Page 351 - Mechatronics with Experiments

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JWST499-Cetinkunt
JWST499-c06
SENSORS 337 254mm×178mm
balanced bridge condition is maintained and no voltage is observed across points B and C.
Assume that the sensor resistance R changes as a function of the measured variable. Then,
1
we can adjust R in order to maintain the balanced bridge condition, V BC = 0,
2
R 1 = R 3 (6.26)
R R
2 4
Then, when the V = 0, the resistance of the sensor (R ) can be determined since R , R
BC 1 3 4
are fixed and known, and R can be read from the adjustable resistor,
2
R 3
R (x) = ⋅ R (adjusted) (6.27)
1 2
R
4
Notice that this method of determining the sensor resistance is not sensitive to the changes
in the supply voltage, V . But it is suitable only for measuring steady-state or slowly
i
varying resistance changes, hence slowly varying changes in the measured variable (i.e.,
temperature, strain, pressure). Once R (x) is known, from the transduction relationship of
1
the sensor, the measured variable x can be determined (i.e., from the input–output graph or
map of the transduction principle).
6.3.2 Deflection Method

In order to measure time varying and transient signals, the deflection method should be
used. In this case, three legs of the resistor bridge have fixed resistances, R , R , R .The R 1
2
4
3
is the resistance of the sensor. As the sensor resistance changes, non-zero output voltage
V BC is measured. For our first derivation, let us assume that the voltage measurement device
has infinite input resistance, R → ∞, so that no current flows through it despite a finite
m
voltage potential across points B and C, V BC ≠ 0, i = 0. For the following derivation, let
m
V =−V BC for output voltage polarity;
o
i R + V BC − i R = 0 (6.28)
1 1
3 3
V BC = i R − i R (6.29)
1 1
3 3
V =−i R + i R (6.30)
o 3 3 1 1
Since i = 0, i = i and i = i ,
m 1 2 3 4
i = V ∕(R + R ) (6.31)
i
2
1
1
i = V ∕(R + R ) (6.32)
i
3
3
4
Then,
( )
R 1 R 3
V = V i − (6.33)
o
R + R 2 R + R 4
3
1
In most Wheatstone bridge circuit applications with sensors, the bridge is balanced at a
reference condition, V = 0 and the initial values of the resistance arms are the same,
o
R = R = R = R = R .Let
1 2 3 4 o
R = R +ΔR (6.34)
o
1
where the ΔR is the variation from the calibrated nominal resistance. If we substitute these
relations, it can be shown that
ΔR∕R o
V ∕V = (6.35)
o i
4 + 2ΔR∕R
o