Chebyshev Filter Order

N = acosh(√(ε²s/ε²p)) / acosh(fs/fp)

Quick answer

This calculator solves N = acosh(√((10^(Ar/10)−1)/(10^(Ap/10)−1))) / acosh(fs/fp) for N. With Stopband Attenuation (dB) 200 dB, Passband Ripple (dB) 94 dB, Stopband Frequency 1 MHz, Passband Frequency 0.47 MHz, the result is 9.294.

Calculator

Result
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Formula

N = acosh(√((10^(Ar/10)−1)/(10^(Ap/10)−1))) / acosh(fs/fp)

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.

Symbols and units

Symbol Meaning Default unit Accepted units
Ar Stopband Attenuation (dB) dB dB
Ap Passband Ripple (dB) dB dB
fs Stopband Frequency kHz Hz, kHz, MHz, GHz
fp Passband Frequency kHz Hz, kHz, MHz, GHz

Step by step

  1. 1. What you know: Stopband Attenuation (dB) 200 dB, Passband Ripple (dB) 94 dB, Stopband Frequency 1 MHz, Passband Frequency 0.47 MHz
  2. 2. The relation: N = acosh(√((10^(Ar/10)−1)/(10^(Ap/10)−1))) / acosh(fs/fp)
  3. 3. Substitute: Ar = 200 dB, Ap = 94 dB, fs = 1 MHz, fp = 0.47 MHz
  4. 4. Result: N = 9.294

Worked examples

Minimum range

Given: Stopband Attenuation (dB) 3 dB, Passband Ripple (dB) 1.41 dB, Stopband Frequency 1 kHz, Passband Frequency 0.47 kHz

Result: N = 0.7607

Low range

Given: Stopband Attenuation (dB) 30 dB, Passband Ripple (dB) 14.1 dB, Stopband Frequency 10 kHz, Passband Frequency 4.7 kHz

Result: N = 1.828

Typical

Given: Stopband Attenuation (dB) 200 dB, Passband Ripple (dB) 94 dB, Stopband Frequency 1 MHz, Passband Frequency 0.47 MHz

Result: N = 9.294

High range

Given: Stopband Attenuation (dB) 600 dB, Passband Ripple (dB) 282 dB, Stopband Frequency 5 MHz, Passband Frequency 2.35 MHz

Result: N = 26.88

Maximum range

Given: Stopband Attenuation (dB) 6 dB, Passband Ripple (dB) 2.82 dB, Stopband Frequency 50 kHz, Passband Frequency 23.5 kHz

Result: N = 0.8624

How N changes with Stopband Attenuation (dB)

Stopband Attenuation (dB) (input) N (result)
100 dB 0.947
150 dB 5.145
200 dB 9.294
300 dB 17.59
400 dB 25.89
800 dB 59.07
1400 dB 108.8
2000 dB 158.6

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Frequently asked questions

How do you calculate Chebyshev Filter Order?

Use N = acosh(√((10^(Ar/10)−1)/(10^(Ap/10)−1))) / acosh(fs/fp). With Stopband Attenuation (dB) 200 dB, Passband Ripple (dB) 94 dB, Stopband Frequency 1 MHz, Passband Frequency 0.47 MHz, N works out to 9.294.

What is the formula for Chebyshev Filter Order?

The formula is N = acosh(√((10^(Ar/10)−1)/(10^(Ap/10)−1))) / acosh(fs/fp). This formula calculates the minimum filter order needed for a Chebyshev Type I filter to meet specified passband ripple and stopband attenuation requirements.

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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