Chebyshev Filter Order

Formula

Description

This formula calculates the minimum filter order needed for a Chebyshev Type I filter to meet specified passband ripple and stopband attenuation requirements. Chebyshev filters achieve steeper rolloff than Butterworth filters of the same order by allowing equiripple (controlled amplitude variation) in the passband. The tradeoff is worse phase response and group delay variation. The result is typically rounded up to the next integer. Lower passband ripple or greater stopband attenuation requires higher filter order.

Variables

• N — Minimum required filter order
• Ar — Required stopband attenuation (dB)
• Ap — Allowable passband ripple (dB)
• fs — Stopband edge frequency (Hz)
• fp — Passband edge frequency (Hz)

Practical Notes

Common passband ripple values: 0.1 dB (minimal ripple, close to Butterworth), 0.5 dB (good tradeoff), 1 dB (aggressive rolloff). A 5th-order Chebyshev with 0.5 dB ripple provides about the same stopband rejection as a 7th-order Butterworth. Chebyshev Type II (inverse Chebyshev) filters have flat passband and equiripple stopband.