**Instrumentation engineering semester 4 syllabus – **The Mumbai university syllabus for fourth semester Instrumentation engineering has applied Mathematics 4 that is one of the easiest math to clear.The core Instrumentation subjects are Transducers 2, Analytical Instrumentation and signal conditioning circuit design.

## Instrumentation engineering semester 4 syllabus

### Applied Mathematics 4

Linear Algebra: Vector Spaces

Vectors in n-dimensional vector space: properties, dot product,

cross product, norm and distance properties in n-dimensional vector

space.

Vector spaces over real field, properties of vector spaces over real

field, subspaces.

The Cauchy-Schwarz inequality, Orthogonal Subspaces, GramSchmidt

process.

06 CO1

2 Linear Algebra: Vector Matrix Theory

Characteristic equation, Eigen values and Eigen vectors, properties

of Eigen values and Eigen vectors

Cayley-Hamilton theorem, examples based on verification of

Cayley- Hamilton theorem.

Similarity of matrices, Diagonalisation of matrices.

Functions of square matrix, derogatory and non-derogatory

matrices.

10 CO2

3 Random Variables

Discrete & continuous random variables, expectation, Variance,

Probability mass function and Density Function, Probability

distribution for random variables

Moments, Moment Generating Function.

Functions of one random variable and their distribution and density

functions

10 CO3

4 Probability distribution

Probability distribution: Binomial distribution, Poisson & normal

distribution (For detailed study)

6 CO4

5 Complex integration

Complex Integration: Line Integral, Cauchy’s Integral theorem for

simply connected regions, Cauchy’s Integral formula.

Taylor’s and Laurent’s Series

Zeros, singularities, poles of f(z), residues, Cauchy’s Residue

theorem.

Applications of Residue theorem to evaluate real Integrals of

different types.

12 CO5

6 Correlation & Regression

Karl Pearson’s coefficient of correlation, covariance, Spearman’s

Rank correlation.

Lines of Regression.

## TRANSDUCERS 2

Strain Measurement

Introduction, types of strain gauge, gauge factor calculation,

materials for strain gauge, resistance strain gauge bridges,

temperature compensation and applications of strain gauges

04 CO1

2 Pressure Measurement

Pressure scales, units and relations, classification

Primary pressure sensors – elastic elements like bourdon tube,

diaphragm, bellows, properties and selection of elastic

materials, Calibration using dead weight tester.

Electrical/Secondary Pressure Transducers: Capacitive,

piezo-electric and its material, variable reluctance, LVDT,

strain gauge.

High Pressure Measurement: Bulk modulus cell, Bridgeman

type, capsule.

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Differential pressure measurement: Force balance, motion

balance, DP Cell, semiconductor strain gauges.

Pressure measurement using manometer: U-tube types, well

type, inclined type, micro manometer

3 Vacuum Measurement

Units and relations, McLeod gauge, Pirani gauge, thermocouple

gauge, hot and cold cathode ionization gauge, Knudsen gauge

04 CO3

4 Flow Measurement

Introduction to fluid flow: properties of fluid, types of fluid,

dimensionless numbers, types of fluid flow, continuity equation,

Bernoulli’s equation, hydrostatic law, Pascal’s law, flow

through pipes – major and minor losses, flow measurement

through open channel-weirs and notches. Materials used for

flow sensors, performance of materials, corrosion resistors,

erosion, effect of vapour pressure

Head Type: orifice, venturi, nozzle, pitot tube, annubar,

characteristics of head type flow meters.

Variable Area Type: Rotameter

Velocity and Inertia based flowmeters: Turbine,

electromagnetic, ultrasonic, positive displacement,

anemometers, mass flow meters, solid flow measurements

16 CO4

5 Electro-chemical Sensors

Terminology, equations, units. pH measurement-electrodes,

measuring circuits, maintenance, temperature compensation,

calibration. Conductivity measurement-probes and measuring

circuits

04 CO5

6 Miscellaneous Measurement

Force Measurement: strain gauge, LVDT, piezoelectric.

Torque: Torsion bar, strain gauge.

Power: Dynamometer, instantaneous power measurement,

alternator power measurement.

Density Measurement – Displacement and float type

densitometers

Hydrometers, Radiation and Ultrasonic densitometers

Viscosity Measurement – Capillary tube viscometer, Efflux

type viscometer, Variable area viscometer

Introduction to Advances in sensors technology: Smart sensors,

MEMS, Nano sensors, Semiconductor sensors, Optical fiber

sensors.

## FFEEDBACK CONTROL SYSTEM

Introduction

Definition of control system and related terms, open loop and closed

loop system, examples. Development of automatic control systems,

classification of control system, examples

4 CO1

2 Mathematical Models of

Physical Systems

Definition of physical systems, principle of superposition and

homogeneity, linear/non-linear, time variant/time invariant

systems. Types of dynamic model, linear elements of electrical

and mechanical systems, differential equations of p h y s i c a l

systems-mechanical systems, electrical systems – RLC series,

parallel circuits, Analogous systems.

8 CO2

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3 Transfer Function and Feedback Characteristics

Definition of transfer function, sinusoidal transfer function, transfer

functions of physical systems, block diagram algebra, reduction

rules, signal flow graphs-definition, construction, properties, and

Mason’s gain formula, sensitivity of closed loop and open loop

systems, effect of feedback, effect of disturbances signals,

regenerative feedback with examples

10 CO3

4 Time Response Analysis

Standard test signals, pulse and impulse function, step function,

ramp function, parabolic function, sinusoidal function, dynamic

response, time response of first order system, time response of

second order system, specifications, steady –state error, system

types and error constants, design specifications of second order

system-desired closed loop pole location and the dominant closed

loop pole concept. Time response analysis of electrical RLC circuits

– first and second order differential equations, steady-state, and

transient response by using Laplace transform.

10 CO4

5 Stability Analysis and Root Locus Method

Concept of stability, definitions, bounded input-bounded output

stability, relative stability, necessary and sufficient conditions for

stability, Routh’s stability criterion, relative stability analysis, root

locus technique, applications, concept, construction of root loci, root

loci of different systems, electrical RLC circuits, etc.

08 CO5

6 Frequency Response and Stability Analysis

Correlation between time and frequency response, polar plots, Bode

plots, Nyquist stability criterion, frequency response

specifications, stability analysis using-bode plots, polar plots,

definition and significance of gain margin and phase margin,

sensitivity analysis in frequency domain, Frequency response and

analysis of electrical RLC circuits.

## ANALYTICAL INSTRUMENTATION

Introduction: Introduction to analytical Instrumentation.

Compare classical analytical techniques with instrumental

techniques.

Fundamentals of Spectroscopy: Nature of Electromagnetic

Radiation, Electromagnetic spectrum, Beer Lambert’s Law

statement and derivation. Deviations from Beer’s law.

Numerical on EMR and laws of photometry.

Interaction of radiation with matter. Instrumentation of

spectroscopic analytical system – Radiation sources,

Wavelength selectors, Detectors, signal processors and readout

modules.

06 CO1

2 Molecular Spectroscopy: Molecular Energy levels, correlation

of energy levels with transitions.

Electronic transitions and Vibrational transitions –

Introduction to UV-VIS molecular spectroscopy – basics of

single beam, double beam spectrophotometer and filter

photometer, its instrumentation and applications.

Basic principle of Fluorescence, Phosphorescence and Raman

Spectroscopy, components and instrumentation of Fluorimeters,

Phosphorimeters and Raman spectrometers.

Nuclear/Rotational transitions – Nuclear Magnetic Resonance

(NMR) spectroscopy, basic principle and numerical problems

based on NMR principle, instrumentation and constructional

details of NMR Spectrometer.

Electron Spin Resonance (ESR) Spectroscopy – Basic principle

and construction of ESR spectrometer.

10 CO2

3 Atomic Spectroscopy: Atomic Energy levels, Atomic

absorption spectrometers- components, working and absorption

spectra.

Atomic Emission spectrometers – components, working and

emission spectra, comparison between AAS and AES.

03 CO3

4 Separation Science:

Chromatography: Fundamentals of chromatographic

Separations, Classification, Gas chromatographic system with

components, factors affecting separation, applications. Analysis

of Gas Chromatogram.

HPLC – Its principle and instrumentation.

Mass Spectrometers: Basic principle, components and types of

mass spectrometers, sample handling techniques for liquids and

solids, resolution and numerical problems based on resolution.

Interfacing Gas Chromatography and Mass spectrometry

(GCMS).

09 CO4

5 Radio Chemical Instrumentation:

Basics of Radioactivity, properties of radiations (?, ?, ?). Halflife

period and numerical problems based on half-life period.

Radiation detectors – Ionization chamber, Proportional counter,

Geiger Muller counter, Scintillation detector, Semiconductor

detectors, Pulse height analyzers.

05 CO5

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6 Industrial Gas Analyzers:

Oxygen, Carbon dioxide(CO2), Carbon monoxide(CO) and

NO2 analyzers, Gas density analyzer.

### Signal conditioning circuit design

Principles of Analog Signal Conditioning:

Standard analog signals, Signal Level and bias changes,

Linearization, signal conversion, filtering and impedance

matching, concept of loading.

Passive circuits – Divider Circuits, Bridge circuits (Current,

Voltage, Balanced and Unbalanced), RC filters

06 CO1

2 Analog signal conditioners and their design 12 CO2

University of Mumbai, Instrumentation Engineering, Rev 2016-17 46

Practical applications of Op amp based circuits with design:

Differentiators, Integrator, Instrumentation amplifier using 3 op

amps

Half wave, full wave milivolt rectification, absolute value circuit,

Log and antilog amplifier with temperature compensation, active

filters, threshold detector, zero crossing detector, window

detector, Phase locked loops (PLL), Voltage to Current converter

and Current to Voltage Converter, 555 Timer: modes of operation

with applications.

Guidelines for analog signal conditioning design and design

based problems

3 Components of Digital Signal Conditioning:

Block diagram of Digital signal conditioning, Characteristics of

digital data: digitized value, sampled data system and

linearization, sample and hold circuit, peak detector, ADC

(Successive Approximation, Flash, Ramp, dual slope) and DAC

(R/2R, Weighted resistors) their types and specifications, V to F

and F to V converters.

10 CO3

4 Thermal and Pressure Transducers Signal Conditioning

Design:

Thermal sensor signal conditioning, design considerations and

application for RTD, Thermistor, thermocouple and solid state

temperature sensor.

Pressure Transducer signal conditioning Design: design

considerations and applications for various pressure sensors.

8 CO4

5 Optical and Other Transducer Signal Conditioning Design:

Optical Sensor signal conditioning – photo-diode with photoconducting

and photovoltaic modes, photo-transistor and

photomultiplier tube.

Optical encoder signal conditioning for linear displacement,

velocity and angular displacement applications.

Other sensor signal conditioning: Potentiometer, LVDT, strain

gauges, piezoelectric and capacitive transducers

6 CO5

6 Power Supply Design:

Power supply design using 78xx series, 79xx series and

adjustable voltage IC regulators like 723 and LM317.

Switched Mode Power Supply (SMPS): Block diagram with

advantages and disadvantages over conventional power supply.

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