sensor - week 02 - sensor characteristic
TRANSCRIPT
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7/23/2019 Sensor - Week 02 - Sensor Characteristic
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SENSORS PERFORMANCECHARACTERISTICS
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Input and Output
Input: stimulus or measurand (temperature pressure, lightintensity, etc.)
Ouput: electrical signal (voltage, currentfrequency, phase, etc.)
Variations: output can sometimes be displacement
(thermometers, magnetostrictive and piezoelectricsensors). Some sensors combine sensing and actuation
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Transfer function
Relation between input and output Other names:
Input output characteristic function
transfer characteristic function Response characteristic
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Type of Transfer function
Linear or nonlinear Single valued or not
One dimensional or multi dimensional Single input, single output
Multiple inputs, single output In most cases: Difficult to describe mathematically (given graphically)
Often must be defined from calibration data
Often only defined on a portion of the range of the device
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Transfer function approximation
T1 to T2 - approximately linear Most useful range
Typically a small portion of the range
Often taken as linear
S =f(x)
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Data taken from Transfer function
Other data from transfer function saturation
sensitivity
full scale range (input and output)
hysteresis
deadband
etc.
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Transfer function (cont.)
Other types of transfer functions Response with respect to a given quantity
Impulse response, Step response, Linier response, etc
Performance characteristics (reliability curves, etc.)
Viewed as the relation between any two characteristics
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Impedance and impedance matching
Black box theory of two port devices Input impedance: ratio of the rated voltage and the resulting
current through the input port of the device with the output
port open (no load)
Output impedance: ratio of the rated output voltage and
short circuit current of the port (i.e. current when the output is
shorted)
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Sensor Impedance
Only output impedance of the sensor is relevant As it is mainly in electrical circuit, hence electrical impedance
is importance especially for further processing of signals
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Importance of Impedance
Impedance affects sensor (system) performance Example: 500 W sensor (output impedance) connected to
a processor Processor input impedance is infinite (Fig. b)
Processor input impedance is 500 W (Fig. c)
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Strain Gauge Impedance Example
Case: impedance is 500 W at zero strain, 750 W atmeasured straina. sensor output: 2.5V (at zero strain), 3V at measured strain
b. sensor output: 1.666V to 1.875V
Result: Case b:
the sensor is loaded
Sensitivity is reduced (smaller output change for the same strain input)
Case a: Loading effect not exists (infinite impedance of the processor)
Better sensitivity than case b
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Impedance matching
To avoid loading effect Often need a matching circuit : from high to low or from
low to high impedancesmo
Sometimes can be done directly (C-MOSdevices/processors have very high input impedances)
Voltage output: impedance is highneed high impedanceat processor
Current output: impedance is low - need low impedance atprocessor
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Why Impedance Matching ?
Achieve maximum signal transmission with less (without)reflection
In addition to the previous: Conjugate matching (Zin=Zout*) - maximum power transfer
Zin=R+jX, Zout*=R-jX.No reflection matching (Zin=Zout) - no reflection from load Important at high frequencies (transmission lines)
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Range and Span
Range: lowest and highest values of the stimulusSpan: the arithmetic difference between the highest and
lowest values of the stimulus that can be sensed withinacceptable errors
Input full scale (IFS) = spanOutput full scale (OFS): difference between the upper and
lower ranges of the output of the sensor corresponding tothe span of the sensor
Dynamic range: ratio between the upper and lower limitsand is usually expressed in db
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Range and Span (Cont)
Example: a sensors is designed for: -30 C to +80 C tooutput 2.5V to 1.2V
Range: -30C and +80 C
Span: 80- (-30)=110 C Input full scale = 110 C
Output full scale = 2.5V-1.2V=1.3V
Dynamic range=20log(140/30)=13.38db
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Range and Span (cont.)
Range, span, full scale and dynamic range may beapplied to actuators in the same way
Span and full scale may also be given in db when the
scale is large. In actuators, there are other properties that come into
play:
Maximum force, torque, displacement
Acceleration
Time response, delays, etc.
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Accuracy, errors, repeatability
Errors: deviation from ideal
Sources:
materials used
construction tolerances ageing
operational errors
calibration errors
matching (impedance) or loading errors
noise
many others
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Accuracy, errors (cont.)
Error: a. As a difference: e = VV0 (V0 is the actual value, V is that
measured value (the stimulus in the case of sensors or output in
actuators).
b. As a percentage of full scale (span for example) e =
t/(tmax-tmin)*100 where tmax and tmin are the maximum and
minimum values the device is designed to operate at.
c. In terms of the output signal expected.
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Example: errors
)30(808.25.18.2
--
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OV
Example: A thermistor is used to measure temperaturebetween30 and +80 C and produce an output voltage
between 2.8V and 1.5V. Because of errors, the accuracy in
sensing is 0.5C.
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Example (cont)
a. In terms of the input as 0.5Cb. Percentage of input: e = 0.5/(80+30)*100 = 0.454%
c. In terms of output. From the transfer function: e= 0.059V.
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More on errors
Static errors: not time dependentDynamic errors: time dependent Random errors: Different errors in a parameter
or at different operating times Systemic errors: errors are constant at all times
and conditions
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Error limits - linear TF
Linear transfer functions Error equal along the transfer function
Error increases or decreases along TF
Error limits - two lines that delimit the output
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Error limits - nonlinear TF
Nonlinear transfer functions
Error change along the
transfer function
Maximum error from ideal Average error
Limiting curves follow ideal
transfer function
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Error limits - nonlinear TF
Calibration curve may beused when available Lower errors
Maximum error from
calibration curve Average error Limiting curves follow the
actual transfer function(calibration)
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Repeatability
Also called reproducibility: failure of the sensor oractuator to represent the same value (i.e. stimulus or input)
under identical conditions when measured at different
times.
usually associated with calibration
viewed as an error.
given as the maximum difference between two readings taken
at different times under identical input conditions. error given as percentage of input full scale.
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Sensitivity
Sensitivity of a sensor is defined as the change in outputfor a given change in input, usually a unit change in input.
Sensitivity represents the slope of the transfer function.
Same for actuators
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Sensitivity
Sensitivity of a sensor is defined as the change in outputfor a given change in input, usually a unit change in input.
Sensitivity represents the slope of the transfer function.
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Sensitivity (cont.)
Can be highly nonlinear along the transfer function Measured in units of output quantity per units of input
quantity (W/C, N/V, V/C, etc.)
For a linear transfer function, sensitivity is the slope ortransfer function.
Example:ddR
aT +b =1 dRdT
=a WC
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Sensitivity analysis (cont.)
A difficult taskthere is noisea combined function of sensitivities of various
components, including that of the transductionsections.
device may be rather complex with multipletransduction steps, each one with its own sensitivity,sources of noise and other parameters
some properties may be known but many may notbe known or may only be approximate.
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Sensitivity analysis (cont.)
An important task provides information on the output range of signals one can
expect,
provides information on the noise and errors to expect.
may provide clues as to how the effects of noise and errors
may be minimized
Provides clues on the proper choice of sensors, their connections
and other steps that may be taken to improve performance(amplifiers, feedback, etc.).
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Example - additive errors
Fiber optic pressure sensor Pressure changes the length of the fiber
This changes the phase of the output
Three transduction steps
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Example-1 - no errors present
Individual sensitivities
Overall sensitivity
But, x2=y1 (output of transducer 1 is the input to
transducer 2) and x3=y2
s1=dy1
dx , s2=dy
2
dx , s3=dy
3
dx
S =s1s2s3=
dy1dx
dy2dx
dy3dx
S =s1s2s3=dy3
dx
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Example -1 - errors present
First output is y1=y01 + y1. y01 = Output without error 2nd output
3rd output
Last 3 terms - additive errors
2=s2y
0
+y1
+y2
=y
0
+s2y1
+y2
3=s3y0+s2y1+y2 +y3=y
0+s2s3y1+s3y2+ y3
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Example -2 - differential sensors
Output proportional to difference between the outputs ofthe sensors
Output is zero when T1=T2
Common mode signals cancel (noise) Errors cancel (mostly)
E l 2 ( )
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Example -2 - (cont.)
s1=dy1dx1
, s2=dy2dx2
y=y1-y2=s1x1-s2yx
s =d y1-y2d x1-x2
E l 3 i i
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Example -3 - sensors in series
Output is in series Input in parallel (all sensors at
same temperature)
Outputs add up
Noise multiplied by product ofsensitivities
y=y1+y2+ y3+...+yn=(s1+s2+s3+...+sn)x =ns
S =ns
H i
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Hysteresis
Hysteresis (literally lag)- thedeviation of the sensorsoutput at any given pointwhen approached from twodifferent directions
Caused by electrical ormechanical systems Magnetization
Thermal properties
Loose linkages
H i E l
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Hysteresis - Example
If temperature is measured, at a rated temperature of50C, the output might be 4.95V when temperatureincreases but 5.05V when temperature decreases.
This is an error of 0.5% (for an output full scale of 10V inthis idealized example).
Hysteresis is also present in actuators and, in the case ofmotion, more common than in sensors.
N li i
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Nonlinearity
A property of the sensor (nonlinear transfer function) or: Introduced by errors
Nonlinearity errors influence accuracy.
Nonlinearity is defined as the maximum deviation from the
ideal linear transfer function. The latter is not usually known or useful
Nonlinearity must be deduced from the actual transferfunction or from the calibration curve
A few methods to do so:
N li it ( t )
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Nonlinearity (cont.)
a. by use of the range of the sensorPass a straight line between the range points (line
1)Calculate the maximum deviation of the actual
curve from this straight lineGood when linearities are small and the span is
small (thermocouples, thermistors, etc.)Gives an overall figure for nonlinearity
N ( )
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Nonlinearity (cont.)
b. by use of two points defining a portion of the span ofthe sensor/actuator.
Pass a straight line between the two points
Extend the straight line to cover the whole span
Calculate the maximum deviation of the actual curve from this
straight line
Good when a device is used in a small part of its span (i.e. a
thermometer used to measure human body temperatures Improves linearity figure in the range of interest
N l ( )
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Nonlinearity (cont.)
c. use a linear best fit(least squares) throughthe points of the curveTake n points on the actual curve, xi,yi, i=1,2,n.Assume the best fit is a line y=ax+b (line 2)Calculate a and b
N l ( )
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Nonlinearity (cont.)
d. use the tangent to the curve at some point on the curve Take a point in the middle of the range of interest
Draw the tangent and extend to the range of the curve (line 3)
Calculate the nonlinearity as previously
Only useful if nonlinearity is small and the span used very small
S t ti
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Saturation
Saturation a property of sensors or actuators when they nolonger respond to the input.
Usually at or near the ends of their span and indicates thatthe output is no longer a function of the input or, more likelyis a very nonlinear function of the input.
Should be avoided - sensitivity is small or nonexistent
S t ti C diti
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Saturation Condition
saturated
saturated
F
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Frequency response
Frequency response: The ability of the device to respond toa harmonic (sinusoidal) input
A plot of magnitude (power, displacement, etc.) as a function
of frequency
Indicates the range of the stimulus in which the device is
usable (sensors and actuators)
Provides important design parameters
Sometimes the phase is also given (the pair of plots is theBode diagram of the device)
Freq enc response (cont)
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Frequency response (cont)
Important design parameters
Bandwidth (B-A, in Hz) Flat frequency range (D-C in Hz)
Cutoff frequencies (points A and B in Hz)
Resonant frequencies
Frequency response (cont )
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Frequency response (cont.)
Bandwidth: the distance in Hz between the half powerpoints Half-power points: eh=0.707e, ph=0.5p
Flat response range: maximum distance in Hz over which
the response is flat (based on some allowable error) Resonant frequency: the frequency (or frequencies) at
which the curve peaks or dips
Half power points
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Half power points
Also called 3db points Power is 3db down at these points:
10*log0.5=-3db or
20*log (sqrt(2)/2)=-3db
These points are arbitrary but are now standard.
It is usually assumed that the device is useless beyond the
half power points
Frequency response (example )
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Frequency response (example.)
Bandwidth: 16.5kHz-70Hz=16.43 kHz
Flat frequency range: 10kHz-120Hz=9880 Hz
Cutoff frequencies: 70 Hz and 16.5 kHz
Resonance: 12 kHz
Response time
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Response time
response time (or delay time), indicates the time needed forthe output to reach steady state (or a given percentage ofsteady state) for a step change in input.
Typically the response time will be given as the time neededto reach 90% of steady state output upon exposure to a unit
step change in input. The response time of the device is due to the inertia of the
device (both mechanical and electrical).
R ti ( t )
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Response time (cont.)
Example: in a temperature sensor: the time needed for the sensors body to reach the temperature it is
trying to measure (thermal time constant) or
The electrical time constants inherent in the device due tocapacitances and inductances
In most cases due to both Example: in an actuator: Due to mass of the actuator and whatever it is actuating
Due to electrical time constants
Due to momentum
Response time (cont )
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Response time (cont.)
Fast response time is usually desirable (not always) Slow response times tend to average readings
Large mechanical systems have slow response times
Smaller sensors and actuators will almost always respond
faster We shall meet sensors in which response time is slowed down
on purpose
C lib ti
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Calibration
Calibration: the experimental determination of the transferfunction of a sensor or actuator.
Typically, needed when the transfer function is not known or,
When the device must be operated at tolerances belowthose specified by the manufacturer.
Example, use a thermistor with a 5% tolerance on a full scalefrom 0 to 100C to measure temperature with accuracy of,say, 0.5C.
The only way this can be done is by first establishing thetransfer function of the sensor.
Calibration Method
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Calibration Method
a. known transfer function: Determine the slope and crossing point (line function) from two known stimuli (say twotemperatures) if the transfer function is linear
Measure the output
Calculate the slope and crossing point in V=aT+b
If the function is more complex, need more points: V = aT + bT2 + cT3 + d
4 measurements to calculate a,b,c,d Must choose points judiciously - if linear, use points close to the range. If not, use equally
spaced points or points around the locations of highest curvature
b. Unknown transfer function: Measure the output R
iat as many input values T
ias is practical
Use the entire span Calculate a best linear fit (least squares for example)
If the curve is not linear use a polynomial fit
May use piecewise linear segments if the number of points is large.
Calibration (cont )
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Calibration (cont.)
Calibration is sometimes an operational requirement(thermocouples, pressure sensors)
Calibration data is usually supplied by the manufacturer
Calibration procedures must be included with the designdocuments
Errors due to calibration must be evaluated and specified
Resolution
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Resolution
Resolution: the minimum increment in stimulus to which it canrespond. It is the magnitude of the input change which results
in the smallest discernible output.
Example: a digital voltmeter with resolution of 0.1V is used
to measure the output of a sensor. The change in input(temperature, pressure, etc.) that will provide a change of
0.1V on the voltmeter is the resolution of the
sensor/voltmeter system.
Resolution (cont )
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Resolution (cont.)
Resolution is determined by the whole system, not only by thesensor
The resolution of the sensor may be better than that of thesystem.
The sensor itself must interact with a processor, the limitingfactor on resolution may be the sensor or the processor.
Resolution may be specified in the units of the stimulus (0.5Cfor a temperature sensor, 1 mT for a magnetic field sensor,0.1mm for a proximity sensor, etc) or may be specified as a
percentage of span (0.1% for example).
Resolution (cont )
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Resolution (cont.)
In digital systems, resolution may be specified in bits (1 bit or6 bit resolution)
In analog systems (those that do not digitize the output) theoutput is continuous and resolution may be said to beinfinitesimal (for the sensor or actuator alone).
Resolution of an actuator is the minimum increment in itsoutput which it can provide.
Example: a stepper motor may have 180 steps perrevolution. Its resolution is 2.
A graduated analog voltmeter may be said to have aresolution equal to one graduation (say 0.01V). ( higherresolution may be implied by the user who can easilyinterpolated between two graduations.
Other parameters
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Other parameters
Reliability: a statistical measure of quality of a devicewhich indicates the ability of the device to perform itsstated function, under normal operating conditions withoutfailure for a stated period of time or number of cycles.
Given in hours, years or in MTBF
Usually provided by the manufacturer
Based on accelerated lifetime testing
Other parameters
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Other parameters
Deadband: the lack of response or insensitivity of a deviceover a specific range of the input. In this range which may be small, the output remains
constant.
A device should not operate in this range unless thisinsensitivity is acceptable.
Example, an actuator which is not responding to inputsaround zero may be acceptable but one which freezesover a normal range may not be.
Other parameters
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Other parameters
Excitation: The electrical supply required for operation of a sensor oractuator.
It may specify the range of voltages under which the device should
operate (say 2 to 12V), range of current, power dissipation, maximum
excitation as a function of temperature and sometimes frequency.
Part of the data sheet for the device
Together with other specifications it defines the normal operating
conditions of the sensor.
Failure to follow rated values may result in erroneous outputs orpremature failure of the device.