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# GATE 2019 Syllabus for Instrumentation Engineering

#### Engineering Mathematics

Linear Algebra
• Matrix algebra

• Systems of linear equations

• Eigen values and Eigen vectors

Ordinary Differential Equation ( ODE )
• First order ( linear and non – linear ) equations

• higher order linear equations with constant coefficients

• Euler – Cauchy equations

• Laplace transform and its application in solving linear ODEs

• Initial and boundary value problems.

Analysis of complex variables
• Analytic functions

• Cauchy's integral theorem and integral formula

• Taylor's and Laurent's series

• residue theorem

• solution of integrals.

Calculus
• Functions of single variable

• Limit, continuity and differentiability

• Mean value theorems

• local maxima and minima

• Taylor and Maclaurin series

• Evaluation of definite and indefinite integrals

• application of definite integral to obtain area and volume

• Partial derivatives

• Total derivative

• Gradient

• Divergence and Curl, Vector identities

• Directional derivatives

• Line, Surface and Volume integrals

• Stokes

• Gauss and Green's theorems.

Probability and Statistics
• Sampling theorem

• conditional probability

• mean

• median

• mode and standard deviation

• random variable

• discrete and continuous distributions

• normal

• Poisson and binomial distributions

Numerical Methods
• Matrix inversion

• solutions of non-linear algebraic equations

• Iterative methods for solving differential equations

• numerical integration

• Regression and correlation analysis

#### Electrical Circuits

• 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.

• Kirchoff's laws

• mesh and nodal analysis

• superposition

• Thevenin, Norton, maximum power transfer and reciprocity theorems.

• Peak-, average- and rms values of ac quantities

• apparent

• active- and reactive power

• 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.

#### 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.

#### Control Systems

• Feedback principles

• signal flow graph

• transient response

• steady – state – errors

• Bode plot

• phase and gain margin

• 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.

#### Analog Electronics

• Characteristics and applications of diode

• Zener diode

• BJT and 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.

#### Digital Electronics

• Combinational logic circuits

• minimization of Boolean functions

• IC families

• TTL and CMOS

• Arithmetic circuits

• Comparators

• Schmitt trigger

• multi – vibrators

• sequential circuits

• flipflop

• shift registers

• timers and counter

• sample – and – hold circuit

• Multiplexer

• analog to digital ( successive approximation, integrating, flash and sigma – delta ) and digital to analog 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.

#### 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 circuit

• 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.

#### 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.

#### 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.