Filter Rolloff Rate

Formula

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.