Separate resolution, sensitivity, and usable range

For a locally linear sensor, sensitivity is the derivative of indication with respect to input. If the input is temperature and output is voltage, sensitivity has units of volts per kelvin. An output increment divided by the magnitude of sensitivity gives a corresponding local input increment. This conversion is only local when the response is nonlinear. Near a point where the derivative vanishes, a small output step can correspond to a substantial or poorly determined input change.

Increasing electronic gain increases output sensitivity but does not automatically improve input-referred uncertainty. Noise generated before amplification is amplified along with the signal, while the larger output can reach saturation sooner. Gain may nevertheless help when downstream quantization or downstream noise dominates. Diagnose which part of the chain sets the limit instead of maximizing gain indiscriminately. Calibration of the complete chain is important because a sensor, amplifier, filter, and digitizer each influence the final relation.

A digital display rounds or quantizes a continuous indication into discrete codes. Under an ideal nearest-rounding model with step size Δ, the difference between the unrounded indication and displayed value lies within half a step. If available information justifies a uniform distribution within that interval, its standard uncertainty is Δ divided by the square root of twelve. This is an information model, not evidence that the physical input is jumping randomly between codes on every reading.

Repeated identical displayed values therefore do not prove zero uncertainty, nor can the rounding contribution automatically be divided by the square root of the number of readings. Such a reduction needs evidence that quantization errors vary appropriately across observations, often because of independent noise or deliberate dithering. Conversely, an observed spread may already include quantization effects. Adding a separate rounding term without examining the model can double count uncertainty. State whether the budget treats raw analog indication, displayed values, or their average.

A dynamic-range ratio needs a declared upper usable value and a declared lower useful value. The upper limit might be clipping, nonlinearity, damage avoidance, or a specified distortion threshold. The lower limit might be a noise-defined detection criterion, a resolution threshold, or a required relative uncertainty. These are not interchangeable conventions. A manufacturer's largest displayed value divided by its last digit is a code-span ratio; it may overstate the range over which meaningful physical measurements are possible.

Saturation loses information: several different inputs can produce the same maximum indication. No arithmetic correction can uniquely recover those inputs from the clipped code alone. Likewise, an instrument's bandwidth affects whether a brief event reaches the display before it is averaged away. Choose sensitivity, range, and response time together for the measurand. After changing gain or filtering, verify that the calibration and uncertainty description still apply to the new configuration and relevant input frequencies.