**GATE Instrumentation Engineering Syllabus:**

Section 1: Engineering Mathematics

Linear
Algebra: Matrix algebra, systems of linear equations, Eigen values and Eigen vectors.

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.

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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.

Analysis of complex variables:
Analytic functions, Cauchy’s integral theorem and integral formula, Taylor’s
and Laurent’s series, residue theorem, solution of integrals.

Probability and Statistics:
Sampling theorems, conditional probability, mean, median, mode and standard
deviation, random variables, 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.

Instrumentation
Engineering

Section 2: 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 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 3: 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 4: 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 5: 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.

Section 6: Digital Electronics

Combinational logic circuits, minimization of Boolean
functions. IC families: TTL and CMOS. Arithmetic circuits, comparators, Schmitt
trigger, multi-vibrators, sequential circuits, flip- flops, shift registers,
timers and counters; 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.

Section 7: 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 8: 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 9: Communication and Optical Instrumentation

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