Circuit Explorer

RLC Resonant Filter (Series Band-Pass)

An RLC circuit combines a resistor, an inductor, and a capacitor. At a specific "resonant frequency," the inductive and capacitive reactances cancel each other out, allowing maximum current to flow. This configuration acts as a Band-Pass filter, passing frequencies near resonance while attenuating others.

f₀ = 1/(2π√LC)
Q = (1/R)√(L/C)
2nd Order System

Circuit Schematic

Interactive Diagram

VinVoutACL10.0 mHC1.00 µFR100 Ωf₀ = 1.59kHz

Adjust Values

Component Controls

100 Ω
100 mΩ10.0 kΩ

Controls the bandwidth and Q-factor (damping)

10.0 mH
1.00 µH1.00 H

Stores energy in magnetic field, opposes current change

1.00 µF
1.00 pF1.00 mF

Stores energy in electric field, blocks DC

Quick Presets

Calculated Values

System Properties

Resonant Frequency (f₀)1.59 kHz
1/(2π√LC)
Quality Factor (Q)1.00
(1/R)√(L/C)
Bandwidth (-3dB)1.59 kHz
BW = f₀ / Q

Bode Plot

Magnitude Response

Peakgain occurs at resonance. Bandwidth is the width at -3dB.

-60.00-43.75-27.50-11.255.0015.915342.8897.387e+31.592e+5Frequency (Hz)Magnitude (dB)
Gain peaks at 0dB (Unity) at f₀

Bode Plot

Phase Response

-90.00-45.000.00e+045.0090.0015.915342.8897.387e+31.592e+5Frequency (Hz)Phase (°)
Positive Phase: Capacitive (Low f)
Negative Phase: Inductive (High f)

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Circuit Behavior

At Resonance (f₀)

Inductive and capacitive reactances are equal and opposite (XL = XC), canceling each other out. The impedance is purely resistive (Z = R), resulting in maximum current and unity gain (0dB).

Quality Factor (Q)

Q determines the "sharpness" of the resonance. A high Q means a narrow bandwidth and high selectivity. Decreasing resistance increases Q.

Below Resonance (f < f₀)

The capacitor's impedance (XC) dominates. The circuit behaves capacitatively, blocking low frequencies with a positive phase shift approaching +90°.

Above Resonance (f > f₀)

The inductor's impedance (XL) dominates. The circuit behaves inductively, blocking high frequencies with a negative phase shift approaching -90°.