Series Notch Filter Calculator

Model resonance, bandwidth, damping, impedance, and attenuation quickly. Compare component choices with clear exportable results. Tune notch behavior for reliable circuit planning and testing.

Calculator Inputs

Example Data Table

Case R L C Resonance Q Factor Bandwidth
Audio hum notch 10 Ω 10 mH 100 nF 5032.92 Hz 31.62 159.15 Hz
Broad test notch 5 Ω 1 mH 1 µF 5032.92 Hz 6.32 795.77 Hz
Narrow signal rejection 20 Ω 50 mH 10 nF 7117.63 Hz 111.80 63.66 Hz

Formula Used

The calculator uses standard series RLC resonance equations for a shunt notch branch.

Resonant frequency: f₀ = 1 / (2π√LC)

Angular resonance: ω₀ = 1 / √LC

Series Q factor: Q = √(L / C) / R

Bandwidth: BW = R / (2πL)

Lower cutoff: f₁ = (√(R² + 4L/C) - R) / (4πL)

Upper cutoff: f₂ = (√(R² + 4L/C) + R) / (4πL)

Reactance: Xₗ = 2πfL, X꜀ = 1 / (2πfC)

Branch impedance: Z = √(R² + (Xₗ - X꜀)²)

The attenuation estimate also uses the source resistance, load resistance, and shunt notch branch divider.

How To Use This Calculator

  1. Select the calculation mode.
  2. Enter resistance, inductance, and capacitance values.
  3. Use the target frequency when solving a missing component.
  4. Enter source and load resistance for attenuation estimates.
  5. Add test frequency to inspect reactance away from resonance.
  6. Press the calculate button.
  7. Review the result block above the form.
  8. Export the calculated table as CSV or PDF.

Series Notch Filter Guide

What This Calculator Solves

A series notch filter removes a narrow band of unwanted frequency. It is often built with a resistor, inductor, and capacitor. At resonance, the inductive reactance and capacitive reactance cancel. The branch impedance becomes mainly resistive. When that branch is placed as a shunt path, it pulls the chosen frequency away from the output node.

Why Resonance Matters

The resonant frequency is the center of the notch. Small changes in inductance or capacitance move this point. That is why unit selection matters. A small capacitor error can shift a high frequency notch. A small inductor error can change both tuning and loss. This calculator helps compare those effects before parts are chosen.

Bandwidth And Selectivity

Bandwidth describes the frequency span affected by the filter. A low resistance creates a sharper notch. A higher resistance creates a wider and softer rejection region. The quality factor shows this selectivity in one value. Higher Q means a narrower notch. Lower Q means broader rejection. The calculator reports both values, so tuning choices are easier to review.

Practical Circuit Planning

Real circuits include source resistance and load resistance. These values change the visible attenuation. A perfect formula may predict resonance correctly, but the actual voltage drop depends on the divider formed by the source, load, and notch branch. Use realistic resistance values when estimating output loss. This gives a more useful design result.

Using The Results

Start with the unwanted frequency. Select a convenient capacitor or inductor. Then solve the missing part. Adjust resistance to reach the desired bandwidth. Check the output ratio at the test frequency. Export the result when documenting a design. The table can also help compare trial values. Always allow tolerance margin in final hardware.

Advanced Checks

The calculator also evaluates reactance at a selected frequency. This is helpful when testing values away from resonance. If inductive reactance is larger, the branch looks inductive. If capacitive reactance is larger, it looks capacitive. The impedance result shows how strongly the branch can divert signal energy. Designers can use this check to judge nearby passband behavior and avoid unexpected loading. It is useful when a design must meet narrow rejection limits during final review.

FAQs

What is a series notch filter?

A series notch filter uses a resistor, inductor, and capacitor to reject a narrow frequency band. At resonance, the inductor and capacitor cancel each other, allowing the branch to create strong attenuation.

What does resonant frequency mean?

Resonant frequency is the center point of the notch. It is the frequency where inductive reactance equals capacitive reactance, making the series branch mostly resistive.

How does resistance affect the notch?

Lower series resistance usually creates a sharper notch and higher Q. Higher resistance widens the affected band and reduces selectivity.

What is Q factor?

Q factor measures selectivity. A high Q filter has a narrow rejection band. A low Q filter rejects a wider range of frequencies.

Why include source resistance?

Source resistance changes the voltage divider around the notch branch. Including it gives a more realistic attenuation estimate for practical circuit behavior.

Why include load resistance?

Load resistance affects output voltage and notch depth. A low load value can reduce the visible rejection and change the final response.

Can this calculator solve missing components?

Yes. It can solve inductance or capacitance from a target resonance. Enter the known component and target frequency, then choose the correct mode.

Are tolerance results exact?

No. Tolerance results are estimates based on component percentage limits. Real circuits may also include parasitic resistance, stray capacitance, and inductor self-resonance.

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