# 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
• Bode plot
• Phase and gain margins
• Routh and Nyquist criteria
• Root loci
• 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

• 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