Page 347 - Mechatronics with Experiments

October 9, 2014 8:1
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JWST499-Cetinkunt
JWST499-c06
SENSORS 333 254mm×178mm
V

R R
R
B
FIGURE 6.6: Resistive type
D 741 sensor signal amplification using
R F an op-amp. The sensor
V V transduction principle is based on
E G the physical relationship that the
resistance of the sensor varies as a
C
function of the measured variable.

and R determine the gain of the amplifier. It can be easily shown that the output voltage
3
from the circuit as a function of the sensor resistance is,
R 3 R (y)
1
V out =− ⋅ ⋅ V c (6.1)
R 2 R (x) + R 1
s
where x represents the measured variable, R (x) is the resistance of the sensor which varies
s
as a function of the measured variable, R (y) represents the potentiometer adjustment of
1
the R as it is connected to the op-amp input to provide the reference voltage. R (y)isthe
1 1
resistance amount from the point it is connected to the R to the ground connection at point
2
C. We can use R (y) to adjust the offset voltage. The sensor gain can further be adjusted by
1
making R or R adjustable resistors (potentiometers).
3
2
6.2 MEASUREMENT DEVICE LOADING ERRORS
Loading errors in measurement systems are errors introduced to the measurement of the
variable due to the sensor and its associated signal processing circuit. There are two types
of loading errors:

1. mechanical loading error,
2. electrical loading error.
An example of mechanical loading error is as follows. Consider that we want to measure
the temperature of a liquid in a container. If we insert a mercury-in-glass thermometer
in the container, there will be a finite amount of heat transfer between the liquid and the
thermometer. The measurement will stabilize when both temperatures of the liquid and
thermometer are the same. Therefore, the fact that the thermometer is inserted into the
liquid and there is a heat transfer between them has changed the original temperature of
the liquid. Clearly, this mechanical loading error would be very large if the volume of the
liquid were small compared to the size of the thermometer, and would be negligable if the
liquid volume were very large compared to that of the thermometer. Strictly speaking, it
is not possible to perfectly measure a physical quantity since the very act of introducing a
sensor changes the original physical environment. Therefore, every measurement system
has some mechanical loading error. The design question is how to make that error as small
as possible.
The electrical loading error issue exists in electrical circuits used in measurement
systems. Consider the voltage measurement across the resistor in the following figure