Band Stop Filter Calculator

Calculator Inputs

Topology

Affects the resistance formula for the same Q.

Center frequency (f0)

Specification mode

You can specify stop‑band width or selectivity.

Bandwidth (BW)

Q factor

Q = f0 / BW.

Preferred component

We compute the other component and R.

Capacitance (C)

Inductance (L)

Component tolerance (%)

Used to estimate f0 range only.

Sweep points

21–301 points. More points increase downloads.

Example Data Table

Topology	f0	BW	Preferred	Computed C	Computed L	Computed R
Series RLC notch	1 kHz	200 Hz	C = 100 nF	100 nF	253.3 mH	7.96 kΩ
Parallel RLC notch	10 kHz	1 kHz	L = 10 mH	25.33 nF	10 mH	6.28 kΩ

Example values are illustrative. Pick standard parts and re-check performance with your target load.

Formula Used

ω0 = 2π f0 and f0 = 1 / (2π √(LC))
Q = f0 / BW and BW = f0 / Q
Series RLC notch (ideal): Q = ω0 L / R so R = ω0 L / Q
Parallel RLC notch (ideal): Q = R / (ω0 L) so R = Q ω0 L
Notch response model: H(s) = (s² + ω0²) / (s² + (ω0/Q)s + ω0²)
Magnitude: |H(jω)| = |ω² − ω0²| / √((ω² − ω0²)² + (ω ω0 / Q)²)

How to Use This Calculator

Choose a topology that matches your planned circuit.
Enter the center frequency you want to reject.
Set bandwidth or Q to control stop‑band width.
Pick a preferred L or C based on availability.
Click Calculate and review R, L, and C outputs.
Use tolerance range to judge stability of the notch.
Download CSV or PDF for documentation and sharing.

Design targets and inputs

A practical band stop design starts with lower edge f1, upper edge f2, and the intended notch depth. The calculator derives the center frequency as f0 = √(f1·f2) and the bandwidth as BW = f2 − f1. Example: f1 = 900 Hz and f2 = 1100 Hz gives f0 ≈ 995 Hz and BW = 200 Hz, suitable for removing a narrow interference tone.

Quality factor and selectivity

Selectivity is summarized by Q = f0/BW. With the example, Q ≈ 4.98. Higher Q narrows the stop band and steepens transitions, but it increases sensitivity to tolerance and loss. A notch aimed at 1 kHz with Q = 10 has about half the bandwidth of Q = 5, preserving more neighboring frequencies.

Second‑order notch transfer behavior

The response follows a second‑order notch: H(s) = (s² + ω0²)/(s² + (ω0/Q)s + ω0²). At ω = ω0 the numerator approaches zero, producing maximum attenuation. Away from ω0 the magnitude rises toward unity, keeping both pass bands near 0 dB, so accurate ω0 placement dominates performance.

Component sizing and impedance checks

For an RLC realization, ω0 = 1/√(LC) links inductance and capacitance. The calculator reports X_L = 2πf0L and X_C = 1/(2πf0C) to confirm reactance balance at f0. In a series notch, R provides damping that influences Q; in a parallel notch, effective loss limits notch depth.

Sweep plot interpretation

The Plotly chart sweeps frequency around f0 and plots magnitude in dB. A sharp dip near computed f0 confirms the reject band. If the dip is too wide, reduce BW or increase Q. If it misses the interference frequency, adjust f1 and f2 to shift f0 while keeping BW aligned to your requirement.

Export, validation, and reporting

Use CSV export to capture each sweep point (frequency, magnitude, dB) for lab comparison, and use PDF export to share the design summary. When tolerances matter, compare the range f0·(1±tol) against interference drift; at 1 kHz, 2% tolerance implies about ±20 Hz center movement. For audio work, check that passband ripple stays below 0.5 dB; for RF, confirm insertion loss meets your link budget and that component Q is realistic at the operating frequency. Document measured and simulated curves together clearly.

FAQs

1) What is a band stop filter used for?

It rejects a specific frequency range while passing lower and higher frequencies, often used to suppress hum, whistle tones, or narrowband interference in sensor and communication paths.

2) How do I choose f1 and f2?

Pick edges that cover the unwanted component plus drift margin. Narrow edges raise Q and deepen selectivity, while wider edges reduce sensitivity to tolerances but remove more desired spectrum.

3) What does Q mean in this calculator?

Q equals f0 divided by bandwidth. Higher Q means a narrower notch and steeper transitions, but practical depth depends on component losses and matching at the intended center frequency.

4) Why can the notch miss the target frequency?

Component tolerances shift ω0 because ω0 = 1/√(LC). Parasitics and finite inductor or capacitor quality also move the effective center, especially when Q is high.

5) Series or parallel notch: which should I use?

Series notches are common in series paths to create low impedance at the reject frequency. Parallel notches create high impedance at the reject frequency and are useful in shunt or tank‑style networks.

6) How should I validate the design?

Export the sweep to CSV, compare it with a simulator and lab measurement, and verify insertion loss in the pass bands. If needed, tighten tolerance or retune L and C to center the notch.