Unit –I Introduction S.Vivekanandan
Vivek_shanaras@yahoo.co.in

Contents :

Contents Definition and example for Sensor and transducer
General Concept and terminology of measurement system
Transducer classification
General input-output configuration
Static characteristics of measurement system
Dynamic Characteristics of measurement system
Calibration and standards
Error analysis in measurement system

Definition of Sensor :

Definition of Sensor Formal definition: “A device that receives and responds to a signal or stimulus” (American Heritage Dictionary of the English Language)
Informally, a sensor is a device that takes in information from the outside world. Based on the information, the sensor creates a signal on which a system can base a decision
In our case, a sensor will measure some physical quantity and convert it into some electrical signal (e.g., voltage, current)
Examples: Resistive sensor, optical sensors, physical sensor chemical, Biomedical sensors etc..

Definition for Transducer :

Definition for Transducer A Device which converts energy from one form to another form
A Device which converts a physical quantity into an electrical quantity
A Device which for the purpose of measurement converts the physical input quantity into electrical output quantity, its output-input and its output-time relationship being predictable to a known degree of accuracy at specified environmental conditions.
Examples : Thermocouple, LDR, LVDT, Piezo-electric transducer, Magnetostrictive transducer, capacitive and inductive transducer

Difference between Sensor and Transducer :

Difference between Sensor and Transducer A sensor is a device that responds to a physical stimulus (as heat, light, sound, pressure, magnetism, or a particular motion) and transmits a resulting impulse (a signal relating to the quantity being measured).
For example, certain sensors convert temperature into a change in resistance.
A transducer is a device that is actuated by power from one system and supplies power usually in another form to a second system.
For example a loudspeaker is a transducer that transforms electrical signals into sound energy. Often the words transducer and sensor are used synonymously.

Slide 6:

All sensors are Transducer
But
All Transducer are not Sensor

Concepts of Generalized Measurement system :

Concepts of Generalized Measurement system Sensor Signal
Conditioner End/display
Device Sensor Variable
Manipulation
Element Data
Transmission
Element Data
Presentation
Element Variable
Conversion
Element

Transducer Classification -1 :

Transducer Classification -1 Based on source of Energy Active Transducer: a transducer which does not require auxiliary energy source for conversion. (e.g. Thermocouple, piezoelectric, photovoltaic cell)
Passive Transducer: a transducer which requires auxiliary energy source for conversion. (e.g. LDR, Strain Gauge, LVDT)

Transducer Classification -2 :

Transducer Classification -2 Based on Parameter of Measurement Displacement transducer - (1)linear (2)Angular
Velocity transducer - (1)linear (2)Angular
Acceleration transducer - (1)Linear (2)Angular
Force
Temperature
Light
Time

Transducer Classification -3 :

Transducer Classification -3 Based on Transduction Principle Variable Resistance Transducers
Variable Inductance Transducers
Variable Capacitance Transducers
Piezoelectric Transducers
Hall effect Transducers
Magnetostrictive Transducers
Eddy Current Transducers
Fiber optic Transducers
IC sensors

General input and output configuration :

General input and output configuration Measuring
Instrument Desired input Interfering input Modifying input Output Example: Strain Gauge Desired Input – Strain, Interfering Input – Temperature ?R1 ?R2 Change in resistance due to strain Change in resistance due to temperature R = R + ?R

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Example: Thermistor Thermistor Temperature Light Strain Resistance Modifying Input Modifying input changes relationship between desired input and output and/or interfering input and output

Characteristics of measurement system :

Characteristics of measurement system Static Characteristics
Involves measurement of quantities that are either constant or vary slowly with time
Dynamic Characteristics
Applications like aerospace and bio-logical inputs are subjected to vary with time

Static Characteristics :

Static Characteristics D A L R Re S T S H I P?

List of Static Characteistics :

List of Static Characteistics Static sensitivity
Linearity
Precision/Repeata-bility
Accuracy
Threshold
Drift, Zero Drift Stability
Resolution
Hysteresis
Range & Span
Input Impedance/ Loading effect

Input and Output Range :

Input and Output Range Input Range
the interval between the maximum and minimum admissible input range: Imax, Imin
Output Range
the interval between the maximum and minimum reachable output range:
Omax, Omin

Slide 17:

Span and Zero Zero: the system output corresponding to a zero input.

Slide 18:

Accuracy & Error Bands Error Bands ±h
manufacturer defined performance values
Error bands is an indication of accuracy in terms of a statistical density function.

Resolution :

Resolution Resolution is the smallest detectable incremental change of input that can be detected in output signal.
For any devices, their resolution is fixed.

Slide 20:

Sensitivity & Gain Sensitivity (Gain) is the rate of change in output corresponding to the rate of change in input dO/dI.
At different range, the sensitivity may be different a device dI dO

Slide 21:

Repeatability Inability of a sensor to represent the same valve under identical conditions.

Slide 22:

Bias (offset)
the residual error between the output and the true value after all possible compensations.
Drift
rate of change of the output with time NOT caused by input. Bias Drift True value Bias and Drift

Deadband :

Deadband Deadband (Dead Band)
range of input in which the output remains at 0: Xd i o d

Hysteresis :

Hysteresis Hysteresisthe delay phenomenon in output due to energy dissipation.
The actual output is either smaller or greater than the theoretical output depends on increasing or decreasing in input.

Non-Linearity :

Non-Linearity

Dynamic Characteristics :

Dynamic Characteristics Speed of Response
The rapidity with which a measurement system responds to changes in the measured quantity
Dynamic error
Difference between the true value of the quantity changing with time and the value indicated by the measurement system
Fidelity
Degree of which a measurement system indicates changes in the measured quantity without any dynamic error

Dynamic analysis of measurement system :

Dynamic analysis of measurement system Time domain Analysis
Time is used as an independent variable
inputs is applied to the system and the behavior of the system is studied
For the purpose of analysis and design it is necessary to assume some basic types of input signal like step, ramp, parabolic, impuls
Frequency domain Analysis :
Frequency is used as an independent variable
Sinusoidal, cosine are input signals

ZERO ORDER INSTRUMENT :

ZERO ORDER INSTRUMENT ZERO ORDER SYSTEM (Example: Potentiometer)
Characterized by a zero order differential equation
Infinite bandwidth
Instantaneous response
Static gain / Sensitivity
ABSENCE OF ENERGY STORAGE ELEMENT
No time delay
Step response
Frequency response

FIRST ORDER INSTRUMENT :

FIRST ORDER INSTRUMENT FIRST ORDER SYSTEM (Example: Thermocouple without thermo well, mercury in glass thermometer)
Characterized by a first order differential equation
Static gain (which determines the dynamic response)
Time Constant ( which determines the dynamic response)
Settling time ( 2%, 5 % and 10 %)
Slope at time t=0 will be 1/ (time constant) { based on step response of I-order instrument)
Slope at time t=infinity will be zero.
PRESENCE OF ONE ENERGY STORAGE ELEMENT.

Contd.. :

Contd.. Step Response of first order Instrument
Ramp Response of first order Instrument
Impulse Response of first order Instrument
Terminated Ramp response of first order Instrument
Frequency Response ( 3 dB bandwidth of first order instrument {0,1/Time constant} –
first order instrument will behave like a low pass filter
FIRST PRINCIPLES MODEL ( TIME CONSTANT AND GAIN WILL BE FUNCTION OF PARAMETERS LIKE HEAT TRANSFER AREA, HEAT TRANSFER COEFFICIENT, MASS OF THE SENSING ELEMENT ETC.)
Estimation of first order parameters ( Gain and Time constant)
Least Square Method (pseudo inverse)
Number of Data Points (N)

SECOND ORDER SYSTEM :

SECOND ORDER SYSTEM SECOND ORDER SYSTEM (Example: Thermocouple with thermo well)
Characterized by a second order differential equation
Damping ratio ( Under damped -Galvanometers, over damped- T/C with thermo well, critically damped)
Damping ratio recommended – 0.6 to 0.7 ( Linear phase characteristics and amplitude ratio being constant)
Undamped Natural Frequency ( Larger natural frequency will have lower settling time)
Damped Natural Frequency
Rise time
Peak time
Settling time ( Percentage Tolerance)
Percentage Overshoot

SECOND ORDER SYSTEM – Cont’d :

SECOND ORDER SYSTEM – Cont’d Step Response of second order under damped, critically damped and over damped systems
Ramp Response of second order under damped, critically damped and over damped systems
Frequency Response second order under damped, critically damped and over damped systems
Slope at time t=0 will be zero for second order over damped system.
Estimation of Second order parameters from step response
Least Square Method ( pseudo inverse)
For all second order critically damped and over damped instruments the time for 73 % recovery will be at about t = 1.3* (tau1+tau2)
Higher order Instrument
As the order of the instrument increases the response of the instrument will become sluggish.

Calibration :

Calibration CALIBRATION is the method of checking the accuracy of an instrument
It is the comparison of two measurement devices or systems one of known uncertainty and other of unknown uncertainty to estimate the correct value of the unknown and its uncertainty

Why Calibration? :

Why Calibration? Result of Calibration enables the estimation of errors of measuring instrument or the assignment of values to mark or arbitrary scales
In many Instruments, suitable adjustments (range, span) are made during calibration in order to reduce the error
Calibration is an accredited laboratory enables to establish TRACEABILITY
When products are exported to other countries, they insist on traceability
In short calibration enhances CREDIBILITY in measurement Note: Traceability is a document able link between the accuracy of the Instrument and the highest level of standard as maintained by a national/international laboratory

Standards Standard is a physical representation of unit of measurement
Standard is a material measure, measuring instrument, reference material or system intended to define, realize, conserve, reproduce a unit in order to transmit them to other instruments by comparison

Classification of Standards :

Classification of Standards Primary Standards International Standard Working Standards Secondary Standards

Errors in measurement system :

Errors in measurement system Gross Error
Random error
Limiting error
Relative limiting error
Known error
Systematic error
Instrumental error
Environmental error
Observational error

Error Analysis :

Error Analysis Arithmetic Mean
Deviation
Average Deviation
Standard deviation
Variance
Median
Mode
Probable error
Standard deviation of mean
Standard deviation of Standard deviation

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