Circuit Response
every model has an edge, and the figure carries it
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The thread: Measured, not tabulated

Butterworth is flat, Chebyshev is steep, Bessel has good delay — three adjectives and no quantities, in the most reproduced table in the subject. Every comparison on this site is taken off a solved network instead, which is how the third column, the one that decides whether a filter can pass an edge, turns out to have been missing.
passband deviationdecibels, peak to trough below 0.8 f_cButterworth0.443 dBChebyshev0.500 dBBessel1.882 dBattenuation at three times the cornerdecibels downButterworth47.7 dBChebyshev64.0 dBBessel28.3 dBgroup-delay variation across the passbandper cent, slowest against fastestButterworth48.0%Chebyshev49.0%Bessel0.1%solved, then checked — nine measurements, three networksevery number here moves with the order Filters, measured not tabulated

What a steep skirt costs

A filter's order buys attenuation at a known rate — twenty decibels per decade per pole, and no arrangement of components changes it. What varies between families is how quickly the slope is reached, and the currency it is paid for in is delay: the steepest of the three distorts delay eight hundred times more than the gentlest.

 0501001500200400600closed-loop output (volts) for a 1 V stepthe 100× the divider asks for35.1% overphase margin, measured two waysfrom the loop gain34.9°from the overshoot35.0°apart by 0.1° — the relation assumes two poles and this loop has threesolved, then checked — margin against overshootthe second-order relation is 0.1° out here Feedback, and the margin

Two measurements of one margin

A phase margin is computed from the loop gain in the frequency domain, without ever looking at a step. An overshoot is measured from the closed-loop step response in the time domain, without ever looking at a Bode plot. Inverting the standard relation on the second returns 34.9° against the first's 34.9°, and the residue is the third pole.

 00.5011.521001kfrequency (hertz)group delay (milliseconds)ButterworthChebyshevBesselthe corner, 1.00 kHzsolved, then checked — −dφ/dω on the unwrapped phaseflat magnitude is not flat delay Filters, measured not tabulated

Flat magnitude, unflat delay

A filter that passes every frequency in its band at the right amplitude and the wrong time has not passed the signal. Group delay is the measurement that says so, it is absent from the classical comparison, and it varies by fifty per cent across the passband of the two families everybody uses.

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