Chapter 3
Outlines
Basic Sensor Technology
Sensor Systems
Application Considerations
Measurement Issues and Criteria
Sensor Signal Conditioning
Conditioning Bridge Circuits
DAC for Signal Conditioning
ADC for Signal Conditioning
Signal Conditioning High Impedance Sensors
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Basic Sensor Technology
• What are Sensors?
– A device which provides a usable output in response to a
specified measurand
Input Signal
Output Signal
Sensor
– Convert a Signal or Stimulus (Representing a Physical Property) into an Electrical Output
– Sensing technology uses sensors to acquire information by
detecting the physical, chemical, or biological property
quantities and convert them into readable signal
• They embedded in our bodies(eg: eyes, ear…), automobiles,
airplanes, cellular telephones, radios, chemical plants, industrial
plants and countless other applications
• Without the use of sensors, there would be no automation !!
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Sensor Technology - Terminology
• Sensors can improve the world through
 diagnostics in medical applications
 improved performance of energy sources like fuel cells and
batteries and solar power
 improved health, safety and security for people
 sensors for exploring space
 improved environmental monitoring.
• The seed technologies are now being developed for long-term
vision that includes intelligent systems that are
 self-monitoring,
 self-correcting and repairing, and
 self-modifying
• The ability for a system to see (photonic technology), feel (physical
measurements), smell (electronic noses), hear (ultrasonics),
think/communicate (smart electronics and wireless), and move (sensors
integrated with actuators), is progressing rapidly and suggests an exciting
future for sensors.
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Classification of Sensors
o 1. Active and Passive sensors
 Active sensor: a sensor that requires external power to operate.
 Passive sensor: generates its own electric signal and does not
require a power source
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Classification of Sensors(…)
o 2. Contact and noncontact sensors
 Contact sensor: a sensor that requires physical contact with the stimulus.
Examples: strain gauges, most temperature sensors
 Non-contact sensor: requires no physical contact.
Examples: most optical and magnetic sensors, infrared thermometers, etc.
o 3. Absolute and relative sensors
 Absolute sensor: a sensor that reacts to a stimulus on an absolute scale.
Examples: Thermistors, strain gauges, etc.,
 Relative sensor: the stimulus is sensed relative to a fixed or variable reference.
Examples: Thermocouple measures the temperature difference, pressure is
often measured relative to atmospheric pressure
o 4. Other schemes
 Classification by broad area of detection
• Chemical sensors
• Optical
• Mechanical
• Biological, etc…
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Classification of Sensors(…)
o 4. Other schemes(…)
 Classification by physical law
• Photoelectric
• Magnetoelectric
• Thermoelectric
• Photomagnetic, etc…
 Classification
by area of
 happlication
• Consumer products
• Healthy
• Transportation
• Scientific, etc…
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Sensor Systems
• Deals with sensors and associated signal conditioning circuits
• Sensors and their associated circuits are used to measure various
physical properties such as temperature, force, pressure, flow,
position, light intensity, etc
• Their outputs must be properly conditioned before further
analog or digital processing can occur.
• Sensors do not operate by themselves.
• Composition:
 signal conditioners,
 various analog or digital signal processing circuits.
• Generally part of a larger system.
• The system could be a measurement system, data acquisition
system, or process control system, etc…
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Sensor Systems(…)
• Most sensor outputs are nonlinear with respect to the stimulus,
and their outputs must be linearized in order to yield correct
measurements.
• Analog techniques may be used to perform this function.
• The application of sensors in a typical process control system is
shown in Figure below.
• Assume the physical property to be controlled is the temperature.
• The output of the temperature sensor is conditioned and then
digitized by an ADC.
• The microcontroller determines if the temperature is above or
below the desired value, and
• outputs a digital word to the digital-to-analog converter (DAC).
• The DAC output is conditioned and drives the actuator, in this
case a heater.
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Sensor Systems(…)
• Notice that the interface between the control center and
• The remote process is via the industry-standard 4–20mA loop.
Figure: Typical industrial process control
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Sensor Systems(…)
• What are the selection criteria for sensors?
o Accuracy-should be high
o Stability-maintain under abnormal conditions
o Environmental conditions -usually has limits for
temperature & humidity
o Range-Measurement limit of sensor
o Calibration-essential for most of the measuring devices as
the readings changes with time
o Resolution-smallest increment detected by the sensor
o Cost-should be low
o Power consumption -low
o Repeatability -the reading that varies is repeatedly measured
under the same environment
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Sensor Performance Characteristics
• General characteristics of sensors are two, namely
• Static characteristics
 The static characteristic of a sensor refers to the relationship between the
output and the input of a sensor with respect to a static input signal.
Because the input and output are independent of time at this time
 Examples: Accuracy, Drift, Dead Zone ,Static Error, Sensitivity,
Reproducibility, Static correction, Scale range, Scale span, Noise, Dead
Time, Hysteresis, Linearity.
• Dynamic Characteristics
 dynamic characteristics of the sensor refer to the characteristics of the
sensor's output when the input changes.
 Examples: Speed of response, Measuring lag , Fidelity and Dynamic
error
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Application Considerations
• The highest quality, most up-to-date, most accurately calibrated
and most carefully selected sensor can still give totally erroneous
data if it is not correctly applied.
• The instrumentation engineer must carefully analyze every
aspect of the test to be performed,
• Test article,
• Environmental conditions
• Analytical predictions (if available).
• In most cases, this process will indicate a clear choice of
acceptable system components
 What is the most difficult tasks facing an instrumentation engineer?
Ans: The selection of the proper measuring system.
 Why do we need to select the proper measuring system?
Ans: obtain accurate, reliable data on each and every measurement.
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Application Considerations(…)
Sensor Characteristics
• The prospective user is generally forced to make a selection
based on the characteristics available on the product data sheet
• Many performance characteristics are shown on a typical data
sheet
• Many manufacturers feel that the data sheet should provide as
much information as possible.
System Characteristics:• The sensor and signal conditioners must be selected to work
together as a system
• The system must be selected to perform well in the intended
applications
• Overall system accuracy is usually affected most by sensor
characteristics such as environmental effects and dynamic chxs.
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Sensor Application Considerations(…)
• Sensing Range
•
•
•
•
Photoelectric controls: 0 to 1000 ft range
Ultrasonic sensors: 0 to 11 ft range
Inductive proximity sensors: 0 to 65 mm range
Capacitive proximity sensors: 0 to 50 mm range
• Target Material
•
•
•
•
Inductive proximity: metal type will determines sensing range
correction factor
Capacitive proximity : Material type will determines sensing range
dielectric constant
Photoelectric: target color will determine sensing range excess gain
Ultrasonic: Target porosity or density will determine sensing range
• Environment
•
•
•
•
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Sealing: IP rating-IP65 dust tight, IP67 temp immersion, IP68 NEMA
ratings: NEMA 1, 2, 2, 4, 12, 13, 6P 1200psi Rated
Weld Field Immune: 20,000 Amps/ Sparks and Splatter Resistant
Temperature ratings: Above 158 degree f, use fiber optic or high temp
Hazardous Locations: Intrinsically safe/ with Zener diodes barriers
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Sensor Application Considerations(…)
• Mounting
 Side to side
 Face to face
• Control Interface
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Sensor Application Considerations(…)
• Control Interface(…)
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Sensor Application Considerations(…)
• Response time
 AC applications that requires response time of less than 50
milliseconds(20Hz switching frequency)
 DC applications that require response time of less than 10
milliseconds(75 Hz switching frequency) may require special attention
• Wiring Options
 Pre-Corded, or
 Allen-Bradley Cordsets
 889N Mini
• 3 and 5 Pin AC
• 4 Pin DC
 889 D DC micro
• 4 Pin DC
 889R AC micro
• 3 Pin AC/DC
 889P Pico
• 3 & 4 Pin DC
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Others
• Accuracy
• Shock and Vibration
• Surrounding
Temperature
Conditions
• Resistance to corrosion
• Output repeatability
• Lifespan
17
Instrument selection
• Selecting a sensor/signal conditioner system for highly accurate
measurements requires very skillful and careful measurement
engineering.
• Must be considered:
 All environmental,
 Mechanical
 Measurement conditions
 Installation must be carefully planned and carried out
• The following guidelines are offered as an aid to selecting and
installing measurement systems for the best possible accuracy.
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Instrument selection(…)
o Sensor
 The most important element in a measurement system is the sensor.
 If the data is distorted or corrupted by the sensor, there is often little
that can be done to correct it.
o Will the sensor operate satisfactorily in the measurement
environment?
Check:
 Temperature Range
 Maximum Shock and Vibration
 Humidity
 Pressure
 Acoustic Level






Corrosive Gases
Magnetic and RF Fields
Nuclear Radiation
Salt Spray
Transient Temperatures
Strain in the Mounting Surface
o Will the sensor characteristics provide the desired data
accuracy? Check:
 Amplitude Linearity and Hysteresis




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Sensitivity
Frequency Response
Internal Capacitance
Transverse Sensitivity




Temperature Deviation
Weight and size
Calibration Accuracy
etc.
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Instrument selection(…)
o Is the proper mounting being used for this application?
Check:
 Is Insulating Stud Required?
 Ground Loops
 Calibration Simulation
 Is Adhesive Mounting Required?
 Thread Size, Depth and Class
o Cable
 Will the cable operate satisfactorily in the measurement environment?
 Will the cable characteristics provide the desired data accuracy?
o power supply
 Will the power supply operate satisfactorily in the measurement environment?
 Is this the proper power supply for the application?
 Will the power supply characteristics provide the desired data accuracy?
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Instrument selection(…)
o Amplifier 
The amplifier must provide gain, impedance matching,
output drive current, and other signal processing
 Will the amplifier operate satisfactorily in the measurement
environment?
 Is this the proper amplifier for the application?
 Will the amplifier characteristics provide the desired data accuracy?
o Data acquisition
o
 The followings are essential when choosing correct data acquisition
hardware
• Signal/signal type compatibility
• Maximum sampling rate required
• Minimum measurement resolution required
• Does my DAQ system need resolution?
Readout
 This is the display of a measuring system
o Installation
 Even the most carefully and thoughtfully selected and calibrated
system can produce bad data if carelessly or ignorantly installed
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Types of Instruments to make Measuring Devices
o PMMC type:
o Moving iron
 m/s of dc voltage and current used in dc
galvanometer
 Cannot be used for ac m/s
 Some errors are caused by temperature
type
 Less expensive
variations.
 Can be used for both dc and ac
 Reasonably accurate.
o Electro-Dynamometer type

Can be used for both dc and ac m/s.
 Free from hysteresis and eddy
current errors.
o Hot wire type
 Can be used for both dc and ac
 Unaffected by stray magnetic fields
 Readings are independent of frequency and
waveform.
oElectrostatic type
oInduction type
oRectifier type
oThermocouple type
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Permanent magnet moving coil
 This permanent magnet moving
coil meter movement is the basic
movement in most analog (meter
with a pointer indicator hand)
measuring instruments.
 It is commonly called d'Arsonval
movement
 This type of meter movement is a
current measuring device which is
used in the ammeter, voltmeter,
and ohmmeter.
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Permanent magnet moving coil …
 Suspension Galvanometer
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Permanent magnet moving coil …
o Deflection Toque
 It has been mentioned that interaction between the induced field
and the field produced by the permanent magnet causes a
deflecting torque, which results in rotation of the coil.
 Deflection torque is controlling the deflection and tries to stop
the pointer at its final position.
 But due to inertia, the pointer oscillates around its final position
before coming to rest. Hence damping torque is provided to
avoid this oscillation and bring the pointer quickly to its final
position
 Thus the damping torque is never greater than the controlling
torque.
 In fact it is the condition of critical damping which is sufficient
to enable the pointer rising quickly to its deflected position
without overshooting
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Permanent magnet moving coil …
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DC Voltmeter
1. Multiplier Resistor
A basic d’Arsonval movement can be converted into dc voltmeter by adding in
series resistor multiplier as shown
IM = full scale deflection current of the
movement (Ifsd)
RM = internal resistance of the movement
RS = multiplier resistance
V = full range voltage of the instrument
Current in series; IS = IM
DC Voltmeter
The multiplier limitscircuit.
the current through the movement
so as not to exceed the value of the full scale deflection
current (Ifsd)
EX: A basic D’ Arsonval movement with a full-scale deflection of 50
µA and internal resistance of 500Ω is used as a DC voltmeter.
Determine the value of the multiplier resistance needed to measure a
voltage range of 0-10V.
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DC Voltmeter(…)
2. Multi Range Multiplier Resistor
A DC voltmeter can be converted into a multirange voltmeter by connecting a number of
resistors (multipliers) in series with the meter movement. A practical multi-range DC
voltmeter is shown in Figure
DC Multi-range
Voltmeter circuit
EX: Convert a basic D’ Arsonval movement with an internal resistance of 100Ω and
a full scale deflection current of 1mA into a multirange dc voltmeter with voltage
ranges of 0-15V and 0- 50V
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DC Voltmeter(…)
Example: A basic d’Arsonval movement with internal resistance, Rm=100Ω,
and full scale current, Ifsd = 1 mA, is to be converted into a multirange dc
voltmeter with voltage range of 0-10V, 0-50V, 0-250V, and 0-500V. The circuit
arrangement of Figurer below is to be used for this voltmeter
EX: Convert a basic D’ Arsonval movement with an internal resistance of 100Ω and
a full scale deflection current of 1mA into a multirange dc voltmeter with voltage
ranges of 0-15V and 0- 50V
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DC Ammeter
1. Shunt Resistor
The basic movement of a DC ammeter is PMMC galvanometer. Since the coil
winding of a basic movement is small and light, it can carry only very small
currents. When large currents are to be measured, it is necessary to bypass the
major part of the current through a resistance, called a shunt.
IM = full scale deflection current
of the movement (Ifsd)
RM = internal resistance of the
movement(coil)
RS = resistance of shunt
I= full scale current of the
ammeter including the shunt
Voltages in parallel; Vshunt =Vmovement
I S RS = I M RM
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Basic DC Ammeter
ckt
For each required of full scale meter
current we can then solve for the
value of the shunt resistance required.
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DC Ammeter(…)
2. Ayrton Shunt
The current range of the dc ammeter may be further extended by a number of
shunts, selected by a range switch,. Such a meter is called a multi range ammeter
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DC Ammeter(…)
Example:
Design an Ayrton shunt to provide an ammeter with current ranges of 1A, 5A
and 10A. A d’Arsonval movement with an interval resistance Rm = 50 Ω and
full-scale deflection current of 1mA is used in the configuration of Figure below.
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Ohmmeter
1.Series Ohmmeter
R1 = Limited Current Resistor
R2 = Zero Adjust Resistor
Rx = unknown Resistance
Rm = Meter Resistance
Operation of Series Ohmmeter Individual Series Ohmmeter
• When Rx = 0 ( AB terminal short), circuit
the current in circuit is
maximum and the pointer shown the full reading. Adjust the R2
until the full scale, IM. The pointer at full scale is mark as 0 ohm.
• When Rx = infinity (AB terminal open), the current in circuit is 0.
The unknown resistance must connect series with basic meter
movement. This circuit use to measure higher resistance and the
pointer is mark as infinity.
When Rx connected;
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The pointer
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Ohmmeter(…)
.
2. Shunt Resistor in Series
Type Ohmmeter
R1 = Limited Current Resistor
R2 = Zero Adjust Resistor
Rx = unknown Resistance
RM = Meter Resistance
Individual Shunt resistor in series type
ohmmeter circuit
the ratio between current reading when Rx is connected and
full scale current.
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Ohmmeter(…)
3. Parallel (Shunt) Ohmmeter
Individual Shunt Ohmmeter
circuit.
Operation of Shunt Ohmmeter
• S1 is using for cut-off the battery (Vin) when not using the circuit.
When Rx = 0 ( AB terminal short), no current in circuit and the
pointer is mark as 0 ohm.
• When Rx = infinity (AB terminal open), the current (I M) in circuit is
maximum. Adjust R1 until the meter movement is full scale, and the
pointer is mark as ∞Ω (Infinity)
The pointer location
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Alternating current indicating instruments
•The d'Arsonval movement responds to the average or dc value of
the current through the moving coil.
•If the movement carries an alternating current with positive and
negative half cycles, the driving torque would be in one direction for
the positive alternation and other direction for the negative
alternation.
•If the frequency of the ac is very low, the pointer would swing back
and forth around zero point on the meter scale.
•At higher frequencies, the inertia of the coil is so great that the
pointer cannot follow the rapid reversals of the driving torque and
hovers around the zero mark, vibrating slightly.
•To measure ac on d'Arsonval movement, we may need:
–
–
–
(a) unidirectional torque that does not reverse each half cycle,
(b) rectification of the ac,
(c) to use the heating effect of the alternating current to produce an indication of its magnitude.
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Alternating current indicating instruments(…)
• Electrodynamometer
Figure 1 shows the electrodynamometer movement. Unlike to the D’Arsonval
movement, Electrodynamometer uses the current under measurement to
produce the necessary field flux. The fixed coil is splitted into two halves and
they are connected in series with moving coil.
The movable coil movement is controlled by the springs
The expression for the
torque developed is the
same as the D’Arsonval
movement:
where T = torque (Nm)
B = flux density in the air gap (tesla)
A = effective coil area (A = bxh) (m2)
I = current in the movable coil (A)
N = turns of wire on the coil.
Since the flux density (B) depends
on the current through the fixed coil,
B is also directly proportional to
current (I). Hence the torque is
proportional to current squared (I2).
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Schematic diagram of an electrodynamometer movement.
Eg:
wattmeter, Power Measurement in 3 phase 3 wire
system, Energy meters (1p/3p)
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Alternating current indicating instruments(…)
•
Rectifier-type Instruments
This method is very attractive, because it has a higher sensitivity
than either the electrodynamometer or the moving-iron
instrument.
o Half wave rectifier
o Full-wave rectifier
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Alternating current indicating instruments(…)
• Moving Iron(coil): these instruments use movable
piece of iron placed in the pointer over the scale
and hence moving iron instrument
 Eg: AC voltmeters, Ammeters & Ohmmeter
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Alternating current indicating instruments(…)
• Thermo instruments
Schematic representation of a basic thermocouple instrument
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Alternating current indicating instruments(…)
•
•
Example:
Thermo instrument was designed for voltage measurement with 0-5V, 0- 10V, and 025V ranges. Full scale deflection for the galvanometer is 50μA and internal resistance
is 200Ω. The resistance of the heating elements is 200 Ω and current-temperature
characteristics of heating element and temperature-potential difference characteristics
of thermo instrument are shown in Figure. Find the potential difference across the
thermo instrument and range resistors. Ifsd = 50μA Rm = 200Ω R = 200Ω Potential
difference across the thermo instrument is:
•
If Figure c is examined it is found that 10 mV potential difference is resulted from the
temperature increase of 200 ˚C. That increase is the direct effect of the current
through the heating element. From Figure b 5mA current causes that increase so:
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Alternating current indicating instruments(…)
•
Example(…)
Figure: Thermo instrument with 3 ranges
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Alternating current indicating instruments(…)
• Electrostatic Voltmeter
‣ Electrometer, is the only
instrument that measures
voltage directly rather than by
the effect of the current it
produces.
‣ This instrument has one
distinguishing characteristic:
‣ It consumes no power (except
during the brief transient
Schematic representation of an electrostatic voltmeter.
period of initial connection to
the circuit)
The instantaneous energy stored in the electric field is:
• Peak Value Voltmeter
All voltmeters covered so far measures the effective value. They are calibrated in rms
values of the sinusoidal signal. If the measured signal is not sinusoidal form, the peak
value is used for the measurement. Figure in page 44 shows the typical peak value
voltmeter.
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Alternating current indicating instruments(…)
•
The instantaneous torque may be found by keeping e constant and permitting the
movable plates to undergo a small angular displacement, ∂θ . The developed torque
then is:
•
The average torque over an entire period T of the alternating voltage is
Peak value voltmeter with differential amplification
• Differential amplification is used to strength the sensitivity decreased due to the
nonlinearity of the diode characteristics. The peak value voltmeter can measure the
signals up to 1GHz. However leakage capacitors in the long cables decrease the
output impedance in the high frequencies
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Exercises
1.
2.
3.
Design an ammeter to measure 100mA using a 50mA PMMC meter
movement with internal resistance 3kW.
State the ohmmeter scale when the current is 0A, ½ FSD, ¼ FSD and FSD
An experimental AC voltmeter uses the circuit of Figure below, where PMMC
movement has an internal resistance of 50 Ω and requires a DC current of
1mA for full-scale deflection. Assuming ideal diodes (zero forward resistance
and infinite reverse resistance), calculate the value of the multiplier Rs to
obtain full-scale meter deflection with 10 V ac (rms) applied to the input
terminals
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Exercises(…)
4.
• Rsh shunt resistor is used in order to draw more current through the diode D1
and Diode D2 prevents the leakage current across D1 in the reverse direction. A
meter movement has an internal resistance of 100Ω and requires 1mA dc for
full scale deflection. Shunting resistor Rsh, placed across the movement, has a
value of 100Ω. Diodes D1 and D2 have an average forward resistance of 400Ω
each and are assumed to have infinite resistance in the reverse direction. For a
10V ac range, calculate (a) the value of multiplier Rs, (b) the voltmeter
sensitivity on the ac range.
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Measurement Issues and Criteria
• The requirements of the measurement will determine the
selection and application of the sensor.
• How then can we quantify the requirements of the
measurement?
• First, we must consider what it is we want to measure. Such as
To, P, Flow.
• Second, we must consider the environment of the sensor.
• Third, we must consider the requirements for accuracy
(uncertainty) of the measurement.
• Last, but not least, the user must assure that the whole system is
calibrated and traceable to a national standards organization
(such as National Institute of Standards and Technology [NIST]
in the United States).
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Sensor Signal Conditioning
• Typically a sensor cannot be directly connected to the
instruments that record, monitor, or process its signal,
• Because the signal may be incompatible or may be too weak
and/or noisy.
• The signal must be conditioned-i.e., cleaned up, amplified, and
put into a compatible format.
Functions of Signal Conditioner:





Signal amplification (OpAmp)
 Current – voltage change circuits,
Filtering (OpAmp, RLC)
 resistance change circuits (Wheatstone
Interfacing with P (ADC)
bridge)
Protection(Zener & photo isolation)  error compensation…. etc.
Linearization
• The followings are the important aspects of sensor signal conditioning.
• Analog-to-Analog Conversion Signal Conditioning
• Conditioning Bridge Circuits
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Analog-to-Analog Conversion Signal Conditioning
• Current-to-Voltage Converter
Example:
Find a value R that converts a
4 mA to 20 mA
current signal into a 1 – 5 V
output
Voltage.
Vo
Vo I in R  R 
I in
Input current converted to
voltage by R.
Since V+ = VVo = Iin∙R
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Vo 1 V @ I in 4 mA
R
1V
250 
4 mA
Check output at 20 mA
Vo 250  (20 mA) 5 V
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Analog-to-Analog Conversion Signal Conditioning(…)
• Voltage-to-Current Converter
• V-to-I Converter (Transconductance Amps)
V+ = V- =Vin and Iin =0
So Io – IR =0 or Io=IR
Ungrounded load
V
I o I R 
but V - V  Vin
R
V
I o  in
R
Note: RL < R for practical circuit operation. OP AM
output voltage determines magnitude of RL for
constant current
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Signal Conditioning Example
• Convert a 0-5 V dc voltage signal to a 4-20 mA current signal
using OP AMP circuits.
19.22mA
DC A
R6
Vbias
1V
R2
470k
Vin
5V
R1
470k
R5
100k
R3
470k
-12V
U1A
LM324
R4
100k
-12V
-12V
U1B
LM324
U1C
LM324
RLoad
100
+
12V
+
+
12V
12V
• Determine the ratio of spans
Vin Vin (max)  Vin (min)
5V-0V
5V
R6 



312.5 
I0
I 0 max  I 0 min
20 mA - 4 mA 16 mA
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Signal Conditioning Example…
• Compute the value of Vbias to give the value of
minimum output
current
Check
the output What in max value of RL?
with Vin = 5 V
I 0 min 4 mA
Vin
 I 0 R Vin
R
Vbias I 0 min R
I0 
Assume Vsat = 10.5 V
Vin
Vsat  Vin (max)
R L (max) 
R
I o max
Vmax Vin(max)  Vbias V 10.5 V
sat
Vmax 5 V  1.25 V I o max 0.020 A 20 mA
I0 
R 312.5 
Vin (max) 6.25 V
6.25 V
I 
Vbias (4 mA) (312.5 ) 0 312.5 
10.5 V  6.25 V
R L (max) 
212.5 
0.02 A
Vbias 1.25 V
I 0 0.02 A 20 mA
Assumes OP AMP has sufficient
current output
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Signal Conditioning-Bridge Circuits
Dc bridges (Wheatstone bridges) Used to detect small
resistance changes in sensors. Typically used with sensors that
measure force, temperature, and pressure.
Rs = sensor R
R3= variable resistor used to balance bridge
When bridge is balanced:
Iab = 0 since Va = Vb
so I1Rs = I2R3 and I1R2 = I2R4
Rs
R
 3
R2
R4
Solve for
Rs
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Rs 
R3
R2
R4
DMU, ECEG-5323: Instrumentation
Engineering
Adjust R3 until Iab = 0
compute Rs
53
Bridge Use Methods
• There are two operating modes for a dc bridge:
balanced (null) and unbalanced
Null Mode - adjust R3 variable resistor until Iab = 0.
Need automatic nulling circuit for automatic
operation.
Unbalanced Mode - insert sensor and null bridge for
sensor measurement. When initial value
of sensor changes measure difference in
voltage. Bridge only balanced at one
point
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Unbalanced Bridge Operation
• Note the unbalanced bridge shown below. U1 and U2
provide high-Z input. Circuit gain provided by U3
using the following formula.
Rs
U1
Rf
Ra
U3
Vo 
Rf
(Vb  Va )
Ra
Ra
Rf
U2
Find expression for bridge equation. in terms of the change
in sensor resistance Rs.
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Unbalanced Bridge Analysis
• Bridge Circuit Find the voltage V
ba
in terms of the resistors
 R2 
Va 
 Vdc
 Rs  R2 
 R4 
Vb 
 Vdc
 R3  R4 
 R4
R2 
Vb  Va 

 Vdc
R

R
R

R
 3
4
s
2
Rbal 
R2R3
R4
Normalize Vba by dividing by
supply V.
Find common denominator
Vb  Va  R4
R2  R4 (Rs  R2 )  R2 (R3  R4 )


 
Vdc
(R3  R4 )(Rs  R2 )
 R3  R4 R s  R2 
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Unbalanced Bridge Analysis(...)
• Expand terms and simplify
Vb  Va R4Rs  R4R2  R2R3  R2R4
R4Rs  R2R3


Vdc
(R3  R4 )(Rs  R2 )
(R3  R4 )(Rs  R2 )
From the previous balance equation
RbalR4
R2
R3
Substitute these equations into the above relationship
Vb  Va
R4Rs  RbalR4

Vdc
(R3  R4 )(Rs  RbalR4 / R3 )
2
(R3  R4 )(Rs  RbalR4 / R3 ) R3Rs  R4Rs  RbalR4  RbalR4 / R3
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57
Unbalanced Bridge Analysis(...)
• Combine the past two equations and clear R3 from the
denominator.
Vb  Va
R 3 R 4 (R s  R bal )
 2
2
Vdc
R 3 R s  R 3 R 4 R s  R 3 R 4 R bal  R bal R 4
Now let R4=R3 and simplify further
2
2
Vb  Va
R (R s  R bal )
R 3 (R s  R bal )
 23
 2
2
2
2
Vdc
R 3 (2(R s  R bal ) R 3 R s  R 3 R s  R 3 R bal  R bal R 3
2
2
Vb  Va
R 3 (R s  R bal )
R 3 (R s  R bal )


2
2
2
Vdc
2R 3 R s  2R 3 R bal R 3 (2(R s  R bal ))
Vb  Va
(R  R bal )
 s
Vdc
2( R s  R bal )
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Desired
Relationship
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58
Unbalanced Bridge Analysis(...)
• Equation below relates the output voltage change (per
volt of supply V) to the change in sensor resistance.
Original Bridge
Vb  Va
(R  R bal )
 s
Vdc
2( R s  R bal )
When R3=R4
Make
Equal
Determine the output voltage
linearity compared to the sensor
resistance change.
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Instrumentation Amps with High Impedance Input
• Two-stage circuit
 E2  E1  2 R1
A v1  
1

 V 2  V1 R2
V0
R4
A v2 

E2  E1 R3
V1
U1
U1 and
U2
Noninvertin
g
Hi-Z
input
R5 = R1
V2
R1
E
1
R4
 R4 
*

 R3 
R3
R2
U3
R5
U2
R6
E2
R7
Overall circuit gain
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 2 R1 
A v 1( A v 2 )  
 1
 R2

U3 = basic
differential amp
configuration with
R3=R6 and R4=R7
 2 R1   R4 
V0 
 1 *   *  V 2  V1
 R2
  R3 
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Unbalanced Bridge Analysis Example
• ex
2.) Plot the output voltage over the range of operation at 5 ohm increments for
both designs a.) R3=R4 = 1000 ohms b.) R3=120 and R4 = 1000 ohms
3.) Find the zero based linear approximation of the bridge output responses.
4.) Determine the maximum non-linearity for each case
5.) Determine the gain required for the instrumentation amplifier gain if a span
of 15 V dc is required.
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Unbalanced Bridge Analysis Example(…)
xample
• eSolution (Part 1a) Balance bridge with R3=R4=1000 ohms
Balance
Equation
120
10 Vdc
1000
ohms
???
Rs R3

R2 R 4
Plug in known values
120 1000

R2
1000
R2 120
Ans
xample Solution (Part 1b) Balance bridge with R3= 120 ohms R4=100
Rs R 3

R2 R4
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120 120

R2
1000
R2 1000
DMU, ECEG-5323: Instrumentation
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Ans
62
Unbalanced Bridge Analysis Example(…)
xample
• eSolution (Part 2a) plot output V with R3=R4=1000 ohms
Vb  Va 
R bal 
 R s  R bal 
Vdc
2 R s  R bal 
R 2R 4
120(1000)

120
R3
1000
Rbal = 120
Plot values of Rs from 90 to 150 with Excel or MathCAD using
the equation below
Vd Vb  Va 
Sample
calculation
Rs =90
ohms
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 R s  120 10
2 R s  120 
  90  120 
 2 90  120 
Vd  
 10V


Non-linear output
Vd   0.714V
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Unbalanced Bridge Analysis Example(…)
xample
• eSolution (Part 2b) plot output V with R3= 120 R4=1000 ohm
Use the alternative formula written as function of rs, sensor resistance
R4 rs  Rbal


 V
Vd1 rs   
RbalR4   dc


  R3  R4  rs  R  
3 


Less output voltage than
first case
R R
(1000 )(120 )
Wher R bal  2 3 
120 
R
1000

4
e


 1000
   r s  120 10V
Substitute
V d  r s  
Values
 1120
   r  1000


Sample
Calculatio
n
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Vd1 
 1000
   90 
 1120
   90
s

120  10V
 1000
 
Vd1   0.246V
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Unbalanced Bridge Analysis Example(…)
xample
• e Solution (Part 3) Find zero based linear approximation. Assum
asses through zero and the average of the end points
For bridge with R3=R4=1000 ohms
at Rs = 90 Vd = -0.714
at Rs =150 Vd = 0.556
Average max value (|-0.714|+|0.556|)/2 = 0.635
For bridge with
Use two data points:
Rs1=120 Vd1 = 0
R3=R4=1000
ohms
Rs2=150 Vd2=Vave =0.635
Use twopoint form
of line to
Non-linearity
find
( Vd 2  Vd1 )
(Vd  Vd1 ) 
equation(R s 2  R s1 ) (rs  R s1 ) Increase as
(0.635  0)
( Vd  0) 
( rs  120)
(150  120)
Vd 0.021167 rs  2.54
Rs moves
from balance
point
Equation
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Unbalanced Bridge Analysis Example(…)
at Rs1 = 90 Vd1 = -0.246
e with R3= 120, R4=1000 ohms
For•bridge
at Rs2 =150 Vd2 = 0.233
Average max value (|-0.246|+|
0.233|)/2 = 0.2395
(V  V )
( Vd  Vd1 ) 
d2
d1
(rs  R1 )
(R2  R1 )
(0.2395  0)
( Vd  0) 
(rs  120)
(150  120)
Vd 0.007983rs  0.958
Equation
Less output voltage but greater linearity
Dc bridge approximately linear for small
deviations around balance point
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Unbalanced Bridge Analysis Example(…)
Example
Solution (Part 4) Determine the maximum non• e
linearity for each bridge.
Take difference between actual bridge output and the zero
based lines. Maximum occurs at either end of the graph.
termine the percent non-linearity using the following formula
Output % Non-linearity
8
% Non-linearity
6
%error 
4
| Vdl  Vd |
100%
| 2 Vdl (max) |
Where Vdl(max) max linear output
2
0
90
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Non-linearity greatly
100
110
120
130
140
150
improved by making R3
Sensor Resistance (Ohms)
R3=R4
equal to nominal
R3=120, R4=1000
resistive sensor value
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Unbalanced Bridge Analysis Example(…)
xample
• eSolution (Part 5) Determine the gain necessary for a span of
Use average
value of Vd to
compute gain
For R3 =R4=1000 ohms
Average max value
Rf
Vb-Va =
Vd
Vo 
Ra
Rf
(Vb  Va )
Ra
(|-0.714|+|0.556|)/2 = 0.635 V
For R3=120 and R4=1000 ohms
Average max value
Instrumentation Amplifier
Gains
(|-0.246|+|0.233|)/2 = 0.2395 V
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DAC for Signal Conditioning
• A DAC, inputs a binary number and outputs an analog voltage
or current signal. In block diagram form, it looks like this:
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DAC for Signal Conditioning(…)
•
is a variation on the inverting summer op-amp circuit. If you recall,
the classic inverting summer circuit is an operational amplifier
using negative feedback for controlled gain, with several voltage
inputs and one voltage output. The output voltage is the inverted
(opposite polarity) sum of all input voltages:
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DAC for Signal Conditioning(…)
• The R/2R DAC
An alternative to the binary-weighted- input DAC is the so-called R/2R
DAC, which uses fewer unique resistor values. A disadvantage of the
former DAC design was its requirement of several different precise input
resistor values: one unique value per binary input bit.
6 bit binary weighted
DAC
Simulation result using
SPICE
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ADC for Signal Conditioning
•
An ADC inputs an analog electrical signal such as voltage or current and outputs a
binary number. In block diagram form, it can be represented as such:
• Flash
ADC
Also called the parallel A/D converter, this circuit is the simplest to
understand. It is formed of a series of comparators, each one comparing the
input signal to a unique reference voltage. The comparator outputs connect to
the inputs of a priority encoder circuit, which then produces a binary output.
The following illustration shows a 3-bit flash ADC circuit:
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ADC for Signal Conditioning(…)
• V
i ref is a stable reference voltage
provided by a precision voltage
regulator as part of the converter
circuit, not shown in the
schematic. As the analog input
voltage exceeds the reference
voltage at each comparator, the
comparator outputs will
sequentially saturate to a high
state. The priority encoder
generates a binary number based
on the highest-order active input,
ignoring all other active inputs.
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ADC for Signal Conditioning(…)
•
Digital ramp ADC
Also known as the stairstep-ramp, or simply counter A/D converter,
this is also fairly easy to understand but unfortunately suffers from
several limitations. The basic idea is to connect the output of a freerunning binary counter to the input of a DAC, then compare the analog
output of the DAC with the analog input signal to be digitized and use
the comparator's output to tell the counter when to stop counting and
reset. The following schematic shows the basic idea:
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ADC for Signal Conditioning(…)
• Slope (integrating) ADC
It is possible to avoid using a DAC if we substitute an analog ramping circuit
and a digital counter with precise timing.
The is the basic idea behind the so-called single-slope, or integrating ADC.
Instead of using a DAC with a ramped output, we use an op-amp circuit
called an integrator to generate a sawtooth waveform which is then compared
against the analog input by a comparator. The time it takes for the sawtooth
waveform to exceed the input signal voltage level is measured by means of a
digital counter clocked with a precise- frequency square wave (usually from a
crystal oscillator). The basic schematic diagram is shown here:
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Practical considerations of ADC circuits
.
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Practical considerations of ADC circuits(…)
. Because the ADC is fixed at 10 bits of binary data output, it will interpret any
given tank level as one out of 1024 possible states. To determine how much
physical water level will be represented in each step of the ADC, we need to
divide the 40 feet of measurement span by the number of steps in the 0-to1024 range of possibilities, which is 1023 (one less than 1024). Doing this,
we obtain a figure of 0.039101 feet per step. This equates to 0.46921 inches
per step, a little less than half an inch of water level represented for every
binary count of the ADC
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Practical considerations of ADC circuits(…)
.
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Practical considerations of ADC circuits(…)
. Another important consideration of ADC circuitry is its sample frequency, or
conversion rate.
This is simply the speed at which the converter outputs a new binary number.
Like resolution, this consideration is linked to the specific application of the
ADC.
If the converter is being used to measure slow-changing signals such as level in
a water storage tank, it could probably have a very slow sample frequency and
still perform adequately. Conversely, if it is being used to digitize an audio
frequency signal cycling at several thousand times per second, the converter
needs to be considerably faster.
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Q?
Thank you!!!
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