Active Filter Order Calculator

Determine the minimum filter order needed to achieve a given stop-band attenuation at a given frequency ratio. Covers Butterworth, Chebyshev, and Bessel.

Calculator Electronics Updated Apr 23, 2026
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How to Use
  1. Enter cutoff fc and stop-band edge fs.
  2. Enter required stop-band attenuation (dB below passband).
  3. Tool computes minimum integer order N for Butterworth, Chebyshev (1 dB ripple), and Bessel.
Input
Hz (kHz, MHz OK)
Hz (kHz, MHz OK)
dB
dB (Chebyshev)
Presets
Filter Response
Butterworth N
—
Chebyshev N
—
Bessel N
—
fs/fc ratio
—

Show Work

Enter values.

Formulas

Butterworth
N = log(10^(A/10) − 1) / (2·log(fs/fc))
Round up.
Chebyshev
N = acosh(√((10^(A/10)-1)/ε²)) / acosh(fs/fc)
ε = √(10^(Ap/10) − 1)
Bessel
~1.5 − 2× Butterworth
Rough approximation.
Asymptotic slope
20·N dB/decade
Far from cutoff.
Octave slope
6·N dB/octave
Near the transition.
Physical build
ceil(N/2) op-amps
One 2nd-order section per op-amp.

History

Stephen Butterworth published his maximally-flat filter design in 1930 in the British journal Experimental Wireless, derived from the roots of the equation s^(2N) + 1 = 0. Pafnuty Chebyshev\'s equal-ripple polynomials had been known since 1859, but their application to filter design came through Wilhelm Cauer and Sidney Darlington in the 1930s-40s.

Friedrich Bessel\'s 1824 polynomials, originally for describing planetary motion, found filter-design application in the 1950s when W.E. Thomson showed that Bessel-polynomial poles produce linear phase — critical for pulse-fidelity applications like oscilloscopes and telephone transmission.

Modern filter-design software (RF Tool, Analog Filter Wizard, Filter Solutions) handles the order-selection math automatically and synthesizes schematics. But every student of analog electronics still computes these order formulas by hand as a first exercise — they show clearly why Chebyshev beats Butterworth on roll-off, why Bessel trades steepness for phase linearity.

About This Calculator

Enter passband cutoff fc, stopband edge fs, required stopband attenuation (dB), and for Chebyshev the allowed passband ripple (1 dB typical, 0.5 dB for tight passband). The tool computes the minimum integer order N for Butterworth, Chebyshev type I, and approximates Bessel (which needs roughly 1.5-2× the Butterworth order).

The returned N tells you how many 2nd-order Sallen-Key or MFB sections to cascade (ceil(N/2) stages, with an extra 1st-order if N is odd). Standard filter tables (included in Analog Devices\' AD723 app note and TI\'s SLOA093) give the exact Q and cutoff values for each stage. Everything runs client-side.

Frequently Asked Questions

What is filter order?

The highest power of s (or z) in the transfer function. Higher order = more poles = steeper roll-off. Each order adds 6 dB/octave or 20 dB/decade to asymptotic stopband slope.

Butterworth vs Chebyshev order?

Chebyshev achieves the same attenuation with lower order (fewer stages) at the cost of passband ripple. Bessel needs higher order (slower roll-off) to preserve linear phase.

Even vs odd order?

Odd orders have an extra 1st-order section (single pole) plus (N-1)/2 biquad stages. Even orders use N/2 biquads. Cascade of 2nd-order Sallen-Key or MFB stages implements any order.

Common Use Cases

Anti-Alias for 48 kHz ADC

Need -80 dB at 24 kHz with cutoff at 20 kHz: 7th-order Butterworth or 4th-order Chebyshev.

Audio Crossover

4th-order Linkwitz-Riley at 2 kHz: 24 dB/octave slopes each side; seamless acoustic sum.

SDR IF Filter

100 kHz BP at 10 MHz with -60 dB 500 kHz away: 6th-order Chebyshev 1 dB.

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