2nd-Order RLC Filter Calculator with Bode Plot
Calculate resonant frequency, Q factor, damping ratio, and cutoff bandwidth for series and parallel 2nd-order RLC circuits. Visualizes the Bode plot interactively.
Parameters
Ω
mH
μF
Key Formulas:
Resonant freq: f₀ = 1 / (2π × √(L × C))
Q factor: Series = (1/R)√(L/C) / Parallel = R√(C/L)
Resonant freq: f₀ = 1 / (2π × √(L × C))
Q factor: Series = (1/R)√(L/C) / Parallel = R√(C/L)
Results
Resonant Frequency (f₀)5.033kHz
Quality Factor (Q)6.325
Damping Ratio (ζ)0.079
Bandwidth (BW)795.8 Hz
Lower Cutoff Frequency (f₁)4.65 kHz
Upper Cutoff Frequency (f₂)5.45 kHz
Bode Plot
Enter parameters to load the chart.
Understanding 2nd-Order RLC Filters
A 2nd-order RLC filter combines a resistor (R), inductor (L), and capacitor (C) to create a frequency-selective circuit. Compared to a 1st-order RC filter (−20 dB/decade roll-off), a 2nd-order filter achieves a much steeper −40 dB/decade attenuation slope beyond the cutoff frequency.
Series vs. Parallel Topology
Components are wired in series or parallel to control how current or voltage is distributed across the load as a function of frequency.
- Series RLC: Impedance is minimum at resonance (Z = R), so peak current flows through the circuit. When used as a band-pass filter, output is measured across R.
- Parallel RLC: Impedance is maximum at resonance (Z = R), so current through the tank is minimized and resonant voltage is maximized.
Filter Classification by Output Tap
For a series RLC circuit, the filter function changes entirely depending on which component's voltage is used as the output.
- Low-Pass: Output taken across C. High-frequency components are bypassed to ground.
- High-Pass: Output taken across L. DC and low-frequency components are blocked.
- Band-Pass: Output taken across R. Only the narrow band around resonance passes with minimal attenuation.
- Notch / Band-Stop: Output taken across the series LC combination. Eliminates a specific frequency (e.g., 60 Hz power-line noise).