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The power, P 1 ¼ I
2
1 R 1 þ dR
ð
Þ , that must be dissipated from the sensor is 0.25 W, which,
depending on the surface area and local heat transfer conditions, may cause a change in the
temperature of the sensor.
COMMENT The current flow through the sensor results in a sensor temperature higher than
would occur with zero current flow due to I
2
R heating. This is a loading error that offsets the
indicated temperature, a systematic error. There is a trade-off between the increased sensitivity,
dE o /dR 1 , and the correspondingly increased current associated with E 1 . The input voltage must be
chosen appropriately for a given application.
6.5 LOADING ERRORS AND IMPEDANCE MATCHING
In an ideal sense, an instrument or measurement system should not in itself affect the variable
being measured. Any such effect will alter the variable and be considered as a ‘‘loading’’ that the
measurement system exerts on the measured variable. A loading error is the difference between
the value of the measurand and the indicated value brought on by the act of measurement.
Loading effects can be of any form: mechanical, electrical, or optical. When the insertion of a
sensor into a process somehow changes the physical variable being measured, that is a loading
error. A loading error can occur anywhere along the signal path of a measurement system. If
the output from one system stage is in any way affected by the subsequent stage, then the signal
is affected by interstage loading error. Good measurement system design minimizes all loading
errors.
To illustrate this idea, consider measuring the temperature of a volume of a high-temperature
liquid using a mercury-in-glass thermometer. Some finite quantity of energy must flow from the
liquid to the thermometer to achieve thermal equilibrium between the thermometer and the liquid
(i.e., the thermometer may cool down or heat up the liquid). As a result of this energy flow, the liquid
temperature is changed, and the measured value does not correspond to the initial liquid temperature
sought. This measurement has introduced a loading error.
Or consider the current flow that drives the galvanometer in the Wheatstone bridge of
Figure 6.13. Under deflection conditions, some energy must be removed from the circuit to deflect
the pointer. This reduces the current in the circuit, bringing about a loading error in the measured
resistance. On the other hand, under null balance conditions, there is no perceptible pointer
deflection, and so a negligible amount of current is removed from the circuit. There is then
negligible loading error.
In general, null balance techniques minimize the magnitude of loading error to negligible
levels. Deflection methods derive energy from the process being measured. Therefore, deflection
methods need careful consideration to make sure the resulting loading errors are kept to an
acceptable level.
Loading Errors for Voltage-Dividing Circuit
Consider the voltage-divider circuit shown in Figure 6.9 for the case where R m is finite. Under these
conditions, the circuit can be represented by the equivalent circuit shown in Figure 6.15. As the
sliding contact at point A moves, it divides the full-scale deflection resistance R into R 1 and R 2 , such
226 Chapter 6 Analog Electrical Devices and Measurements
11:55:5 Page 226
The power, P 1 ¼ I
2
1 R 1 þ dR
ð
Þ , that must be dissipated from the sensor is 0.25 W, which,
depending on the surface area and local heat transfer conditions, may cause a change in the
temperature of the sensor.
COMMENT The current flow through the sensor results in a sensor temperature higher than
would occur with zero current flow due to I
2
R heating. This is a loading error that offsets the
indicated temperature, a systematic error. There is a trade-off between the increased sensitivity,
dE o /dR 1 , and the correspondingly increased current associated with E 1 . The input voltage must be
chosen appropriately for a given application.
6.5 LOADING ERRORS AND IMPEDANCE MATCHING
In an ideal sense, an instrument or measurement system should not in itself affect the variable
being measured. Any such effect will alter the variable and be considered as a ‘‘loading’’ that the
measurement system exerts on the measured variable. A loading error is the difference between
the value of the measurand and the indicated value brought on by the act of measurement.
Loading effects can be of any form: mechanical, electrical, or optical. When the insertion of a
sensor into a process somehow changes the physical variable being measured, that is a loading
error. A loading error can occur anywhere along the signal path of a measurement system. If
the output from one system stage is in any way affected by the subsequent stage, then the signal
is affected by interstage loading error. Good measurement system design minimizes all loading
errors.
To illustrate this idea, consider measuring the temperature of a volume of a high-temperature
liquid using a mercury-in-glass thermometer. Some finite quantity of energy must flow from the
liquid to the thermometer to achieve thermal equilibrium between the thermometer and the liquid
(i.e., the thermometer may cool down or heat up the liquid). As a result of this energy flow, the liquid
temperature is changed, and the measured value does not correspond to the initial liquid temperature
sought. This measurement has introduced a loading error.
Or consider the current flow that drives the galvanometer in the Wheatstone bridge of
Figure 6.13. Under deflection conditions, some energy must be removed from the circuit to deflect
the pointer. This reduces the current in the circuit, bringing about a loading error in the measured
resistance. On the other hand, under null balance conditions, there is no perceptible pointer
deflection, and so a negligible amount of current is removed from the circuit. There is then
negligible loading error.
In general, null balance techniques minimize the magnitude of loading error to negligible
levels. Deflection methods derive energy from the process being measured. Therefore, deflection
methods need careful consideration to make sure the resulting loading errors are kept to an
acceptable level.
Loading Errors for Voltage-Dividing Circuit
Consider the voltage-divider circuit shown in Figure 6.9 for the case where R m is finite. Under these
conditions, the circuit can be represented by the equivalent circuit shown in Figure 6.15. As the
sliding contact at point A moves, it divides the full-scale deflection resistance R into R 1 and R 2 , such
226 Chapter 6 Analog Electrical Devices and Measurements