Biomedical Engineering Reference
In-Depth Information
FIGURE 2-17
Dynamic
unbalanced bridge
circuit.
Substituting into equation (2.14) and simplifying gives
R
s
R
3
=
R
1
R
2
(2.17)
If
R
1
and
R
2
are known and
R
3
can be determined accurately from the angular dis-
placement of the potentiometer, then
R
s
can be determined
R
1
R
3
R
2
R
s
=
(2.18)
Note that this result is independent of the excitation voltage.
In the dynamic deflection mode shown in Figure 2-17, the bridge is first balanced
under no-load conditions, and then the measured output voltage can be used to determine
the strain gauge resistance as a load is applied.
The output voltage can be written in terms of the volt drop from the
+
ve terminal and
also in terms of the volt drop from the negative terminal
V
o
=
i
1
R
s
−
i
2
R
1
=
i
2
R
2
−
i
1
R
3
(2.19)
and the applied excitation voltage can also be written in terms of the current and resistance
in each arm
V
=
i
1
(
R
s
+
R
3
)
=
i
2
(
R
1
+
R
2
)
(2.20)
Solving for
i
1
and
i
2
in terms of
V
and substituting into equation (2.19) gives
V
o
=
V
R
s
R
1
R
1
+
R
2
R
s
+
R
3
−
(2.21)
If the bridge is balanced under no-load conditions so that
V
o
=
0 in this case, then
V
o
will be related to the new resistance
as the strain gauge is loaded the voltage change
R
s
+
R
s
according to
V
o
V
R
s
+
R
s
R
s
+
R
s
+
R
3
−
R
1
R
1
+
R
2
=
(2.22)
This equation can be rearranged to give the relationship between the relative change
in resistance and the measured output voltage.
