Equivalent Noise Bandwidth Calculator

Calculator

Choose a method, enter your values, and submit. The result appears above this form, directly below the header.

Calculation Method

Cutoff Frequency fc (Hz)

Measured 3 dB Bandwidth (Hz)

Correction Factor k

Center Frequency f0 (Hz)

Q Factor

Response Gain Format

Reference Gain (optional)

Sampling Frequency fs (Hz)

Window Type

Window Length N

Voltage Noise Density (optional)

Power Spectral Density (optional)

Frequency Response Data

Enter one pair per line using frequency and gain. Example: 1000,0.707 or 1000,-3.01 for dB mode.

Custom Coefficients

Used only when Window Type is set to Custom Coefficients. Separate values with commas, spaces, or line breaks.

Example Data Table

This example reflects a low-pass style response sampled in linear magnitude. You can paste similar values into the sampled-response method.

Frequency (Hz)	Magnitude	\|H(f)\|²	Comment
0	1.000	1.000	Reference passband point
500	0.894	0.799	Still near passband
1000	0.707	0.500	Classic 3 dB point
1500	0.555	0.308	Moderate attenuation
2000	0.447	0.200	Further roll-off
5000	0.196	0.038	Tail contribution remains finite

Formula Used

General definition

ENBW = ∫ |H(f)|² df / |Href|²

The numerator is the area under the squared magnitude response. The denominator normalizes by the chosen reference gain, usually the passband peak.

Sampled data form

ENBW ≈ Σ [ (|Hi|² + |Hi+1|²) / 2 ] × Δf / |Href|²

This page uses trapezoidal integration for entered frequency-response samples.

One-pole RC low-pass

ENBW = (π / 2) × fc

A first-order low-pass passes more integrated noise than an ideal brick-wall filter with the same cutoff.

Band-pass approximation

BW3dB = f0 / Q

ENBW ≈ (π / 2) × BW3dB

This is useful for narrow Lorentzian-like band-pass systems.

Window-based ENBW

ENBWbins = N × Σw[n]² / (Σw[n])²

ENBWhz = fs × Σw[n]² / (Σw[n])²

This is common in FFT and spectrum-analyzer workflows.

How to Use This Calculator

Select the method that best matches your data source.
Enter the required frequencies, Q factor, window settings, or sampled response.
Optionally add voltage noise density or power spectral density.
Press Calculate ENBW to generate the result.
Review the result cards and the Plotly graph above the form.
Use the CSV or PDF buttons to export the summary.

FAQs

1. What is equivalent noise bandwidth?

Equivalent noise bandwidth is the width of an ideal rectangular filter that would pass the same total noise power as the real response when both share the same reference gain.

2. Why is ENBW often larger than 3 dB bandwidth?

Real filters usually have skirts and tails. Noise from those regions still contributes to total integrated power, so ENBW often exceeds the nominal 3 dB width.

3. When should I use the sampled response method?

Use it when you have measured or simulated gain values versus frequency. It is especially helpful when the filter shape is irregular or does not match a simple closed-form equation.

4. What does window ENBW in bins mean?

ENBW in bins shows how many FFT bins of white-noise power the selected window effectively spans. It is a normalization measure used in spectral estimation and analyzer calibration.

5. Why does the formula square the gain?

Noise power scales with the square of amplitude gain. That is why the area is computed from |H(f)|² rather than from amplitude magnitude alone.

6. Can I enter response data in dB?

Yes. Switch the response format to dB magnitude. The calculator converts dB to linear magnitude before integrating the squared response.

7. How does noise density connect to ENBW?

If the input noise density is flat, output RMS voltage is found by multiplying the density by the square root of ENBW. Power spectral density is multiplied directly by ENBW.

8. Is the Q-based band-pass result exact?

No. It is an approximation for narrow Lorentzian-like band-pass responses. For high accuracy, use measured or simulated response data and integrate the sampled spectrum.