GATE Instrumental Engineering Syllabus


Subject Code: IN

Course Structure

Sections/Units Topics
Section A Engineering Mathematics
Unit 1 Linear Algebra
Unit 2 Calculus
Unit 3 Differential Equations
Unit 4 Analysis of complex variables
Unit 5 Probability and Statistics
Unit 6 Numerical Methods
Section B Electric Circuits
Section C Signals and Systems
Section D Control Systems
Section E Analog Electronics
Section F Digital Electronics
Section G Measurements
Section H Sensors and Industrial Instrumentation
Section I Communication and Optical Instrumentation

Course Syllabus

Section A: Engineering Mathematics

Unit 1: Linear Algebra

  • Matrix algebra
  • Systems of linear 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 (linear and nonlinear)
  • Higher order linear 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: Probability and Statistics

  • Sampling theorems
  • Conditional probability
  • 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-linear 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, realization 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 linear 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, hydraulic 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 applications of −

    • Diode

    • Zener diode

    • BJT

    • MOSFET

  • Small signal analysis of transistor circuits, feedback amplifiers

  • Characteristics of operational amplifiers

  • Applications of opamps −

    • Difference amplifier

    • Adder

    • Subtractor

    • Integrator

    • Differentiator

    • Instrumentation amplifier

    • 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 families: TTL and CMOS

  • Arithmetic circuits, comparators, Schmitt trigger, multi-vibrators, sequential circuits, flipflops, 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/settling time)

  • Basics of number systems, 8-bit microprocessor and microcontroller: applications, 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 scaling

    • 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 (linear 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

  • Amplitude- and frequency modulation and demodulation

  • Shannon's sampling theorem, pulse code modulation

  • Frequency and time division multiplexing, amplitude-, phase-, frequency-, pulse shift keying for digital modulation

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

  • Interferometer − applications in metrology

  • Basics of fiber optic sensing

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