Transcript Instrument Characteristics

Instrument Characteristics
Scientific Instrument:

A device for making a measurement.
Measurement:

An action intended to assign a number as the
value of a physical quantity in stated units.
The function of a scientific instrument,
therefore, is primarily to convert the
quantitative aspect of some natural
phenomenon into a series of recognizable
coincidences in time and space.
No instrument will perfectly indicate the
“true” quantitative aspect of the phenomenon.
Therefore, no statement of the result of a
measurement is complete unless it includes an
estimate (necessarily in statistical terms) of the
probable magnitude of the uncertainty. The
uncertainty is the interval within which the
true value of a quantity can be expected to lie
with a stated probability.
Characteristics of Instruments
Static Performance Characteristics:

A measure of how well a sensors observed output
reflects the input at one particular time. (After the
sensor has ceased changing in response to the
input.)
Dynamic Performance Characteristics:

A measure of how well a sensor responds to
changing input over time.
Static Characteristic Determinations
All input variables other than the primary one
should be minimized and quantified as much as
possible so the user may know what change in
the sensor response was due to the primary
input.
Typically, the instrument is placed in a
controlled environment chamber, allowed to
come to steady state and the “read.” This is
done over a range of input values..
The better the secondary inputs are
understood, the better the response of the
instrument to the primary input and the
instruments measurement ability can be
understood.
Input-Outpud Diagram
Static Performance Characteristics
True Value


An ideal value which could be known only if all
the causes of error were eliminated (never
knowable).
The value which is assumed to characterize a
quantity in the conditions which exit at the
moment the quantity is observed.
Correction
The value added to the result of a
measurement to allow for any known errors.
Accuracy
Degree to which the response of a sensor
conforms to the true environment. The
closeness to the truth.
Expression of how close are the limits
between which the “true value” exists.
The accuracy of a sensor depends upon the
degree and speed of reaction between the
sensor and its environment.
Sensor Accuracy
Instrument or System Accuracy
Accuracy
Sensor Accuracy

How well the sensor itself responds and
conforms to the true environment.
Instrument or System Accuracy

How well the instrument, including the
mechanisms, electronics, optical, chemical,
mechanical devices respond and indicate the
quantitative value of the true environment.
Error
Difference between the result of a
measurement and the “true value.”
E  Qr  QI
E
Percent Error 
 100
Qr
Systematic error: (can correct for)

Either:
• Remains constant.
• Varies in a known manner. Input/Output Curve
Random Error

Varies in an unpredictable manner in
magnitude or sign. (cannot correct for)
Spurious (outlier) Errors:

In a series of measurements, the errors may be
normally distributed. Outliers fall outside of
the normal distribution.
• Human error
• It is legitimate to discard them
Precision
Closeness of agreement between independent
measurements of a single quantity obtained by
applying a stated measurement procedure
several times under prescribed conditions.
Accuracy has to do with closeness to the true
value.
Precision has only to do with closeness
together of measured values, whether they are
accurate or not.
Repeatability
Closeness of agreement when random errors
are present.
Measurement of the same value determined
under the same conditions:





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Same environmental conditions
Same observer
Same instrument
Same location
Same technique
Short interval of time between measurements
Time interval is short enough for real
differences to be unable to develop.
A subset of Precision.
Stability/Reproducibility
A measure of how well an instrument
maintains it I/O characteristics.
The closeness of agreement between
measurements of the same value of a quantity
under different conditions.

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Different observer
Different location
Long time interval
Resolution
Smallest change in a physical variable which
will cause a variation in the response of a
measuring system. In some fields of
measurement it is synonymous with
discrimination.
Representativeness
The degree to which the value indicated by the
instrument portrays the environment in the spatial
and time region of the environment desired.

E.g.; How well do values of temperature, pressure and
rainfall at a point source (automatic weather station
site) represent the mass of air that those values are
supposed to represent?
• Pressure - fairly well,
• Temperature - less well
• Rainfall - least of all
Sensitivity
The degree to which the instrument responds
to changes in the environment.
The slope of the I/O curve.
If the slope changes with time, the instrument
is displaying sensitivity (scale factor) drift.
Zero Effect / Bias
The amount of displacement of the output
from zero when the input is zero.
May require re-calibration of the instrument.
Zero Drift
The amount of change of zero bias with time.
Range
The maximum and minimum values the
instrument can indicate. Also used to refer to
the maximum and minimum values for which
the instrument remains within its stated
accuracy.
Span
The difference between the maximum and
minimum values.
This usually refers to the values which lie
within the stated accuracy of the instrument.
The instrument may respond to values outside
these maximum and minimum values but its
accuracy decreases beyond stated accuracy.
Linearity
The degree to which the I/O curve approaches
a straight line.
It is customary to express this measure in
terms of the maximum deviation from the
reference line divided by the full scale range.
For most instruments, it is desired that they be
linear. There is less expense involved to show
the instrument output from the sensor input if
the input to output relationship is constant.
Non-linearity can be important for some
instruments.
A dew point hygrometer, which responds nonlinearly to humidity, is also highly sensitive in
the low humidity range but decreasingly so in
the higher hujidity range. Its low humidity
sensitivity makes it very suitable for upper-air
soundings of humidity.
Hysteresis
The difference in output (indicated value)
when an input
value is
approached first
with increasing,
then with
decreasing
values, vice
versa.
Threshold
Smallest measurable input to start / stop
indicating as a sensed parameter increases
from or decreases toward zero.
Dead Band
The range through which the input varies
without initiating a response (or indication)
from the instrument.
Traceability
The property of the result of a measurement or
the value of a standard whereby it can be
related to stated references, usually national
and/or international standards through an
unbroken chain of comparisons all having
stated uncertainties.
Uncertainty
The interval within which the true value of a
quantity can be expected to lie with a stated
probability.
The uncertainty of a measurement generally
consists of several components which may be
grouped into two categories according to the
method used to estimate the numerical values:

Those uncertainties which may be evaluated by
statistical methods.

Those uncertainties which may be evaluated by
other means:
• Previous measured data,
• Experience with the sensor,
• General knowledge of the behavior of relevant materials
and instruments,
• Manufacturer’s specifications,
• Calibration reports and uncertainties assigned to
reference date in handbooks.
Upon examining the various static response
characteristics, it is evident that not all are of
equal significance or importance. An
instrument must be chosen that has values of
those properties suitable for a particular
scientific use.
Hysteresis, drift, threshold, and dead-band are
more serious errors which are generally
difficult or unable to be corrected.
Dynamic Performance Characteristics
Involves evaluating the instruments output as
time changes and the element which is being
measured changes.
dx(t)
l
 x(t)  xI
dt
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Evaluation is by use of differential equations; as
above:
Where, x(t) = Output (response) function, the
dependent variable.
xI = Input (forcing) function; the final atmospheric
value to which the sensor is trying to respond. It is a
constant value.
T = Time, the independent variable.
l = Time constant, the system dynamic performance
parameter.
Rearranging
dx(t) 1
 x I  x(t )
dt
l
dx(t)
1
  x(t)  x I 
dt
l
dx(t)
1
  dt
x(t)  xI  l
Integrating
x
t
dx(t)
1
x x(t)  xI    l 0 dt
0
Where,
 x0 = Temperature output at time = 0
x = Temperature output at time = t.
xI = Value attempting to reach; final temp.
Integrating between the limits
t
gives:
lnx  x  x  x 
I
0
I
x  xI  t

ln

x 0  x I  l
t
x  xI
e l
x0  x I
x  xI  e
t
l
x 0  x I 
l
x  xI  e
t
l
x0  xI 
1
X  X I  X0  XI 

If t = l
e
1
X  XI 
X 0  XI 
2.718
X  X I  0.37X 0  XI 
Thus, when elapsed time, (t), equals the time
response of the instrument, (l), then the amount of
change that yet needs to occur, (x - xI), is equal to
37% of the total change, (x0 - xI); Or, 63% of the
change has occurred when t = l.
Time Response
The time elapsed between the signal input
and that signal output which is 63% of the
amount of change that must occur to
indicate the true value.
Time Response for liquid thermometers
Varies with
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Air Density
Wind velocity
K
l
n
v
Temp.
20
Fluctuations of
Temperature
10
0
Indicated
Temp.
-10
-20
10
0
Response of
Sensor
-10
T im e
Standardization of Instruments
Standard Unit 
A quantity agreed upon to have a value of one
by which other units can be measured or
expressed.
Standard Procedure 
A method of reproduction of a unit of
measurement making use either of fixed values
of certain properties of bodies or of physical
constants.
Standard Instrument 


A measuring device intended to define, to
represent physically, to conserve or to
reproduce the unit of measurement of a
quantity.
Used to calibrate other instruments.
Collective Standard • A group of instruments which together provide the
standard of measurement
Primary Standard 
A standard which has the highest qualities in a
given field. From its measurement, the closest
value to the “true value” can be obtained.
Secondary Standard 
Its value is determined by comparison with a
primary standard.
Reference Standard 
Used to calibrate measuring instruments of
lower accuracy.
Working Standard 
Standard by which ordinary measuring
instruments can be calibrated.
International Standard

A standard recognized by international
agreement as a basis for fixing the value of
other standards.
National Standard

A standard for a nation.
Regional Standard

A standard for a region
Traveling Standard

Portable standard instrument.
End