Page 96 - Mechanical Engineers' Handbook (Volume 2)

4 The Wheatstone Bridge 85

For an equal-arm bridge, this becomes
RE FE
e ex ex (13)
o
4R 2 R 4 2F
For an equal-arm bridge, Eq. (11) becomes
FE
dR E ex
e ex (14)
o
4R 4
The difference between Eqs. (14) and Eq. (13) is that Eq. (14) describes a linear process
while Eq. (13) describes a nonlinear one. Semiconductor gages, because of their large gage
factor, require analysis using Eq. (13).
Semiconductor gages may be used in constant-voltage four-arm bridge circuits when
two or four gages are used in adjacent arms and strained so that their outputs are additive.
Analysis of the bridge equations for this situation will show that if gages in adjacent arms
are subjected to equal but opposite values of R, the output signal is doubled and the
nonlinearity in the bridge output is eliminated. Another approach to eliminating this nonlin-
earity is to design a circuit where the current through the strain gage remains constant.
Table 3 provides generalized bridge equations for one, two, and four equal-active-arm
bridges of various configurations. The dimensionless bridge output is presented in millivots
per volts for a constant-voltage power supply. Strain is presented in microstrain. No small-
strain assumption is built into these equations. For large strains with semiconductor gages,
F may not be a constant and this correction also has to be built into the equations. In this
table, the Poisson gage is one which measures the lateral compressive strain accompanying
an axial tension strain. As noted earlier, only for two adjacent active gages with equal and
opposite strains or for four active gages with pairs subjected to equal and opposite strains
is the bridge output a linear function of strain.

4.2 Lead Wire Effects
There has been a historical lack of agreement between manufacturers of strain gages as to
color codes and wiring designations. This is particularly true in bridge transducers. Figures
11 and 12 are suggested industry standards which have assisted in lessening this confusion.
Figure 11 covers the situation where all bridge elements are remote from the power supply,
while Fig. 12 covers the situation where only one bridge arm is remote from the power
supply. The bridge balance network and shunt calibration are discussed in Sections 5 and 6,
respectively. Table 4 presents guidelines for multiconductor strain gage cable.
The previous discussion has assumed that the only resistive elements in the circuits are
the gages themselves. Resistance of circuit lead wires also is a consideration.
One possible need for remote recording occurs when the bridge power supply and the
readout instrumentation are at one location and the bridge transducer is at a remote location.
In this situation, the resistance R of each lead wire between the bridge and the power supply
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or readout must be accounted for. Most readout instruments have very high input impedances,
so the effect of R in series with them can be ignored. The significant effect of lead-wire
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resistance is to modify the resistance in series with the power supply from R bridge to R bridge
2R . For example, a lead-wire resistance of 3 and a bridge resistance of 120 will
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produce loading effects which, if not corrected, will result in a 5% error in bridge transducer
output.
There are at least three simple techniques to eliminate this error source: