# 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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