonant frequency f_0

—

Q-factor

—

Bandwidth BW

—

Gain at observation f

Phase at observation f: —

Series RLC band-pass circuit

Bode plot (magnitude)

Theory & Key Formulas

Transfer function (output taken across R):

$$H(j\omega) = \dfrac{R}{R + j\!\left(\omega L - \dfrac{1}{\omega C}\right)}$$

Resonant frequency, Q-factor and bandwidth:

$$f_0 = \dfrac{1}{2\pi\sqrt{LC}},\quad Q = \dfrac{1}{R}\sqrt{\dfrac{L}{C}} = \dfrac{\omega_0 L}{R},\quad \mathrm{BW} = \dfrac{f_0}{Q}$$

At resonance the amplitude ratio is one and phase is zero. The asymptotic slopes are +20 dB/decade below resonance and −20 dB/decade above it. The exact half-power relations are fL·fH=f0² and fH−fL=BW. Using f0±BW/2 is only a high-Q approximation, not valid for the default Q=1 example.

Model and input definitions

An ideal voltage source drives series R, L and C, with an unloaded output across R. Enter L in mH and C in μF; the solver converts them to H and F. Real source resistance and inductor winding resistance require separate treatment.

Reproduce a result

Set R in Ω, L in mH and C in μF using the numeric fields or sliders.
Change observation frequency f in Hz and read resistor-voltage gain and phase. The ideal resonant gain is 0 dB.
Increase only R: Q falls and bandwidth grows, while resonant frequency stays unchanged.

Worked example

R=100 Ω, L=10.0 mH and C=1.000 μF give f0=1/(2π√LC)=1591.55 Hz, Q=√(L/C)/R=1 and BW=R/(2πL)=1591.55 Hz. The half-power frequencies are fL=983.63 Hz and fH=2575.18 Hz, with fH−fL=BW. At f=1592 Hz, displayed gain is approximately 0.00 dB and phase approximately 0.0°.

Only R changes: compare the bandwidth while the resonant frequency stays the same.

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What should I check in this example?

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Change one input at a time and compare the formula with the displayed result. Increase only R: Q falls and bandwidth grows, while resonant frequency stays unchanged.

Limits and interpretation

The passive resistor-voltage transfer cannot exceed unity. With source or winding resistance, distinguish total series resistance from the resistor across which output is measured. Parasitics, self-resonance and output loading are omitted. The plot explicitly samples resonance and half-power points so a narrow high-Q peak is not missed.

Frequently asked questions

No. f0=√(fL fH) is their geometric mean. The difference from the arithmetic mean is significant at low Q.

Not for this ideal series circuit with resistor-voltage output. f0=1/(2π√LC), while Q decreases and bandwidth increases.

Across R, the ideal output equals the input in magnitude. This is different from the voltages across L or C.

The distance between half-power points, where amplitude is 1/√2 of the peak or −3.0103 dB. Here BW=R/(2πL).

Sources for the model

Checks cover displayed units, reference calculations, input sensitivity, boundary conditions and cross-language results. They do not certify code compliance or real-world accuracy.