GATE Instrumental Engineering Syllabus

Subject Code: IN

Course Structure

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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