Strain Gauge Bridge Completion Circuit Design

Measuring strain with a single gauge means completing the bridge with fixed resistors on the board, and that simple statement hides most of the practical difficulty. The completion arms must match the gauge in resistance and in temperature behaviour, and the wiring to the gauge has to be arranged so that its resistance does not appear in the reading.

Bridge Configurations and Their Output

A quarter bridge uses one active gauge and three fixed arms. It produces the largest output for a given strain in terms of signal per gauge, but it also has the poorest rejection of temperature and of the lead resistance in the active arm.

A half bridge uses two active gauges, which doubles the output and cancels the effect of uniform temperature change when the two are on the same material. A full bridge uses four and gives the greatest output and the best rejection, at the cost of bonding four gauges to the specimen.

The choice follows from the measurement. A load cell uses a full bridge because it is built once and used for years, while a stress survey on an existing structure often uses a single gauge because there is only one place to bond it.

Choosing the Completion Resistors

The three fixed arms must equal the gauge resistance at the same temperature, so a hundred and twenty ohm gauge needs hundred and twenty ohm completion resistors with a matching temperature coefficient. A mismatch of a few parts per million per degree produces an output that looks exactly like strain.

Use resistors with a low temperature coefficient and mount them close together so that they share a temperature. If they are spread across the board, a gradient across the board appears as an offset that changes with the airflow, and the drift is difficult to explain without knowing where to look.

A resistor network in a single package is the best answer, because all the elements are on one substrate and track each other. The absolute tolerance matters less than the matching, and a network with a ratio tolerance of a few parts per million is available at modest cost.

The Effect of lead resistance

The resistance of the wire from the board to the gauge adds to the active arm. Two metres of thin copper wire is a fraction of an ohm, which against a hundred and twenty ohm arm is about half a percent, and that is a permanent gain error rather than a drift.

lead resistance also changes with temperature, and since the copper wire is exposed to a different environment from the gauge, its contribution drifts. The three wire connection solves this for the active arm by placing the lead resistance in two arms at once, where it cancels.

The three wire arrangement requires equal lead resistance in the two wires, which is satisfied by a cable with identical conductors. Where the installation uses two wires because the cable is already in place, the lead resistance is measured and corrected in software, which is acceptable when the temperature is stable.

Excitation and Self Heating

The excitation voltage sets the output and the power dissipated in the gauge. A hundred and twenty ohm gauge with five volts across the bridge dissipates about fifty milliwatts, which for a small foil bonded to a plastic specimen is enough to raise its temperature measurably.

Self heating produces an apparent strain that grows over minutes and then settles, and it also changes the gauge factor slightly. A lower excitation reduces it, and a pulsed excitation that is on only during the measurement reduces it further at the cost of a more complex circuit.

The excitation source has to be stable, because the output is proportional to it. Where a long cable is used, the wire resistance drops part of the excitation voltage before it reaches the bridge, and a four wire connection to the excitation terminals removes that error as well.

Temperature Compensation

A strain gauge responds to temperature as well as to strain, through the change in its own resistance and through the difference in expansion between the gauge and the specimen. Self temperature compensated gauges match the expansion of a particular material, and their part number includes that material.

The residual error is corrected with a dummy gauge on an unstressed piece of the same material, wired into the bridge as the second active arm. That is the classic half bridge arrangement and it works because both gauges see the same temperature but only one sees the strain.

A thermocouple can also form at the junction between the gauge leads and the terminal, producing a voltage that appears in series with the bridge output. Keeping the two junctions at the same temperature cancels it, which is another reason to keep the connections close together.

Layout and Wiring Practice

Keep the completion resistors, the amplifier and the connector in one small area. The bridge output is a differential signal of microvolts to millivolts at a common mode of half the excitation, so the two input traces should be equal in length and routed together.

Bring the excitation out on its own pair and keep the return separate from the signal return. The bridge current is milliamps while the signal is microvolts, and sharing a return trace puts the current in series with the measurement. The layout thinking behind this split is the same as in any mixed signal board and is covered in our guide to mixed signal board design.

Cable Screening and Noise

The cable to the gauge is part of the measurement circuit and needs screening whenever the specimen sits in an electrically noisy place. Connect the screen to the instrument ground at one end only, because a screen earthed at both ends carries the ground current of the building and couples it straight into the bridge.

A twisted pair for the excitation and a separate twisted pair for the signal keep the loop areas small. Where the gauge is bonded to a large metal structure, that structure is usually earthed already, and the instrument should be earthed at the same point so that the difference between the two does not appear as a common mode voltage.

Calibration and Verification

Verify the bridge with a shunt calibration. A precision resistor placed across one arm produces a known unbalance, and the reading it produces is compared with the value calculated from the bridge equations. The error is a gain error and can be corrected.

Check the zero with the specimen unloaded and at two temperatures. A zero that changes with temperature in a way that follows the completion resistors points to a mismatch, while one that follows the gauge points to the gauge installation.

Record the bridge resistance and the excitation current at commissioning. A later change in either indicates a damaged gauge or a corroded connection, and catching it before a test series is cheaper than discovering it afterwards. The release and inspection practices that keep these boards consistent are collected in our PCB design release checklist and judging PCB quality.

FAQ

Can I use ordinary resistors to complete a strain gauge bridge? Only for a rough measurement. The arms must match the gauge in temperature coefficient, so a resistor network is the practical choice.

Why does my quarter bridge reading change when the cable moves? The lead resistance is part of the active arm. Use a three wire connection so the lead resistance cancels, or measure and correct it.

How much excitation voltage can a strain gauge take? Follow the datasheet recommendation. A small foil gauge on a plastic specimen may only tolerate a volt or two before self heating becomes visible.