Circuit Response
every model has an edge, and the figure carries it
Generator

A 1.0% doublet: 0.078 dB in the magnitude, 36× the settling time

computed by solving, not by drawing. Above, the magnitude of a fast circuit followed by a pole and a zero that were meant to cancel and miss by 1.00%, against the same circuit with the cancellation exact: the worst disagreement anywhere up to the fast corner is 0.0777 dB. Below, the error left in the step response, in units of the tail's own amplitude of 0.909%. Settling to 0.10% takes 245.2 fast time constants against 6.9 with the cancellation exact, and the closed form τ·ln(A/B) gives 245.2 — a time that contains nothing of the fast circuit at all.
A 1.0% doublet: 0.078 dB in the magnitude, 36× the settling timecomputed by solving, not by drawing. Above, the magnitude of a fast circuit followed by a pole and a zero that were meant to cancel and miss by 1.00%, against the same circuit with the cancellation exact: the worst disagreement anywhere up to the fast corner is 0.0777 dB. Below, the error left in the step response, in units of the tail's own amplitude of 0.909%. Settling to 0.10% takes 245.2 fast time constants against 6.9 with the cancellation exact, and the closed form τ·ln(A/B) gives 245.2 — a time that contains nothing of the fast circuit at all.-20-100gain (decibels)0.078 dB from the cancelled one — nothing to see here-10102468time, in slow time constantserror remaining, in units of the tail's own amplitudethe 0.10% bandsettled at 2.21 slow τdoublet mismatch1.00%tail amplitude0.9090%slow τ over fast τ100worst magnitude error0.0777 dBsettle to 0.10%245.2 fast τclosed form245.2 fast τcancelled exactly6.9 fast τthe cost35.6×solved, then checked — swept, then marcheda 1.0% miss costs 36× the settling time

Drawn above at its default parameters, which is almost never how an essay calls it. A placement states the numbers that essay is arguing about, so the figure a reader meets is about that argument rather than about the generator — 98% of the placements on this site pass one, and the phase that raised that number from 12% found eight captions describing a figure the page was not showing.

At those defaults the edge it states is a 1.0% miss costs 36× the settling time — the right-hand slot of the caption strip, which on this site is never used for anything else, and which is read back out of the drawing above rather than out of the code that wrote it. It belongs to Before the steady state, which is to say a change to it is a change to lib/figures/transients.js. It takes a slider on how far the zero misses the pole with 6 settings, and every one of them has passed the same assertions as the frame above — a figure whose circuit stops doing what its caption says at any setting stops the build.

Called by 1 essay

which is the blast radius of changing it

The cancellation that leaves a tail

A pole and a zero placed on top of each other disappear from the response. Miss by one per cent and the magnitude changes by 0.078 decibels, which no measurement would report as a fault, while the time to settle to a thousandth goes from 6.9 time constants to 245 — thirty-six times longer. The settling time has a closed form containing neither the fast circuit nor the doublet's separation as such, and its consequence is blunt: settling to a part in ten thousand needs a cancellation good to a part in ten thousand, however fast the amplifier in front of it is.

Before the steady state

Every generator