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

The ladder's step response, and the sum of its own stages — 0.95 per cent apart at worst

computed by solving, not by drawing. A step of power into a three-stage thermal ladder, and the junction's rise divided by it. The solid curve is exact: the impedance is a continued fraction in s, its denominator has 3 real negative roots, and the partial-fraction expansion of Z(s)/s is a sum of that many ordinary exponentials — no march, no step size. The dashed curve is the sum every account of a thermal path writes, each stage's own resistance times 1 − exp(−t/RC) with its own local time constant, and it is an approximation because the stages load each other. What that costs is 0.950 per cent, once, at 12.9 ms — between the fastest stage's 2.4 ms and the next one's 200 ms, which is the only place two stages are moving together. It is one-sided: the sum never reads low.
The ladder's step response, and the sum of its own stages — 0.95 per cent apart at worstcomputed by solving, not by drawing. A step of power into a three-stage thermal ladder, and the junction's rise divided by it. The solid curve is exact: the impedance is a continued fraction in s, its denominator has 3 real negative roots, and the partial-fraction expansion of Z(s)/s is a sum of that many ordinary exponentials — no march, no step size. The dashed curve is the sum every account of a thermal path writes, each stage's own resistance times 1 − exp(−t/RC) with its own local time constant, and it is an approximation because the stages load each other. What that costs is 0.950 per cent, once, at 12.9 ms — between the fastest stage's 2.4 ms and the next one's 200 ms, which is the only place two stages are moving together. It is one-sided: the sum never reads low.10m100m110100µ1m10m100m110100pulse length (seconds)thermal impedance (kelvin per watt)the total: 9.7 K/Wworst: 0.95% at 12.9 msstage time constants2.4 ms · 200 ms · 480 sfastest separation83.3×exact at that worst1.214 K/Wthe sum says1.226 K/Wone-sided by0.950%solved, then checked — a continued fraction, expandedthe sum is 0.95% high at 12.9 ms

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 the sum is 0.95% high at 12.9 ms — 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 Devices, and where they stop being linear, which is to say a change to it is a change to lib/figures/semi.js. It takes a slider on die heat capacity (mJ/K) 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 1 essay

which is the blast radius of changing it

Two ladders the terminals cannot tell apart

A thermal path drawn as a ladder and the same path drawn as a sum of exponentials are called different models of one object, and the difference between them has never been priced because pricing it needs an exact answer. Solved in closed form, the sum is 0.950 per cent high at worst and never low; the marched netlist is right to a part in 21,169; and the largest disagreement in the picture was 2.919 per cent that has nothing to do with heat at all, which reading the curve one sample differently removes.

Before the steady state

Every generator