Filter Rolloff Rate

Rolloff = N × 20 dB/decade

Quick answer

This calculator solves Rolloff = N × 20 dB/decade for Rolloff (dB/decade). With Filter Order 0.5, the result is 10 dB/decade. It solves in 2 directions, so you can enter the values you have and get the one you need.

Calculator

Rolloff (dB/decade) (dB/decade)
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Formula

Rolloff = N × 20 dB/decade

Description

The rolloff rate (also called the stopband attenuation slope) of a filter is determined by its order. Each order adds one reactive element (capacitor or inductor) and increases the asymptotic attenuation slope by 20 dB per decade (6 dB per octave). A first-order filter has a gentle 20 dB/decade slope, while a fourth-order filter provides 80 dB/decade, meaning it attenuates a signal 10x the cutoff frequency by 80 dB (factor of 10,000). Higher-order filters provide better frequency selectivity but require more components, are more sensitive to component tolerances, and introduce more phase shift.

Variables

  • N — Filter order (number of poles)
  • Rolloff — Asymptotic attenuation rate (dB/decade)

Practical Notes

Equivalent rolloff in dB/octave is N × 6. Common filter orders: 1st-order (simple RC), 2nd-order (Sallen-Key, biquad), 4th-order (common for audio), 8th-order (high-performance anti-aliasing). Each additional order also adds 90 degrees of phase shift at high frequencies, which can cause stability issues in feedback systems.

Symbols and units

Symbol Meaning Default unit Accepted units
rolloff Rolloff (dB/decade) dB/decade dB/decade
N Filter Order — —

Step by step

  1. 1. What you know: Filter Order 0.5
  2. 2. The relation: Rolloff = N × 20 dB/decade
  3. 3. Substitute: N = 0.5
  4. 4. Result: Rolloff (dB/decade) = 10 dB/decade

Worked examples

Minimum range

Given: Filter Order 0.025

Result: Rolloff (dB/decade) = 0.5 dB/decade

Low range

Given: Filter Order 0.25

Result: Rolloff (dB/decade) = 5 dB/decade

Typical

Given: Filter Order 0.5

Result: Rolloff (dB/decade) = 10 dB/decade

High range

Given: Filter Order 0.8

Result: Rolloff (dB/decade) = 16 dB/decade

Maximum range

Given: Filter Order 8

Result: Rolloff (dB/decade) = 160 dB/decade

Solving for each variable

Solve for Rolloff (dB/decade)

Filter Order 0.025 → 0.5 dB/decade

Solve for Filter Order

Rolloff (dB/decade) 2 dB/decade → 0.1

How Rolloff (dB/decade) changes with Filter Order

Filter Order (input) Rolloff (dB/decade) (result)
0.05 1 dB/decade
0.125 2.5 dB/decade
0.25 5 dB/decade
0.375 7.5 dB/decade
0.5 10 dB/decade
0.75 15 dB/decade
1 20 dB/decade
2 40 dB/decade
3.5 70 dB/decade
5 100 dB/decade

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Frequently asked questions

How do you calculate Filter Rolloff Rate?

Use Rolloff = N × 20 dB/decade. With Filter Order 0.5, Rolloff (dB/decade) works out to 10 dB/decade.

What is the formula for Filter Rolloff Rate?

The formula is Rolloff = N × 20 dB/decade. The rolloff rate (also called the stopband attenuation slope) of a filter is determined by its order.

How do you find Filter Order when you know the other values?

Rearrange for Filter Order: with Rolloff (dB/decade) 2 dB/decade, Filter Order is 0.1.

Related Concepts

All Filters formulas →
RC Low-Pass Filter RC High-Pass Filter Bandpass Bandwidth Filter Rolloff Rate Notch Frequency Butterworth Q Factor Sallen-Key Cutoff Frequency Chebyshev Filter Order

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