Two-Wire Circuit

For an initially balanced bridge, if one of the bridge arms is replaced with a strain gage of precisely the same resistance value and connected with two leadwires having negligible resistance, the bridge remains at balance. But in practice the leadwires will have some measurable resistance (R _L ) as shown in Fig. 2, which may result in a significant lack of symmetry in the bridge. This occurs because both leadwires are in series with the strain gage between, for example, the positive (+) input corner and the negative (-) output corner, adding to the gage arm resistance. That is, the gage arm resistance becomes R _G + 2R _L .

Fig. 516.2 - Two-wire quarter-bridge circuit.

As a measure of the magnitude of this effect, consider a 120-ohm strain gage installed at a distance of 20 ft (6 m) from the instrument, and connected to the instrument with a pair of AWG26 (0.4 mm dia.) copper leadwires. At room temperature, the total resistance in series with the strain gage is about 1.7 ohms. For an instrument gage factor setting of 2.0, this produces an initial imbalance in the bridge corresponding to approximately 7000 microstrain. Further, the leadwires are a parasitic resistance in the gage arm of the bridge and effectively reduce or desensitize the gage factor of the strain gage, resulting in a reduced signal output when the test part is subjected to test loads. For modest values of leadwire resistance, the percentage of loss in signal is approximately equal to the ratio of leadwire resistance to strain gage resistance. In the example given here, this results in about a 1.5% loss in sensitivity.

The initial imbalance may be offset using a strain indicator that has a sufficient balance range, or may be (mathematically) subtracted from measured strain readings. However, a more serious problem may result if the temperature of the leadwires changes during the measurement process, causing a corresponding change in resistance of the interconnecting leadwires. Copper leadwires change in resistance approximately 22% of their room-temperature resistance value for a 100 deg F (55 deg C) temperature change. For the 120-ohm gage circuit above, this would result in an error equivalent to approximately 156 microstrain for a 10 deg F (5.5 deg C) temperature change in the leadwire system.

The errors and problems specifically caused by the two-wire circuit are due to the pair of leadwires in series with the strain gage. All three of the effects discussed here increase in severity with increased leadwire resistance; and the two-wire circuit offers no intrinsic compensation. It is worth noting that use of a 350-ohm strain gage circuit will reduce each of these effects, but cannot eliminate completely the associated measurement errors. But a straightforward method exists to reduce the loss in sensitivity, and essentially eliminate the initial imbalance problem and the error that results from temperature changes in the leadwire system. This method involves simply adding a third leadwire to the strain gage circuit as shown in Fig. 516.3 on the next page.

Page 3 of 4