What is the formula for Noise-Equivalent Bandwidth (1-pole)?

The Noise-Equivalent Bandwidth (1-pole) formula is NEB = (π/2) × f−3dB ≈ 1.57 × f−3dB, where NEB—Noise-equivalent bandwidth (Hz); f−3dB—Filter −3 dB cutoff frequency (Hz).

What does NEB mean in the Noise-Equivalent Bandwidth (1-pole) formula?

NEB is Noise-equivalent bandwidth (Hz).

Noise-Equivalent Bandwidth (1-pole)

Q: How do you calculate Noise-Equivalent Bandwidth (1-pole)?

Use the formula NEB = (π/2) × f−3dB ≈ 1.57 × f−3dB. The noise-equivalent bandwidth is the width of an ideal brick-wall filter that would pass the same total noise power as a real filter. Enter the values you know in the calculator above and it solves for the remaining variable.

NEB = (π/2) · f−3dB

Calculator

Noise Bandwidth

−3 dB Bandwidth

Result

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Formula

NEB = (π/2) × f−3dB ≈ 1.57 × f−3dB

Description

The noise-equivalent bandwidth is the width of an ideal brick-wall filter that would pass the same total noise power as a real filter. For a single-pole RC roll-off it is π/2 times the −3 dB bandwidth, because the gentle skirt passes extra noise beyond the corner. Use this, not the −3 dB bandwidth, when computing total RMS noise.

Variables

NEB — Noise-equivalent bandwidth (Hz)
f−3dB — Filter −3 dB cutoff frequency (Hz)

Practical Notes

Higher-order filters have NEB closer to f−3dB (e.g. ×1.22 for 2-pole, ×1.16 for 3-pole). Always convert a real corner to NEB before multiplying by noise density.

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