Extreme metrology: computed tests

Computed. The two noise floors that set almost every extreme measurement, at representative impedances and bandwidths.

1. Johnson noise

R, bandwidth	Noise (nV)
1e+03ohm_1e+03Hz	128.716
1e+06ohm_1e+03Hz	4070.355
1e+06ohm_1e+06Hz	128715.92
1e+09ohm_1e+03Hz	128715.92

At 1 MΩ and 1 MHz the floor is ≈0.13 mV. Practical: any voltage measurement below that is a measurement of the resistor, not the sample.

2. Shot noise

Current, bandwidth	Noise (pA)
1e-12A_1e+00Hz	0.0006
1e-09A_1e+00Hz	0.0179
1e-09A_1e+03Hz	0.5661
1e-06A_1e+03Hz	17.9007

At 1 nA and 1 Hz the floor is ≈0.018 pA; widening to 1 kHz raises it 31.6×. Practical: bandwidth is the single cheapest lever on a shot-noise floor.

3. The design rule

Compute both floors before choosing the instrument. In every extreme regime one of them dominates, and the regime's name tells you which: high impedance is Johnson-limited, low current is shot-limited.

Incoprea Research · 3 November 2026. Composition and computation. No experiment performed.