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15:40:34 Page 16
Dynamic Calibration
When the variables of interest are time (or space) dependent and such varying information is
sought, we need dynamic information. In a broad sense, dynamic variables are time (or space)
dependent in both their magnitude and frequency content. A dynamic calibration determines the
relationship between an input of known dynamic behavior and the measurement system output.
Usually, such calibrations involve applying either a sinusoidal signal or a step change as the
known input signal. The dynamic nature of signals and measurement systems is explored fully in
Chapter 3.
Static Sensitivity
The slope of a static calibration curve provides the static sensitivity
4 of the measurement system. As
depicted graphically in the calibration curve of Figure 1.9, the static sensitivity, K, at any particular
static input value, say x 1 , is evaluated by
K ¼ K x 1
ð Þ ¼
dy
dx
x¼x 1
ð1:1Þ
where K is a function of x. The static sensitivity is a measure relating the change in the indicated
output associated with a given change in a static input.
Range
A calibration applies known inputs ranging from the minimum to the maximum values for which the
measurement system is to be used. These limits define the operating range of the system. The input
operating range is defined as extending from x min to x max . The input operating range may be
expressed in terms of the difference of the limits as
r i ¼ x max À x min
ð1:2Þ
This is equivalent to specifying the output operating range from y min to y max . The output span or
full-scale operating range (FSO) is expressed as
r o ¼ y max À y min
ð1:3Þ
It is important to avoid extrapolation beyond the range of known calibration during measurement since the behavior of the measurement system is uncharted in these regions. As such, the range
of calibration should be carefully selected.
Resolution
The resolution represents the smallest increment in the measured value that can be discerned. In
terms of a measurement system, it is quantified by the smallest scale increment or least count (least
significant digit) of the output readout indicator.
4 Some texts refer to this as the static gain.
16 Chapter 1 Basic Concepts of Measurement Methods
15:40:34 Page 16
Dynamic Calibration
When the variables of interest are time (or space) dependent and such varying information is
sought, we need dynamic information. In a broad sense, dynamic variables are time (or space)
dependent in both their magnitude and frequency content. A dynamic calibration determines the
relationship between an input of known dynamic behavior and the measurement system output.
Usually, such calibrations involve applying either a sinusoidal signal or a step change as the
known input signal. The dynamic nature of signals and measurement systems is explored fully in
Chapter 3.
Static Sensitivity
The slope of a static calibration curve provides the static sensitivity
4 of the measurement system. As
depicted graphically in the calibration curve of Figure 1.9, the static sensitivity, K, at any particular
static input value, say x 1 , is evaluated by
K ¼ K x 1
ð Þ ¼
dy
dx
x¼x 1
ð1:1Þ
where K is a function of x. The static sensitivity is a measure relating the change in the indicated
output associated with a given change in a static input.
Range
A calibration applies known inputs ranging from the minimum to the maximum values for which the
measurement system is to be used. These limits define the operating range of the system. The input
operating range is defined as extending from x min to x max . The input operating range may be
expressed in terms of the difference of the limits as
r i ¼ x max À x min
ð1:2Þ
This is equivalent to specifying the output operating range from y min to y max . The output span or
full-scale operating range (FSO) is expressed as
r o ¼ y max À y min
ð1:3Þ
It is important to avoid extrapolation beyond the range of known calibration during measurement since the behavior of the measurement system is uncharted in these regions. As such, the range
of calibration should be carefully selected.
Resolution
The resolution represents the smallest increment in the measured value that can be discerned. In
terms of a measurement system, it is quantified by the smallest scale increment or least count (least
significant digit) of the output readout indicator.
4 Some texts refer to this as the static gain.
16 Chapter 1 Basic Concepts of Measurement Methods