Advanced Instrumentation
and Signal Conditioning
DR. SOUGATA KAR
Purpose of Measurement Systems
Input
True value
of variables
Measurement
System
Process,
machine or
system being
measured
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Output
Measured value
of variables
Observer
2
Measurement System
Information
variables
Jet fighter
Chemical reactor
Human heart
Car
A process can be defined as a
system which generates information
Driver: velocity, acceleration
Plant operator: temp. pressure
Nurse: heart rate, blood pressure
Purpose of a measurement system
to link the observer to the process.
True Value: Input to the measurement system
Measured variable: Information variable
Measured value: Output of the measurement
system
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Measurement System
Accuracy: defined as the closeness of the measured value to the true value.
In a real system accuracy is quantified by:
E= Measured value – True value
E= System output – System input
Structure of a instrumentation System
4 Elements
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Structure of Measurement System
• In contact with the system
• Its o/p depend on the variable
to be measure
• Thermocouple: e.m.f. depends on
temp.
• Strain Gauge: Resistance depends on
strain
• If more than one element, the element
in contact with the process is called
primary sensing element, others
secondary sensing element.
• It takes the o/p of the sensing
element and converts it to a more
suitable form for further processing,
usually d.c. voltage, d.c. current or
frequency
• Deflection bridge: converts an
impedance change into voltage
signal
• Amplifier: amplifies mV to Volt.
• Oscillator: impedance change to
variable frequency
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Structure of Measurement System
• It takes the output of the conditioning
element and provide a more suitable form
for presentation.
• ADC and signal processors
• ADC converts the voltage signal to digital
form more suitable for display and data
interpretation by a computer
• Computer may calculate the measured
value from the digital data
• Computer can compute the mass of a gas
from the flowrate and density
• Can correct the sensing element
nonlinearity.
• Presents the measured value in a
suitable form that can be easily
recognised by the observer
• Simple pointer-scale indicator
• Chart recorder
• Alphanumeric display
• Visual display unit
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Structure of Measurement System
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Static Characteristics
Static or steady-state characteristics, the output O and
input I of an element when I is either at a constant
value or changing slowly.
Systematic characteristics: that can be exactly quantified by mathematical or
graphical means.
Range: The input range of an element is specified by the minimum and maximum
values of I, i.e. IMIN to IMAX. Similarly for output OMIN to OMAX.
Span: Span is the maximum variation in input or output, i.e. input span is IMAX – IMIN,
and output span is OMAX – OMIN
Linearity: An element is said to be linear if corresponding values of I and O lie on a
straight line. The ideal straight line connects the minimum point A(IMIN, OMIN ) to
maximum point B(IMAX, OMAX) and therefore has the equation:
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Static Characteristics
Example: A pressure transducer
Input range: 0-104 Pa, Output range 4-20mA
Input span: 104 Pa, Output span: 16mA
Ideal straight line characteristics:
Non-linearity: In many cases the straight-line relationship is not obeyed and the
element is said to be non-linear. It can be defined by a function N(I).
Non-linearity is often quantified in terms of max non-linearity (N), expressed as the
percentage of full scale deflection.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Static Characteristics
Example: for the pressure sensor if the
maximum difference between actual and
ideal straight-line output values is 2 mV and
output span is 100 mV, then the maximum
percentage non-linearity is 2% of f.s.d.
In many cases O(I ) and therefore N(I ) can be expressed as a polynomial in I:
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Static Characteristics
Example: For a thermocouple junction, the first four terms in the polynomial relating
e.m.f. E(T ), expressed in μV, and junction temperature T °C are:
for the range 0 to 400 °C. Since E = 0 μV at T = 0 °C and E = 20869 μV at T = 400 °C,
the equation to the ideal straight line is:
the non-linear correction function is:
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Static Characteristics
Sensitivity: This is the change ΔO in output O for unit change ΔI in input I, i.e. it is
the ratio ΔO/ΔI.
In the limit that ΔI tends to zero, the ratio ΔO/ΔI tends to the derivative dO/dI,
which is the rate of change of O with respect to I.
Sensitivity is the slope or gradient of the output versus input characteristics O(I ).
In thermocouple the gradient and therefore the sensitivity may vary with
temperature: at 100 °C it is approximately 35 μV/°C and at 200 °C approximately 42
μV/°C.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Static Characteristics
Hysteresis: For a given value of I, the output O may be different depending on
whether I is increasing or decreasing. Hysteresis is the difference between these two
values of O, i.e.
Again hysteresis is usually quantified in terms of the maximum hysteresis H
expressed as a percentage of f.s.d., i.e. span. Thus:
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Static Characteristics
Hysteresis is most commonly found
in instruments that contain springs,
such as the passive pressure gauge
Also occur in instruments that
contain electrical windings
formed round an iron core, due
to magnetic hysteresis in the
iron like LVDT and the rotary
differential transformer.
Dead space:
Dead space is defined as the range of different input values over which there is no change in
output value. Any instrument that exhibits hysteresis also displays dead space
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Static Characteristics
Resolution: Some elements are characterised by the output increasing in a series of
discrete steps or jumps in response to a continuous increase in input. Resolution is
defined as the largest change in I that can occur without any corresponding change
in O.
Resolution is defined in terms of the width ΔIR of the widest step;
Resolution also expressed as a percentage of f.s.d.
A common example is a wire-wound potentiometer; in response to a continuous
increase in x the resistance R increases in a series of steps, the size of each step
being equal to the resistance of a single turn. Thus the resolution of a 100 turn
potentiometer is 1%.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Static Characteristics
Drift:
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Static Characteristics
Environmental Effects: In general, the output O depends not only on the signal input
I but on environmental inputs such as ambient temperature, atmospheric pressure,
relative humidity, supply voltage, etc.
A modifying input IM causes the linear sensitivity of an element to change.
The sensitivity changes from: K to K + KMIM,
An interfering input II causes the straight line intercept or zero bias to change.
The zero bias changes from: a to a + KI II
O = KI + a + N(I ) + KMIMI + KI II
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Static Characteristics
Precision: Precision is a term that describes an instrument’s degree of freedom from
random errors. It defines the closeness of the readings if large no of readings are
taken. High precision does not imply anything about measurement accuracy.
Repeatability/Reproducibility: Repeatability describes the closeness of output
readings when the same input is applied repetitively over a short period of time,
with the same measurement conditions, same instrument and observer, same
location and same conditions of use maintained throughout.
Reproducibility describes the closeness of output readings for the same input when
there are changes in the method of measurement, observer, measuring instrument,
location, conditions of use and time of measurement.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Static Characteristics
Wear and ageing: These effects can cause the characteristics of an element, e.g. K
and a, to change slowly but systematically throughout its life.
One example is the stiffness of a spring k(t) decreasing slowly with time due to wear,
k(t) = k0 − bt
where k0 is the initial stiffness and b is a constant.
Another example is the constants a1, a2, etc. of a thermocouple, measuring the
temperature of gas leaving a cracking furnace, changing systematically with time
due to chemical changes in the thermocouple metals.
Tolerance: Tolerance is a term that is closely related to accuracy and defines the
maximum error that is to be expected in some value. tolerance describes the
maximum deviation of a manufactured component from some specified value.
Threshold: The minimum level of input for which there is a detectable change in
output is known as the threshold of the instrument.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Static Characteristics
Error bands: Sometimes manufacturer defines the performance of the element in
terms of error bands. Here the manufacturer states that for any value of I, the output
O will be within ±h of the ideal straight-line value OIDEAL. Here an exact or systematic
statement of performance is replaced by a statistical statement in terms of a
probability density function p(O).
Here the area of the rectangle is equal to unity: this is the probability
of O lying between OIDEAL − h and
OIDEAL + h.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Identification of Static Characteristics - Calibration
Calibration: The static characteristics of an element can be found experimentally by
measuring corresponding values of the input I, the output O and the environmental
inputs IM and II, when I is either at a constant value or changing slowly. This type of
experiment is referred to as calibration, and the measurement of the variables I, O,
IM and II must be accurate if meaningful results are to be obtained. The instruments
and techniques used to quantify these variables are referred to as standards.
Ultimate or primary measurement standards for key physical variables such as time,
length, mass, current and temperature are maintained at the National Physical
Laboratory (NPL), UK.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Identification of Static Characteristics - Calibration
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Calibration - Experimental Measurements
Experimental measurements and evaluation of results:
O versus I with IM = II = 0
Ideally this test should be held under ‘standard’ environmental conditions so that IM
= II = 0; if this is not possible all environmental inputs should be measured. I should
be increased slowly from IMIN to IMAX and corresponding values of I and O recorded
at intervals of 10% span (i.e. 11 readings), allowing sufficient time for the output to
settle out before taking each reading. A further 11 pairs of readings should be taken
with I decreasing slowly from IMAX to IMIN.
Computer software regression packages are readily available which fit a polynomial
These packages use a ‘least squares’ criterion. If di is the deviation of the polynomial
value O(Ii) from the data value Oi, then di = O(Ii) – Oi.
The program finds a set of coefficients a0, a1, a2, etc, such that the sum of the
squares of the deviations
If hysteresis two polynomials:
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Calibration - Experimental Measurements
O versus IM, II at constant I:
 We first need to find which environmental inputs are interfering, i.e. which affect
the zero bias a.
 The input I is held constant at I = IMIN, and one environmental input is changed by
a known amount, the rest being kept at standard values.
 If there is a resulting change ΔO in O, then the input II is interfering and the value
of the corresponding coefficient KI is given by KI = ΔO/ΔII.
 If there is no change in O, then the input is not interfering; the process is
repeated until all interfering inputs are identified and the corresponding KI values
found.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Calibration - Experimental Measurements
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Dynamic characteristics
If the input signal I to an element is changed suddenly, from one value to another, then the
output signal O will not instantaneously change to its new value.
For example, if the temperature input to a thermocouple is suddenly changed from 25 °C to
100 °C, some time will elapse before the e.m.f. output completes the change from 1 mV to 4
mV.
The ways in which an element responds to sudden input changes are termed its dynamic
characteristics, and these are most conveniently summarised using a transfer function G(s).
A linear time invariant system can be represented as:
If only step changes in the measured quantity:
If x1(t) produces y1(t) and x2(t) produces y2(t) then their scaled and summed response
where and are a1 and a2 are real scalars.
Time invariant system: if x(t) produces y(t), then x(t-T) should produce y(t-T).
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Dynamic characteristics
Zero order instrument: If all the coefficients a1 . . . an other than a0 are assumed
zero, then: a0q0 = b0qi
or
q0=b0qi/a0=Kqi
where K is a constant known as the instrument sensitivity as defined earlier.
Following a step change in the measured quantity at time t, the instrument output
moves immediately to a new value at the same time instant t.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Dynamic characteristics
First order instrument: If all the coefficients a2 . . . an except for a0 and a1 are
assumed zero then:
1
0
0
0
0
𝑖
τ
0
While the above differential equation is a perfectly adequate description of the
dynamics of the sensor, it is not the most useful representation. The transfer
function based on the Laplace transform of the differential equation provides a
convenient framework for studying the dynamics of multi-element systems.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Dynamic characteristics
First order instrument:
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Dynamic characteristics
First order instrument:
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Dynamic characteristics
Second order instrument/system:
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Dynamic characteristics
Second order instrument/systems:
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Dynamic characteristics
Second order instrument/systems:
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Dynamic characteristics
Second order instrument/systems:
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Sensing Elements
Broadly Classified: based on outputs: Electrical, Mechanical, Thermal, Optical
Electrical output Sensor: Active and Passive
Active Sensor: Electromagnetic, thermoelectric, Piezoelectric, does not need
power supply
Passive Sensor: Requires external power supply to give voltage or current o/p
Resistive, Capacitive, Inductive
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Resistive Sensing Elements: Potentiometer
•
•
•
•
Linear and angular displacement measurement,
Resistive material is placed on the former, resistance/unit length constant.
Graphite, Carbon particles, Ceramic/metal mix, Cermet
(a) linear (rectilinear), (b) angular (rotary) displacement.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Resistive Sensing Elements: Potentiometer
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Loading Effects
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Loading Effects
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Loading Effects
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Resistive Sensing Elements
The choice of a potentiometer for a given application involves four main
parameters:
Maximum travel dT, θT : Depends on range of displacement to be measured, e.g. 0
to 5 cm, 0 to 300°.
Supply voltage VS: Set by required output range, e.g. for a range of 0 to 5 V d.c., we
need VS = 5 V d.c.
Resistance RP: For a given load RL , choose RP to be sufficiently small compared with
RL so that maximum non-linearity is acceptable..
Power rating Wmax: Wmax should be greater than actual power VS2/RP produced in
RP
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Resistive Sensing Elements
In wire wound potentiometers the resistive track, of total length dT or θT, consists of
n discrete turns of wire. The resistance between A and B therefore increases in a
series of steps for a smooth continuous increase in displacement d or θ. The
corresponding resolution error is therefore dT /n, θT /n.
In conductive plastic film potentiometers the track is continuous so that there is
zero resolution error and less chance of contact wear than with wire wound; the
temperature coefficient of resistance is, however, higher.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Resistive Sensing Elements: Resistance Temperature Detector (RTD)
• Material: metal : Nickel, Copper, Platinum
• Semiconductor sensors: Oxides of Chromium, manganese, iron, cobalt.
• Resistance of most metals increases reasonably linearly with temperature in the
range −100 to +800 °C.
• Replace thermocouples because of higher accuracy and repeatability.
• Cheaper metals, notably nickel and
copper, are used for less demanding
applications.
• Platinum is preferred as it is chemically
inert, has linear and repeatable
resistance/temperature characteristics,
and can be used over a wide
temperature range (−200 to +800 °C)
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Resistive Sensing Elements: Thermistor
• Material: n-type: Fe3O3 doped with Ti, electron carrier, NTC
• P-type: NiO with Li doping , Barium Titanate BaTiO3, holes carrier, PTC
• Highly non-linear
where Rθ is the resistance at
temperature θ kelvin; K and β are
constants for the thermistor.
Glass
enclosures
where Rθ1 Ω is the resistance at
reference temperature θ1 K, usually θ1 =
25 °C = 298 K.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Resistive Sensing Elements: Strain gauges
Metal and semiconductor resistive strain gauges
Elastic modulus, Young’s Modulus=E=stress/strain=(F/A)/(Δl/l) (N/m2)
ν Poisson’s ratio 0.25 – 0.4 for metals
A strain gauge is a metal or semiconductor element whose resistance changes when
under strain.
In general with strain gauges ρ (Ω-m), l and A can change if the element is strained,
so that the change in resistance ΔR is given by:
Pouillet’s Law
Back plate Pasted
The ratio Δl/l is the longitudinal strain eL
in the element.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Resistive Sensing Elements
Since cross-sectional area A = wt
We now define the gauge factor G of a strain gauge
by the ratio (fractional change in resistance)/(strain),
i.e.
For most metals ν ≈ 0.3, and the term (1/e) (Δρ/ρ) representing strain-induced
changes in resistivity (piezoresistive effect) is small (around 0.4), so that the overall
gauge factor G is around 2.0. A popular metal for strain gauges is the alloy ‘Advance’;
this is 54% copper, 44% nickel and 1% manganese. This alloy has a low temperature
coefficient of resistance (2 × 10−5/°C) and a low temperature coefficient of linear
expansion.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Resistive Sensing Elements
• Gauge factor 2.0 to 2.2
• Unstrained resistance 120 ± 1 Ω
• Linearity within ±0.3%
• Maximum tensile strain +2 × 10−2
• Maximum compressive strain −1 × 10−2
• Maximum operating temperature 150 °C.
o Semiconductor gauges: piezoresistive term (1/e) (Δρ/ρ) large so large gauge
factors.
o Common material: silicon doped with small amounts of p-type or n-type material.
Gauge factors: between +100 and +175 are common for p-type silicon,
between −100 and −140 for n-type silicon.
o A negative gauge factor means a decrease in resistance for a tensile strain.
o Advantage of greater sensitivity to strain than metal ones, but have the
disadvantage of greater sensitivity to temperature changes.
o Typically a rise in ambient temperature from 0 to 40 °C causes a fall in gauge
factor from 135 to 120.
o Also the temperature coefficient of resistance is larger, so that the resistance of a
typical unstrained gauge will increase from 120 Ω at 20 °C to 125 Ω at 60 °C.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Resistive Sensing Elements
Metal oxide sensors: semiconducting properties, affected by the presence of
gases. Resistance of chromium titanium oxide: affected by reducing gases such as
carbon monoxide (CO) and hydrocarbons.
Here oxygen atoms near the surface react with reducing gas molecules; this
reaction takes up conduction electrons so that fewer are available for conduction.
This causes a decrease in electrical conductivity and a corresponding increase in
resistance.
The resistance of tungsten oxide: affected by oxidising gases such as oxides of
nitrogen (NOx ) and ozone.
Here atoms near the surface react with oxidising gas molecules; this reaction takes
up conduction electrons, again causing a decrease in electrical conductivity and an
increase in resistance with gas concentration.
To aid the oxidation/reduction process, these sensors are operated at elevated
temperatures well above ambient temperature.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Resistive Sensing Elements
To aid the oxidation/reduction process, these sensors are operated at elevated
temperatures well above ambient temperature.
Al2O3
Typical construction of a metal oxide sensor using thick film technology. This consists
of an alumina substrate with a film of oxide printed on one side and a platinum
heater grid on the other.
A typical NOX sensor has an ambient temperature range of −20 °C to +60 °C and
operating power of 650 mW. The resistance is typically 6 kΩ in air, 39 kΩ in 1.5 ppm
NO2 and 68 kΩ in 5.0 ppm NO2. A typical CO sensor has an ambient temperature
range of −20 °C to +60 °C and an operating power of 650 mW. The resistance is
typically 53 kΩ in air, 85 kΩ in 100 ppm CO and 120 kΩ in 400 ppm CO.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Capacitive Sensing Elements
The simplest capacitor or condenser consists of two parallel metal plates separated
by a dielectric or insulating material. The capacitance of this parallel plate capacitor
is given by
where ε0 is the permittivity of free space (vacuum) of magnitude 8.85 pF/m, ε is the
relative permittivity or dielectric constant of the insulating material, A m2 is the area
of overlap of the plates, and d m is their separation. We see that C can be changed
by changing either d, A or ε ; Next Figures shows capacitive displacement sensors
using each of these methods.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Capacitive Sensing Elements
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Capacitive Sensing Elements
The deformation of the diaphragm means that the average separation of the plates is
reduced. The resulting increase in capacitance ΔC is given by
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Capacitive Sensing Elements
C1 – C2 = εε0A[1/d+x – 1/d-x]
= εε0A[2x/d2-x2]
~ εε0A[2x/d2] if x<<d
C1 + C2 = εε0A[1/d+x + 1/d-x ]
= εε0A[2d/d2-x2]
~ εε0A[2x/d2] if x<<d
C1
C2
No assumption required
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Capacitive Sensing Elements: Humidity Sensor
Polymer Dielectric (C8H8 )n
Polystyrene (2.5)
Vinyl Chloride (2.8)
Thin-film capacitive humidity sensor. The dielectric is a polymer which has the ability to
absorb water molecules; the resulting change in dielectric constant and therefore capacitance
is proportional to the percentage relative humidity of the surrounding atmosphere. One
capacitor plate, a layer of tantalum (Ta) deposited on a glass substrate; the layer of polymer
dielectric is then added, followed by the second plate, which is a thin layer of chromium. The
chromium layer is under high tensile stress so that it cracks into a fine mosaic which allows
water molecules to pass into the dieletric. A sensor of this type has a input range of 0 to 100%
RH, a capacitance of 375 pF at 0% RH and a linear sensitivity of 1.7 pF/% RH. The capacitance–
humidity relation is therefore the linear equation:
C = 375 + 1.7 RH pF
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Inductive Sensing Elements
where l is the total length of the flux path, μ is the relative permeability of the circuit
material, μ0 is the permeability of free space = 4π × 10−7H/m and A is the crosssectional area of the flux path.
Core separated into two parts by an air gap of variable width. The total reluctance of the
circuit is now the reluctance of both parts of the core together with the reluctance of the air
gap. Since the relative permeability of air is close to unity and that of the core material many
thousands, the presence of the air gap causes a large increase in circuit reluctance and a
corresponding decrease in flux and inductance. Thus a small variation in air gap causes a
measurable change in inductance so that we have the basis of an inductive displacement
sensor.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Inductive Sensing Elements
The length of an average, i.e.
central, path through the core is πR
and the cross-sectional area is πr2,
giving:
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Inductive Sensing Elements
Above equation is applicable to any variable reluctance displacement sensor; the
values of L0 and α depend on core geometry and permeability. We see that the
relationship between L and d is non-linear.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Inductive Sensing Elements
Problem of non-linearity is often overcome by using the push-pull or differential
displacement sensor. This consists of an armature moving between two identical
cores, separated by a fixed distance 2a. The relationship between L1, L2 and
displacement x is still non-linear, but if the sensor is incorporated into the a.c.
deflection bridge of Figure 9.5(b), then the overall relationship between bridge out
of balance voltage and x is linear.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Inductive Sensing Elements
Linear Variable Differential
Transformer (LVDT)
displacement sensor
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Inductive Sensing Elements
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Inductive Sensing Elements
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Inductive Sensing Elements
LVDT displacement sensors are available to cover ranges from ±0.25 mm to ±25 cm.
For a typical sensor of range ±2.5 cm, the recommended VP is 4 to 6 V, the
recommended f is 5 kHz (400 Hz minimum, 50 kHz maximum), and maximum
nonlinearity is 1% f.s.d. over the above range.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Inductive Sensing Elements
Linear Variable Differential Transformer (LVDT)
displacement sensor
Phase sensitive demodulator based on (a) a half-wave rectifier and (b) full-wave
rectifier
Advantage
Frictionless (no physical contact between the movable core and coil structure)
Theoretical infinite resolution, resolution limited by the external electronics
Isolation of exciting input and output (transformer action)
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
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Thermoelectric sensing elements
The Seebeck effect is the conversion of temperature differences directly into electricity and is
named after the Baltic German physicist Thomas Johann Seebeck.
The Peltier effect is the presence of heating or cooling at an electrified junction of two
different conductors and is named after French physicist Jean Charles Athanase Peltier.
In many materials, the Seebeck coefficient is not constant in temperature, and so a spatial
gradient in temperature can result in a gradient in the Seebeck coefficient. If a current is
driven through this gradient then a continuous version of the Peltier effect will occur. This
Thomson effect was predicted and subsequently observed by Lord Kelvin in 1851. It describes
the heating or cooling of a current-carrying conductor with a temperature gradient.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
64
Thermoelectric sensing elements
Law of
homogeneous
circuits
Law of intermediate
metals
Law of intermediate
metals
Law of intermediate
temperatures
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
65
Thermoelectric sensing elements
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
66
Thermoelectric sensing elements
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
67
Thermoelectric sensing elements
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
68
Thermoelectric sensing elements
Thermopile
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
69
Thermoelectric sensing elements
Automatic reference junction compensation circuit (ARJCC)
Metal resistance temperature sensor incorporated into a deflection bridge circuit
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
70
Elastic sensing elements
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
71
Elastic sensing elements
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
72
Elastic sensing elements
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
73
Elastic sensing elements
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
74
Elastic sensing elements
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
75
Elastic sensing elements
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
76
Elastic sensing elements
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
77
Deflection Bridge
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
78
Resistive Deflection Bridge
POWER
for
Non-linearity
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
79
Resistive Deflection Bridge
for
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
80
Resistive Deflection Bridge
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
81
Resistive Deflection Bridge
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
82
Resistive Deflection Bridge
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
83
Resistive Deflection Bridge
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
84
Resistive Deflection Bridge
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
85
Resistive Deflection Bridge
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
86
Resistive Deflection Bridge
Vs
R
)(
)
4 R 0  R / 2
Vs R
1
 ( )(
)
4 R 0 1  R / 2 R 0
Vs R
 ( )(1  R / 2 R 0)
4 R0
Vs R 1 R 2
 (
 ( ) )
4 R0 2 R0
Vs R
V 0  ideal  ( )
4 R0
Vs R
ErrorVoltage  ( ) 2
8 R0
1 R
% Error  ( ) *100%  0.5*% Change in resistance
2 R0
V0 (
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
87
Resistive Deflection Bridge
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
88
Amplifying Bridge Output
Single Op-amp Amplifier
Instrumentation Amplifier
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
89
Linearization of Single Element Bridge
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
90
Linearization of Single Element Bridge
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
91
Linearization of Two Element Bridge
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
92
Linearization of Two Element Current Driven Bridge
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
93
Driving Remote Bridge
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
94
Driving Remote Bridge -3 wire Configuration
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
95
Driving Remote Bridge -6 wire Configuration
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
96
Remote Bridge -4 wire Current Driven Bridge
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
97
Piezoelectric Sensing Element
A piezoelectric material produces an electric charge when its subject to a force or
pressure. The piezoelectric materials such as quartz or polycrystalline barium
titanate, contain molecules with asymmetrical charge distribution. Therefore, under
pressure, the crystal deforms and there is a relative displacement of the positive and
negative charges within the crystal.
Material
Quartz: SiO2
Barium Titanate: BaTiO3
Lead Zirconate Titanate: PbZrxTiyO3
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Piezoelectric Sensing Element
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Piezoelectric Sensing Element
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Piezoelectric Sensing Element
q
d   2  1012 C / N
F
Charge Sensitivity
V
electrical  field
g
 t ~ 12  1013V  m / N Voltage Sensitivity
F
stress  applied
Wl
q
VWl V  Wl VC
d
F
d g





Ft
 Ft
F


A

 wl
t
t
  4 1011 F / m
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Piezoelectric Sensing Element
CN
RN
A

 wl
t
t
11
  4 10 F / m
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Piezoelectric Sensing Element
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Piezoelectric Sensing Element
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Piezoelectric Sensing Element
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Piezoelectric Sensing Element
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Piezoelectric Sensing Element
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Piezoelectric Sensing Element
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
108
Piezoelectric Sensing Element
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Piezoelectric Sensing Element
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Capacitive Sensors
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Capacitive Sensors
C 1  C 0  C
C 1  C 0  C
2C

 Vs
2C 0  CP
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Capacitive Sensors
C ( x, t )  C  C 0Cos(t )
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Synchronous Demodulation
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Capacitive Accelerometer
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Capacitive Accelerometer
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Capacitive Accelerometer
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Capacitive Accelerometer
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Signal-to-noise Issues
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Chopper Modulation
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Chopper Modulation
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Chopper Modulation
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Square-waves and Their Fourier Series
•
•
•
•
•
Depend on whether pulse or Square-wave
Also on whether amplitude variation
From 0-1 or ±1
For 0-1, C0 = ½ , a dc pulse at 0 freq.
For ±1, no signal at C0 means C0 = 0
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Chopper Modulation
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Chopper Modulation
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Analog Signal Processing
Measurand
Sensor
Conditioner
Excitation/Bias
Gain
Zero Drift
Filter
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Analog
Processor
ADC
AFE
Demodulation
Linearization
Compression
126
Analog Signal Processing
Measurand
Sensor
Conditioner
Analog
Processor
ADC
AFE
Basic Functions of AFE:
• Conversion: Sensor, ADC, Analog Processor
• Adaptation/Matching: Conditioner and Analog Processor: Amplitude, Level, Power,
Impedance, Terminals, Bandwidth
Dynamic range: Ratio of measurement range and the desired resolution.
Any stage for processing the signal from a sensor must have a dynamic range equal to or
larger than that of the measurand.
Example: To measure a temperature from 0 to 100OC with 0.1OC resolution, we need a
dynamic range of at least (100 – 0)/0.1 = 1000 (60 dB).
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
127
Analog Front-end
Hence a 10-bit ADC should be appropriate to digitize the signal because 210 = 1024.
A 10-bit ADC with input range is 0 to 10V, Resolution: 10 V/1024 = 9.8 mV.
If the sensor sensitivity is 10 mV/OC and is connected to the ADC, the 9.8 mV resolution for
the ADC will result in a 9.8 mV/(10 mV/OC) = 0.98OC resolution !!
In spite of having the suitable dynamic range, can not achieve the desired resolution in
temperature because the output range of our sensor (0 to 1 V) does not match the input
range for the ADC (0 to 10 V).
An amplifier with a gain of 10 would match the sensor output range to the ADC input range
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
128
Signal Classification
Signal & Measurement Range
• Signals classified according to their amplitude level, relationship between their
source terminals and ground, their bandwidth, and the value of their output
impedance.
• Signals lower than around 100 mV are considered to be low level and need
amplification.
• Larger signals may also need amplification depending on the input range of the
receiver.
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
129
Signal Classification
Single-Ended and Differential Signals
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
130
Signal Classification
Narrowband and Broadband Signals
A narrowband signal: A very small frequency range
relative to its central frequency. Narrowband signals
can be dc, or static, resulting in very low frequencies,
such as those from a thermocouple or a weighing
scale, or ac, such as those from an ac-driven
modulating sensor, in which case the exciting
frequency (carrier) becomes the central frequency
Broadband signals: Such as those from sound and
vibration sensors, have a large frequency range
relative to their central frequency. The value of the
central frequency is crucial; a signal ranging from 1
Hz to 10 kHz is a broadband instrumentation signal
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Differential Signals
131
Signal Classification
Low- and High-Output-Impedance Signals
The output impedance of signals determines the requirements of the input impedance
of the signal conditioner.
•
•
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
132
Signal Coupling
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
133
Signal Amplifier
Fully Differential Amplifier
Differential Amplifier
Single-ended
Single-ended to Differential Amplifier
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
134
Op-Amp Characteristics
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
135
Op-Amp Characteristics
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
136
Op-Amp Characteristics
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
137
Measurement of Offset Voltage
- +
Vout
- +
- +
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Measurement of Offset Voltage
- +
- +
VOS
Ideal
Op-amp
Ideal
Op-amp
VOS
Vout ??
=
VOS
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
- +
- +
Ideal
Op-amp
VOS
Ideal
Op-amp
Vout ??
Measurement of Offset Voltage
R2
R1
- +
Ideal
Op-amp
Vout ??
𝑂𝑆
VOS
R2
R1
𝑶𝑺
- +
VOS
R1
Ideal
Op-amp
Vout ??
R2
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
𝑂𝑆
Effect of Offset Voltage
R2
Signal Gain
R1
Vin
- +
Ideal
Op-amp
𝑂𝑈𝑇
Noise Gain
𝑖𝑛
𝑂𝑆
VOS
R2
R1
- +
Vin
Signal Gain
Ideal
Op-amp
VOS
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
𝑂𝑈𝑇
Noise Gain
𝑖𝑛
𝑂𝑆
Effect of Bias Current
R2
R1
Vin
IB1
IB2
Ideal
Op-amp
𝑂𝑈𝑇
𝑖𝑛
𝑩𝟏
1∗
𝟐
R2
R1
Vin
IB1
IB2
Ideal
Op-amp
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
𝑂𝑈𝑇
𝑖𝑛
1∗
Effect of Bias Current
R2
R1
IB1
Vin
V1
IB2
R3
Ideal
Op-amp
-IB2*R3
𝑶𝑼𝑻
𝑩𝟏
𝟏
𝟐
𝑩𝟐
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
𝒊𝒏
𝟏
𝟏
𝟏
Effect of Negative Feedback
R2
R1
AOL
VOUT
Vin
𝛃
𝛃
𝑶𝑳
Advantages:
• Gain Stability
• Input impedance
• Output impedance
)
)
• Bandwidth
• Noise
• Linearity
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
)
)
Effect of Negative Feedback
R2
R1
AOL
VOUT
Vin
𝑂𝐿
𝑂𝐿
𝑶𝑳
𝑶𝑳
𝑪𝑳
If AOL=20,000, ACL~1/
𝑶𝑳
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
𝑪𝑳
𝑶𝑳
Effect of Negative Feedback on Bandwidth
R2
R1
AOL
VOUT
Vin
ACL
𝑶𝑳
ACL*BWCL=AOL*BWOL
𝐂𝐋
𝐎𝐋
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Effect of Negative Feedback on I/P Impedance
Rin
Rout
Vout
AOL
Vin
Rout
Vin
+
Rin
Vout
-
Vin
𝑨𝑶𝑳 ∗ 𝑽𝒊𝒏
𝑖𝑛
𝑖𝑛 𝑖𝑛
𝑖𝑛
𝑖𝑛𝑓
𝑖𝑛
Rout
𝑖𝑛
𝑜𝑢𝑡
𝑖𝑛
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
+
-
Rin
+
-
+
- Vinf
𝛃𝑽𝒐𝒖𝒕
Vout
𝑨𝑶𝑳 ∗ 𝑽𝒊𝒏𝒇
Effect of Negative Feedback on I/P Impedance
Rin
Rout
Vout
AOL
Vin
Rout
Vin
+
Rin
Rout
Vout
-
𝑨𝑶𝑳 ∗ 𝑽𝒊𝒏
𝑥
x
𝑥
𝑜𝑢𝑡
out
Routf
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Rin
+
-
+
- V’
𝛃𝑽x
Ix
𝑨𝑶𝑳 ∗ 𝑽′
Vx
Effect of Negative Feedback on Noise
VN2
VN1
Vin
𝑂𝐿
𝑜𝑢𝑡
Vout
AOL
𝑂𝐿
𝑁1 ∗
Effect Open-loop gain variation on close-loop gain in feedback
𝐶𝐿
𝑂𝐿
CL
CL
𝑂𝐿
OL
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
𝑁2 ∗
Signal Classification
Reference point for voltage measurements
Common, Ground, Earth are different
!!!
Single ended voltage
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Signal Classification
Differential Voltage, floating
Differential Voltage, ground
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Signal Classification
Differential Voltage, in general
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Voltage Amplification
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Fully Differential Amplifier
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Fully Differential Amplifier
Ideal Differential Amplifier
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Fully Differential Amplifier
Figure of Merit
Common-mode Rejection Ratio
Exclusion Ratio
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Fully Differential Amplifier
Non-coupled Stages
𝐼𝐻
𝐼𝐷
𝐼𝐶
𝐼𝐷
𝐼𝐷
𝐼𝐻
𝐼𝐿
𝑂𝐻
1 𝐼𝐻
𝑂𝐿
2 𝐼𝐿
𝑰𝑫
𝑶𝑫
𝟏 𝑰𝑯
𝟏
𝑰𝑪
𝟐 𝑰𝑳
𝑰𝑫
𝟏
𝑰𝑪
𝟐
𝑰𝑪
𝑰𝑫
𝟐
𝟏
𝟐
𝑰𝑪
𝑰𝑫
𝑰𝑫
𝟏
𝟐
𝑶𝑪
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
𝟏
𝑰𝑪
𝟐
𝑰𝑫
𝟏
𝟐
𝑰𝑪
Fully Differential Amplifier
Effect of Impedances: Input Impedance
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Fully Differential Amplifier
Input Impedances: Differential
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Fully Differential Amplifier
Loading Effect
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Fully Differential Amplifier
Input Impedances: Common-mode
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Fully Differential Amplifier
Input Impedances: Common-mode
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Fully Differential Amplifier
Effect of Common-mode Input Impedances
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Fully Differential Amplifier
𝐼𝐷
VIH
𝐼𝐶
GDD1
Two Cascaded Systems
VID‘
GDC1
VIC‘
VIL
𝐼𝐷
GCC1
GCD1
GDD2
GDC2
VOD
GCC2
GCD2
VOC
𝐼𝐶
𝑰𝑫
𝟏 𝑰𝑫
𝑰𝑪
𝟏 𝑰𝑫
𝑶𝑫
𝟏 𝑰𝑪
𝟐 𝑰𝑫
𝑶𝑪
𝟏 𝑰𝑪
𝟐 𝑰𝑫
𝑶𝑫
𝟐
𝑫𝑫𝟏 𝑰𝑫
𝑫𝑪𝟏 𝑰𝑪
𝟐
𝑪𝑫𝟏 𝑰𝑫
𝑪𝑪𝟏 𝑰𝑪
𝑶𝑪
𝟐
𝑫𝑫𝟏 𝑰𝑫
𝑫𝑪𝟏 𝑰𝑪
𝟐
𝑪𝑫𝟏 𝑰𝑫
𝑪𝑪𝟏 𝑰𝑪
𝒆
𝑫𝑫𝟐
𝑫𝑫𝟏
𝑫𝑫𝟐
𝑫𝑪𝟏
𝑫𝑪𝟐
𝟐
𝑪𝑫𝟏
𝑪𝑪𝟏
𝟏
𝟏
𝑪𝟏 𝑫𝟏𝑪𝟐
𝟏 𝟏
𝟏
𝟏
𝟏 𝟐
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
≈
𝟐 𝑰𝑪
𝟐 𝑰𝑪
𝟏
𝟏
𝟏
+
𝑪𝟏 𝑫𝟏𝑪𝟐
𝟏
𝟏 𝟐
Fully Differential Amplifier
𝟏 𝟏
𝟏
𝒆
𝟏
𝟏
𝟏 𝟐
𝟏 𝟐
𝟏
𝟏
Now, Effective CMRR
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
𝟐
𝟐
For two non-coupled stages
Fully Differential Amplifier
Cascade Amplifier Stages
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Fully Differential Amplifier
R1
1
2
𝐷𝐷
R2
Vin
Vout
R1’
R2’
𝑹
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
1
2
1
2
𝑅
Two Buffer Stages
VIH
Ad1/
AC1
VOH
𝑑2
VIL
Ad2/
AC2
VOL
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
𝑑1
1
2
Instrumentation Amplifier
VIH
Ad1/
AC1
VOH
A
Ad2/
AC2
𝑫𝑫
GDD
𝑂𝐷
1
GDC=0
2
VID
R1
1
B
VIL
VID
R2
2
𝐼𝐻
𝑂𝐶
GCC=1
GCD
R2’
VIC
VOL
𝟐
𝟐
𝑫𝑫
𝟏
𝑫𝑪
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
𝑪𝑪
𝟐
Instrumentation Amplifier
VIH
Ad1/
AC1
VOH
R4
R2
R3
R1
Ad2/
AC2
VIL
𝑻
𝑻
𝟏
𝟏
R3
VOUT
R4
R2’
VOL
𝟐
𝟏 𝟐
𝟏 𝑹
Ad1/
AC1
𝟏
𝑹
𝑹 𝑶𝑨
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
𝑹 𝑶𝑨
𝑹
Measurement of Offset Voltage
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Measurement of Offset Voltage
Internal Pins
Inverting Op Amp External Offset Trim Methods
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Auto-zero Techniques
1
2
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Offset Cancellation Techniques-Auto-zero
Open-loop Configuration
Sampling Phase:
S1=gnd, S2=gnd: QOUT=C*AVOS
Amplifying Phase:
S1=Vin, S2=Open: QOUT=C(VOUT-AVin+AVOS)
Charge Balance: VOUT = AVin
Closed-loop Configuration
Sampling Phase:
S1=closed, S2=Vin: Vin-=VOS, QC=C*(Vin-VOS)
Amplifying Phase:
S1=Open, S2=gnd: Vin-=VOS-Vin
Charge Balance: VOUT = AVin
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Switched Capacitor Circuits
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
175
Switched Capacitor Amplifier
𝑜
𝑖𝑛
If offset present:
𝑜
𝑖𝑛
𝑜𝑠
A
𝑜
Correlated Double Sampling (CDS)
𝑖𝑛
Removes Offset and low frequency as well
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Correlated Double sampling
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Switched Capacitor Circuits
RLC Implementation
Active RC Implementation
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Switched Capacitor Circuits
SC Implementation
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Switched Capacitor Circuits
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela
Switched Capacitor Amplifier
Dr. Sougata Kumar Kar, Dept. of ECE, NIT Rourkela