The window a 10 µF capacitor leaves
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 stability wants it large, the step wants it small — 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 Circuits that do a job, and the range they do it over, which is to say a change to it is a
change to lib/figures/applied.js.
It takes a slider on output capacitance (microfarads) 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 6 essays
which is the blast radius of changing it
A source below a frequency
A five-volt regulator's output impedance is 0.43 milliohms, which is the number a datasheet quotes. It has doubled by 4.8 hertz, is ten times worse by 27, and reaches 1.95 ohms at ten kilohertz — four and a half thousand times its own specification, and higher there than the same circuit with its feedback loop cut. Two routes to that curve, sharing only the netlist, agree to a part in ten to the thirteenth.
Two requirements pulling one capacitor
The output capacitor's series resistance is a stability requirement and a transient requirement at once, and they pull it in opposite directions. Below 939 milliohms this loop has less than 45 degrees of margin; above about 850 the droop after a load step starts to grow, because at the first instant of a step the capacitor cannot move and the whole step falls across that resistance. The droop is smallest 10 per cent inside the unstable region, which means the best transient this design can have is one it must not be built with.
The floor a second capacitor removes
Two requirements pulling one capacitor found a regulator whose best transient is one it must not be built with: below 939 milliohms of output-capacitor series resistance the loop has under 45 degrees of margin, and the droop is smallest at 885. The capacitor across the upper divider resistor, added for the reference's sake, dissolves that conflict. At 836.5 picofarads the 45-degree floor leaves the sweep entirely — every series resistance down to a milliohm is stable — and the droop falls 40 per cent at the same time. The band of capacitances that do it runs from 100 picofarads to 5 nanofarads, and above it the conflict returns.
The capacitance the bias takes away
A ceramic output capacitor has a few milliohms of series resistance, which a capacitor across the upper divider resistor made legal, and a capacitance that falls with the voltage across it — a ten-microfarad part at five volts is two microfarads to a small signal. Swept from the full ten down to that fifth, the regulator's margin does not collapse. It rises: with no divider capacitor from 18.0° to 38.5°, because the output pole climbs away from the amplifier's. The corner that binds is the capacitor at full value. One divider capacitor, 423 to 808 pF, holds 45° at every capacitance between. The 836.5 pF that removed the resistance floor sits just above that band, and the lost capacitance is paid for in droop: 103 mV at full value, 202 mV at a fifth.
The lead a divider can give
At an ampere one capacitor across the upper divider resistor holds this ceramic regulator above 45° at every capacitance the part keeps. At 5 mA nothing does. The crossover stays at 13 kHz while the output pole falls from 3.20 kHz to 31.8 Hz, so the loop arrives at unity with every lag it has and the only phase left is the lead the divider capacitor makes — and that lead has a ceiling, arcsin((G − 1)/(G + 1)), set by the divider's ratio alone. For a five-volt output from a 1.25 V reference it is 36.87°, and the best capacitor reaches 36.83°. Over the rectangle from 5 mA to an ampere and ten microfarads to two, the best single capacitor gives 32.4°. Putting 416 mΩ back in series with the ceramic restores 45° over all of it, and lowers the droop rather than raising it.
The load that rises slower than the loop
Every droop a regulator is sized against is a load step with an infinitely fast edge, and a ceramic regulator droops 103 millivolts on its full 10 µF and 203 on a fifth of it. Give the same 100 mA a rise time and the ordering does not survive: past 23 microseconds the full capacitor droops more than the fifth, and a slow ramp's droop is the loop's own 25.2 µH times the load's rate of change — a number with no capacitance in it, raised 18 per cent on the full capacitor by the impedance peak its slower loop leaves. For a 10 mV budget the load must take 298 µs to arrive on the full capacitor and 253 on the fifth.