Bandpass Filter Calculator

Compute center frequency, quality factor (Q), bandwidth, and visualize the magnitude response of a passive RLC bandpass filter. Design your own filter starting from target f₀ and Q.

1. RLC Series Bandpass Analysis

Enter resistance (R), inductance (L), and capacitance (C) values to compute resonant frequency, Q-factor, bandwidth, and cutoff frequencies.

2. Bandpass Filter Design (Target f₀ & Q)

Specify desired center frequency (f₀), quality factor (Q), and reference resistance. The tool calculates required L and C values for a series RLC network.

Quick presets:
? Audio (1kΩ, 22mH, 47nF)
? AM Radio (100Ω, 250µH, 100pF)
✨ High Q (100Ω, 100mH, 10nF)
⚡ Low Q (100Ω, 1mH, 10µF)
Privacy first: All calculations performed locally. The frequency response graph is rendered in your browser — no data is transmitted.
Magnitude Frequency Response |H(f)| (dB)
|H(f)| (dB)
Center frequency f₀
-3dB cutoff frequencies (f₁, f₂)

Theory & Design of Series RLC Bandpass Filters

A series RLC bandpass filter is a classic passive circuit that passes frequencies within a specific band while attenuating signals outside that band. It consists of a resistor (R), inductor (L), and capacitor (C) connected in series. The output voltage is taken across the resistor, providing a bandpass transfer function. At resonance, the impedance of the inductor and capacitor cancel, maximizing the output.

Key design equations (series RLC):

Resonant frequency: f₀ = 1 / (2π √(LC))   |   Quality factor: Q = (1/R) √(L/C) = ω₀L / R
Bandwidth: BW = f₀ / Q   |   Lower cutoff: f₁ = f₀ √(1 + 1/(4Q²)) - f₀/(2Q)
Upper cutoff: f₂ = f₀ √(1 + 1/(4Q²)) + f₀/(2Q)

The magnitude response in dB: |H(f)|dB = 20 log₁₀( R / √(R² + (2πfL - 1/(2πfC))² ) )

Practical Applications & Industry Relevance

Bandpass filters are essential in wireless communications (RF front-ends, channel selection), audio processing (equalizers, crossover networks), biomedical instrumentation (ECG noise filtering), and measurement equipment (spectrum analyzers). The series RLC topology is valued for its simplicity, predictable behavior, and suitability for narrowband or wideband requirements depending on Q.

Case Study: IF Filter in Superheterodyne Receiver

An intermediate frequency (IF) stage in a radio receiver often uses a high-Q bandpass filter to reject adjacent channels. Using our calculator, an engineer can specify f₀ = 455 kHz and Q = 50, with R = 1000 Ω, obtaining L ≈ 17.5 mH and C ≈ 6.8 pF. The narrow bandwidth (9.1 kHz) ensures excellent selectivity. The interactive graph confirms the steep skirt response, validating the design before prototyping.

Step-by-Step Design Procedure

  1. Define specifications: Choose center frequency f₀, desired bandwidth (or Q), and load resistance (R).
  2. Compute L and C: L = Q·R / (2π f₀) , C = 1 / (2π f₀ Q R).
  3. Validate component availability: Adjust values to standard E-series if needed.
  4. Simulate response: Use our interactive graph to verify -3dB points and insertion loss.
  5. Build and test: Real-world parasitics may require fine-tuning.

Common Misconceptions

  • Higher Q always better? Not always: excessive Q can cause instability and sensitivity to component tolerances.
  • Bandwidth = f₂ – f₁ is accurate for high-Q approximation; our calculator uses exact formulas.
  • Response is symmetric on linear scale? On a logarithmic frequency axis, bandpass responses are symmetric only for high Q.

Verification & Accuracy Notes

The implemented algorithms rely on analytic solutions validated against standard filter theory texts (Zverev, "Handbook of Filter Synthesis" and Williams, "Electronic Filter Design Handbook"). The transfer function is calculated without approximations, guaranteeing high numerical precision. The interactive graph uses logarithmic frequency spacing to accurately represent both narrow and wideband responses.

Parameter Example (R=1kΩ, L=10mH, C=100nF) Computed Value Validation
Resonant frequency f₀ 1/(2π√(0.01·100e-9)) 5.033 kHz Matches theoretical 5.033 kHz
Quality factor Q ω₀L/R = (2π·5033·0.01)/1000 0.316 Low Q, wide bandwidth
-3dB bandwidth f₀/Q ≈ 15.9 kHz 15.92 kHz Consistent

Advanced: Transfer Function & Pole Locations

The voltage transfer ratio of a series RLC bandpass filter is H(s) = (sR/L) / (s² + sR/L + 1/(LC)). The poles are complex conjugates with real part -α = -R/(2L) and imaginary part ω₀√(1-1/(4Q²)). This underdamped response creates the characteristic peaking at resonance. For Q > 0.5, the filter provides a bandpass shape; for very low Q, the response resembles a low-pass/high-pass blend. Our calculator accurately models all Q regimes.

Authored by senior RF engineers & educators – This tool is peer-reviewed and aligned with IEEE standards and academic curricula. References: “RF Circuit Design” by C. Bowick, and “The Art of Electronics” by Horowitz & Hill. Updated March 2026 by GetZenQuery Tech team.

Frequently Asked Questions (FAQ)

Series RLC bandpass takes output across the resistor; it offers low impedance at resonance. Parallel RLC bandpass (output across the LC tank) is used for high-impedance loads. Our tool focuses on the series topology, widely used for voltage-mode filtering.

High Q (narrow bandwidth) is suitable for channel selection; low Q (wide bandwidth) is used for audio or video signal shaping. Trade-offs involve passband ripple and component sensitivity.

This calculator is specifically for passive RLC series bandpass filters. For active biquad or multiple-feedback filters, refer to our dedicated active filter tools.

Ideal series RLC provides infinite attenuation at DC and high frequencies. The graph displays values as low as -100 dB (numerical precision).
References & further reading: Analog Devices – Bandpass Filter Design, Wikipedia: RLC Circuit, All About Circuits – Bandpass Calculator.