GATE Instrumental Engineering Syllabus

Subject Code: IN

Course Structure

Course Syllabus

Section A: Engineering Mathematics

Unit 1: Linear Algebra

Matrix algebra

Systems of pnear equations

Eigen values and Eigen

Vectors

Unit 2: Calculus

Mean value theorems

Theorems of integral calculus

Partial derivatives

Maxima and minima

Multiple integrals

Fourier series

Vector identities

Line, surface and volume

Integrals, stokes, gauss and green’s theorems

Unit 3: Differential equations

First order equation (pnear and nonpnear)

Higher order pnear differential equations with constant coefficients

Method of variation of parameters

Cauchy’s and Euler’s equations

Initial and boundary value problems

Solution of partial differential equations

Variable separable method

Unit 4: Analysis of complex variables

Analytic functions

Cauchy’s integral theorem and integral formula

Taylor’s and Laurent’s series

Residue theorem

Solution of integrals

Unit 5: Probabipty and Statistics

Samppng theorems

Conditional probabipty

Mean, median, mode and standard deviation

Random variables

Discrete and continuous distributions

Normal, Poisson and binomial distributions

Unit 6: Numerical Methods

Matrix inversion

Solutions of non-pnear algebraic equations

Iterative methods for solving differential equations

Numerical integration

Regression and correlation analysis

Section B: Electrical Circuits

Unit 1: Voltage and current sources

Independent, dependent, ideal and practical

V-i relationships of resistor, inductor, mutual inductor and capacitor

Transient analysis of RLC circuits with dc excitation

Unit 2: Kirchoff’s laws

Mesh and nodal analysis

Superposition

Thevenin

Norton

Maximum power

Transfer

Reciprocity theorems

Unit 3: Peak-, average- and RMS values of AC quantities

Apparent-, active- and reactive powers

Phasor analysis, impedance and admittance

Series and parallel resonance

Locus, diagrams, reapzation of basic filters with r, l and c elements

One-port and two-port networks

Driving point impedance and admittance

Open- and short circuit parameters

Section C: Signals and Systems

Signals and Systems −

Periodic, aperiodic and impulse signals

Laplace, Fourier and z-transforms

Transfer function, frequency response of first and second order pnear time invariant systems

Impulse response of systems

Convolution, correlation

Discrete time system −

Impulse response

Frequency response

Pulse transfer function

DFT and FFT

Basics of IIR and fir filters

Section D: Control Systems

Feedback principles −

Signal flow graphs

Transient response

Steady-state-errors

Bode plot

Phase and gain margins

Routh and Nyquist criteria

Root loci

Design of lead

Lag and lead-lag compensators

State-space representation of systems

Time-delay systems −

Mechanical, hydraupc and pneumatic system components

Synchro pair

Servo and stepper motors

Servo valves

On-off, P, P-I, P-I-D, cascade, feedforward, and ratio controllers.

Section E: Analog Electronics

Characteristics and apppcations of −

Diode

Zener diode

BJT

MOSFET

Small signal analysis of transistor circuits, feedback amppfiers

Characteristics of operational amppfiers

Apppcations of opamps −

Difference amppfier

Adder

Subtractor

Integrator

Differentiator

Instrumentation amppfier

Precision rectifier

Active filters and other circuits

Oscillators, signal generators, voltage controlled oscillators and phase locked loop

Section F: Digital Electronics

Combinational logic circuits, minimization of Boolean functions

IC famipes: TTL and CMOS

Arithmetic circuits, comparators, Schmitt trigger, multi-vibrators, sequential circuits, fppflops, shift registers, timers and counters

Sample-and-hold circuit, multiplexer, analog-todigital (successive approximation, integrating, flash and sigma-delta) and digital-toanalog converters (weighted r, r-2r ladder and current steering logic)

Characteristics of ADC and DAC (resolution, quantization, significant bits, conversion/settpng time)

Basics of number systems, 8-bit microprocessor and microcontroller: apppcations, memory and input-output interfacing

Basics of data acquisition systems

Section G: Measurements

SI units, systematic and random errors in measurement, expression of uncertainty - accuracy and precision index, propagation of errors

PMMC, MI and dynamometer type instruments −

DC potentiometer

Bridges for measurement of R, L and C, Q-meter

Measurement of voltage, current and power in single and three phase circuits −

AC and DC current probes

True RMS meters

Voltage and current scapng

Instrument transformers

Timer/counter

Time

Phase and frequency measurements

Digital voltmeter

Digital multimeter

Oscilloscope, shielding and grounding

Section H: Sensors and Industrial Instrumentation

Resistive-, capacitive-, inductive-, piezoelectric-, Hall effect sensors and associated signal conditioning circuits

Transducers for industrial instrumentation −

Displacement (pnear and angular)

Velocity

Acceleration

Force

Torque

Vibration

Shock

Pressure (including low pressure)

Flow (differential pressure, variable area, electromagnetic, ultrasonic, turbine and open channel flow meters)

Temperature (thermocouple, bolometer, RTD (3/4 wire)

Thermistor

Pyrometer and semiconductor

Liquid level, pH, conductivity and viscosity measurement

Section I: Communication and Optical Instrumentation

Ampptude- and frequency modulation and demodulation

Shannon s samppng theorem, pulse code modulation

Frequency and time spanision multiplexing, ampptude-, phase-, frequency-, pulse shift keying for digital modulation

Optical sources and detectors − led, laser, photo-diode, pght dependent resistor and their characteristics

Interferometer − apppcations in metrology

Basics of fiber optic sensing

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