4. Sensor characterization

Before a preimpact sensor can be zeroed and its dynamic range validated, we must know how it actually behaves across its input range. Zeroing only fixes the output at one operating point; characterization describes the whole curve. This section covers the five static metrics that define a sensor's usable measurement envelope: the static transfer function, sensitivity, nonlinearity, hysteresis, and cross-axis sensitivity. These are the numbers that determine whether a crash sensor can resolve a 5 g pedestrian impact while surviving a 200 g barrier event, and whether a side-impact accelerometer will mistake vertical road input for lateral intrusion.

Static Transfer Function

The static transfer function maps a steady physical input to the sensor's electrical output. For an accelerometer it is typically expressed as output voltage versus applied acceleration, measured quasi-statically (input held constant long enough for the output to settle). The ideal form is linear:

V_out = V_offset + S · a
where  V_out   = sensor output voltage [V]
       V_offset = zero-g offset [V]
       S       = sensitivity [V/g or mV/g]
       a       = applied acceleration [g]

In practice the transfer function is fitted over a defined input span, for example −2 g to +2 g for a low-g crash sensor, using a least-squares straight line. That fitted line becomes the reference against which every other static metric is judged. The fit span matters: a sensor characterized only over ±1 g may look excellent, then deviate badly at 50 g where the actual deployment decision is made. Always record the characterization span alongside the coefficients.

Sensitivity

Sensitivity is the slope of the fitted transfer function, S = ΔV_out / Δa, usually quoted in mV/g. It is measured by applying at least two known accelerations (for example, using a tilt fixture: 0°, +90°, −90° gives 0 g, +1 g, −1 g) and dividing the output change by the input change. A typical automotive MEMS accelerometer might specify 40 mV/g ±5%. Sensitivity error directly scales into every downstream threshold: if the true sensitivity is 38 mV/g but the ECU assumes 40 mV/g, a commanded 50 g arming threshold is actually reached at 52.6 g, delaying deployment. Sensitivity should be verified at more than two points so that slope variation across the range is visible, not hidden by endpoint-only math.

Nonlinearity

Nonlinearity quantifies how far the measured curve departs from the best-fit straight line, expressed as a percentage of full-scale output (FSO):

NL = (max |V_measured(a) − V_fit(a)| / V_FSO) × 100%

Terminal-based nonlinearity uses the endpoints to define the line; best-fit (least-squares) nonlinearity usually yields a smaller, more honest number. For a sensor with 40 mV/g sensitivity over ±100 g, FSO = 8 V; a worst-case deviation of 80 mV corresponds to 1% FSO. During characterization, sweep the input in discrete steps (e.g., 0, 10, 20, … 100 g and back), record settled output at each step, and compute the residual against the fit. A sensor with 3% nonlinearity near full scale may still be acceptable for a go/no-go threshold but unacceptable for impact-severity estimation, where the ECU integrates acceleration.

Hysteresis

Hysteresis is the difference between the up-scale and down-scale output at the same input, caused by mechanical or magnetic memory in the sensing element. It is measured by sweeping the full range upward, then downward, and comparing outputs at each common input point:

H = (max |V_up(a) − V_down(a)| / V_FSO) × 100%

Hysteresis is distinct from nonlinearity: a perfectly linear sensor can still show hysteresis if the return path is offset. It matters most for sensors that see slow, reversing inputs — seat-occupant weight sensors, pedal position, suspension height — and less for one-shot crash events, but it is still specified because it bounds repeatability. Allow adequate dwell time at each step; reading before the output settles inflates the apparent hysteresis and produces a false failure.

Cross-Axis Sensitivity

An accelerometer intended to measure X-axis acceleration also responds, weakly, to Y and Z input. Cross-axis sensitivity is the ratio of off-axis response to on-axis response at the same acceleration magnitude, usually in percent:

CAS_y = (V_out,y-axis input / V_out,x-axis input) × 100%

For a 2% cross-axis part, a 100 g lateral shock produces an apparent 2 g on the X channel. In a frontal crash sensor this is tolerable; in a side-impact sensor distinguishing a door intrusion from a pothole, it can be decisive. Measure it by rotating the sensor on a shaker or tilt table so each axis in turn faces the input, applying the same acceleration, and comparing outputs. Misalignment of the sensor package on its mounting bracket adds to intrinsic cross-axis error, so characterize the installed orientation, not just the bare component.

Putting the Metrics to Work: A Characterization Procedure

The following procedure characterizes one accelerometer channel on a tilt fixture and a low-g shaker, using a 40 mV/g, ±100 g part as the running example. All values below are illustrative teaching parameters, not measured results.

1. Mount and settle. Fix the sensor to the tilt table with its X axis vertical. Power it from a clean 5.0 V supply and allow 10 minutes warm-up; offset drifts during warm-up and will corrupt every later reading.
2. Capture the zero point. At 0 g (X axis horizontal), record V_out. Repeat 10 times over 60 s; the spread is your repeatability floor and sets the smallest hysteresis you can resolve.
3. Sweep up-scale. Tilt to +1 g, +2 g, … using the sine of the tilt angle (a 30° tilt gives 0.5 g). At each step wait 2 s, average 100 samples, and log V_out. Continue to the characterization limit.
4. Sweep down-scale. Reverse the sequence back to 0 g, logging identically. Compute hysteresis at each common point.
5. Fit and compute. Least-squares fit V_out vs. a over the full span. Report S (slope), V_offset (intercept), NL (max residual / FSO), and H (max up/down difference / FSO).
6. Rotate for cross-axis. Re-mount so Y then Z faces vertical; apply the same ±1 g steps and record the X-channel response. CAS = off-axis response / on-axis response.

A worked example of the arithmetic: suppose the up-scale sweep gives 2.000 V at 0 g and 2.400 V at +10 g, so S = 0.400 V / 10 g = 40 mV/g. If the down-scale reading at +10 g is 2.392 V, hysteresis is 8 mV, or 8 mV / 8 V FSO = 0.1%. If the worst residual against the fit line is 60 mV, nonlinearity is 60 mV / 8 V = 0.75% FSO. If a 10 g Y-axis input produces 8 mV on the X channel while a 10 g X input produces 400 mV, cross-axis sensitivity is 8/400 = 2%.

Interpreting the Results

The five metrics are not independent pass/fail gates; they combine into an error budget. Sensitivity error scales all thresholds, nonlinearity and hysteresis bound the uncertainty at any single operating point, and cross-axis sensitivity sets the false-trigger floor from off-axis events. A sensor with 5% sensitivity error, 2% nonlinearity, and 3% cross-axis sensitivity has a worst-case measurement uncertainty near 10% of reading — which is why preimpact systems that must resolve small pedestrian impacts typically demand tighter parts than those that only need a coarse crash flag. Record the characterization span, temperature, and fit method with every dataset; without them the numbers cannot be compared across builds or used to justify a zeroing tolerance in the next stage.