Sensor Signal Chain Calibration

From the sensing element to the digital value there are several stages, and each of them adds an error. Calibrating the signal chain means measuring the error of the whole path and correcting it, rather than assuming that the sum of the component tolerances is acceptable.

What the Chain Contains

The chain starts at the sensor, passes through protection, amplification, filtering and the converter, and ends in a number in firmware. Each stage contributes an offset and a gain error, and the sensor contributes its own sensitivity and its non linearity.

Errors from the electronics scale with the gain of the stages that follow them, so an error at the input is amplified by the whole chain while one at the converter is not. That is the reason the first stage deserves the most attention.

The sensor error is often the largest. A sensor with a two percent sensitivity tolerance sets a limit that no amount of electronic calibration can remove, unless the sensor itself is calibrated as part of the unit.

gain and offset in the Chain

gain and offset are the two parameters that a linear calibration corrects. They can be measured at the input or at the output, and measuring at the input with a physical standard is what makes the result meaningful.

A correction applied in firmware has to be applied in the right order. The offset is removed first and the gain applied to the result, which corresponds to the physical model of the chain rather than to a convenient algebraic rearrangement.

Where the chain has a non linear element, such as a thermocouple or a bridge sensor, the linear correction leaves a residual. A curve fit or a lookup table removes it, at the cost of more calibration points and more firmware.

The reference standard

A reference standard is the instrument used during calibration, and its own accuracy has to exceed the target by a comfortable margin. A ratio of three to one is the usual minimum and ten to one is better.

The standard has to be traceable, which means that its own calibration can be traced through a documented chain to a national standard. Without traceability, the calibration is a comparison between two instruments of unknown accuracy.

A working standard used daily should be checked against a higher level reference at intervals, so that a drift in the working standard is detected before it corrupts a batch of products.

Building the Calibration Procedure

The procedure defines the points, the conditions, the order of the measurements and the acceptance criteria. Writing it before the first calibration saves a great deal of confusion later.

The points should span the range of the instrument, and they should avoid the exact ends where the sensor or the amplifier may be at its limit. A point at ten percent and one at ninety percent of the range is a common and effective choice.

The conditions include the temperature, the warm up time and the settling time after each change of input. A measurement taken before the chain has settled is a measurement of the filter rather than of the sensor.

traceability and Record Keeping

traceability in a production sense means that a finished unit can be linked to the standard it was calibrated against, the date and the operator. That record is what turns a number into a measurement.

The simplest implementation stores a certificate number and a date with the serial number of the unit. Where the product has a memory, the coefficients themselves are stored, and the record notes the version of the procedure that produced them.

A record also makes drift visible. Comparing the coefficients of units produced over a year shows whether the process is stable, and a change in the average indicates a change in the components or in the procedure rather than in the units.

Drift and Periodic Verification

Every chain drifts, and the question is how fast. The sensor, the amplifier offset, the reference and the mechanical mounting all change with time and temperature, and the sum sets the interval between calibrations.

A periodic verification against a reference standard, without adjusting anything, is a useful intermediate step. It measures the drift and leaves the decision to recalibrate until the drift exceeds a threshold.

For a permanently installed channel the verification can be automatic, using a built in reference such as a precision resistor or an internal source. That checks the electronics and confirms the sensor by inference rather than by measurement.

When the Chain Cannot Be Calibrated

Some sensors cannot be removed for calibration, and some installations cannot be disturbed. In those cases the calibration is transferred from a sister channel or from a model of the sensor behaviour.

A redundant channel measuring the same quantity is the most reliable approach. The two are compared continuously and a divergence indicates a fault in one of them, which is a form of continuous verification rather than calibration.

A model based compensation uses the sensor datasheet and a temperature measurement to correct the reading. It removes the bulk of the error and it cannot correct an individual unit, which is the trade it makes.

Verification and Common Faults

Verify the chain with an independent measurement at a point that was not used in the calibration. The instrument used for the verification should be different from the one used for the calibration, or the check confirms only that the procedure is repeatable.

An error that is proportional to the reading indicates a gain problem, while a constant error indicates an offset. An error that changes sign across the range indicates a non linearity and needs a curve rather than two numbers.

A chain that passes verification on the bench and fails in the installation usually has a grounding or a cable problem rather than a calibration problem. The measures that keep such a channel clean are described in our guide to mixed signal board design, the release checks in our PCB design release checklist, and the assembly points in judging PCB quality.

Process Control and Verification

On a design of this kind, reference standard is the item that decides how the rest of the board is arranged. Where the requirement is not written down, the shop supplies its own default, and the default is chosen for the process rather than for the design. The measurements that matter are the repeatable ones: conductor width and spacing, annular ring, finished hole size, plating thickness and surface finish are all verifiable on a coupon that travels with the panel.

Process Control and Verification

On a design of this kind, reference standard is the item that decides how the rest of the board is arranged. Where the requirement is not written down, the shop supplies its own default, and the default is chosen for the process rather than for the design. The measurements that matter are the repeatable ones: conductor width and spacing, annular ring, finished hole size, plating thickness and surface finish are all verifiable on a coupon that travels with the panel.

FAQ

Should I calibrate the electronics or the whole unit? The whole unit where the sensor can be included. Calibrating the electronics alone leaves the sensor tolerance untouched.

How often should a channel be recalibrated? From the measured drift, not from a fixed rule. Verify periodically and recalibrate when the drift exceeds a set fraction of the tolerance.

What is traceability for? It links the unit to a standard through a documented chain, which is what makes the calibration meaningful to a customer or an auditor.