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

The floor, which bounds from below

Every other boundary here is an upper one. This is the other end, and gain does not help because gain amplifies it too. The only figures on this site whose content is a sample — so every number is run across seeds and quoted with its spread — and the one place a bandwidth is not the −3 dB point but π/2 times it.
±619.3 nV, the root mean square1200 of 192001 stepssampled, this seed621.2 nVsampled, 6 seeds619.3 nV ± 1.79%integrated from |H|²620.6 nV…ignoring the hold626.3 nVnoise bandwidth15.03 kHzthe −3 dB point10.00 kHzsolved, then checked — a sample against an integralagreeing to 0.21%

The floor a resistor sets

A kilohm at room temperature produces 4.00 nanovolts per root hertz, and it does so because it is warm rather than because of anything about how it was made. That is the first boundary in this collection that bounds a model from below — gain does not help, because gain amplifies it too — and it is the only field here whose figures are samples.

 00.500101234frequency ÷ the −3 dB point|H|², the power that gets throughhalf the power: the −3 dB pointthe brick wall: 1.5706× the corner1.571×solved, then checked — the area integrated, not tabulated1.571× the corner, not 1×

The bandwidth noise sees

A single pole passes π/2 times as much noise power as a brick wall at its own corner frequency, so a noise voltage computed with the −3 dB point is twenty-one per cent low. Measured by integrating the solved response rather than taken from the table it usually comes from, the ratio is 1.5706 and π/2 is 1.5708. A five-pole Chebyshev's is 0.964 — less than one.

 1e-81e-71e-61e-51e-41m10m100m1amplitude (volts)Johnson noise of 1 kΩ: 501.6 nV1% distortion, exponential: 1.03 mV1% gain error, exponential: 7.30 mVlinear step, unity follower: 79.58 mV66.3 dB of rangesolved, then checked — a floor and a ceiling, both computed66 dB between them

A floor and a ceiling

Every other boundary on this site is a ceiling. This one puts a floor underneath and measures the distance between them — 4.00 nanovolts per root hertz at the bottom, one per cent of harmonic distortion at 1.03 millivolts at the top, and 66.3 decibels of range in a ten-kilohertz measurement. Both ends are computed, neither is on a datasheet, and the arrangement of the stages decides which one moves.

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