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

3 quarter-wave sections between 50 Ω and 200 Ω

computed by solving, not by drawing. |Γ| computed by cascading exact line impedances from the load back to the source, so every multiple reflection is in it. The binomial design is exact at the centre and holds |Γ| below 0.10 over 67.9% of the centre frequency, against 17.1% for a single section. The equal-ripple design, found by minimax search rather than from a table, covers 98.1% at the same worst reflection — 45% more — and its ripples come out level to 0.0e+0%, which is the check that the search converged.
3 quarter-wave sections between 50 Ω and 200 Ωcomputed by solving, not by drawing. |Γ| computed by cascading exact line impedances from the load back to the source, so every multiple reflection is in it. The binomial design is exact at the centre and holds |Γ| below 0.10 over 67.9% of the centre frequency, against 17.1% for a single section. The equal-ripple design, found by minimax search rather than from a table, covers 98.1% at the same worst reflection — 45% more — and its ripples come out level to 0.0e+0%, which is the check that the search converged.00.1000.2000.50011.50frequency, in units of the centre|Γ|, the reflection|Γ| = 0.10, the specificationsections3transformation50Ω → 200Ωbare, unmatched0.6000|Γ| allowed0.100binomial band67.9%equal-ripple band98.1%…which buys45% moreone section gives17.1%heavy curvebinomialsecond curveequal-ripplefaint curvethe small-reflection sumsolved, then checked — |Γ| as a designed response68% of band, from 3 sections

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 68% of band, from 3 sections — 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 Lines, where a wire has a length, which is to say a change to it is a change to lib/figures/lines.js. It takes a slider on quarter-wave sections with 5 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 2 essays

which is the blast radius of changing it

Several sections, and the band they buy

A quarter-wave transformer is exact at one frequency, and a 4:1 transformation holds |Γ| under 0.1 over 17.1% of it. Several sections whose reflections cancel over a band take that to 47.7, 67.9, 82.1 and 92.6% — which is filter design with the reflection as the shaped quantity. An equal-ripple design found by minimax search buys a further 35 to 46% at the same worst reflection, and its ripples come out level to four decimals.

Lines, where a wire has a length

The number that was wrong

The rung below printed 97.3 per cent of band for a five-section transformer where the answer is 134, said in its own text that the figure was wrong, and blamed a search that had converged to eight digits. The search was fine. The objective was the worst of a grid rather than the worst of a band, the band was then measured by bisecting a function that crosses its threshold five times, and the assertion guarding all of it passed — because 97.3 is still more than 92.6.

Lines, where a wire has a length

Every generator