Following is the syllabus for Gate Exam for Instrumentation Engineering
Linear Algebra: Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.
Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial
Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface
and Volume integrals, Stokes, Gauss and Green’s theorems.
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, Partial
Differential Equations and variable separable method.
Complex variables: Analytic functions, Cauchy’s integral theorem and integral formula, Taylor’s and Laurent’ series, Residue
theorem, solution integrals.
Probability and Statistics: Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random
variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression
Numerical Methods: Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.
Transform Theory: Fourier transform, Laplace transform, Z-transform.
Basics of Circuits and Measurement Systems: Kirchoff’s laws, mesh and nodal Analysis. Circuit theorems. One-port and two-port
Network Functions. Static and dynamic characteristics of Measurement Systems. Error and uncertainty analysis. Statistical
analysis of data and curve fitting.
Transducers, Mechanical Measurement and Industrial Instrumentation: Resistive, Capacitive, Inductive and piezoelectric
transducers and their signal conditioning. Measurement of displacement, velocity and acceleration (translational and
rotational), force, torque, vibration and shock. Measurement of pressure, flow, temperature and liquid level. Measurement of
pH, conductivity, viscosity and humidity.
Analog Electronics: Characteristics of diode, BJT, JFET and MOSFET. Diode circuits. Transistors at low and high frequencies,
Amplifiers, single and multi-stage. Feedback amplifiers. Operational amplifiers, characteristics and circuit configurations.
Instrumentation amplifier. Precision rectifier. V-to-I and I-to-V converter. Op-Amp based active filters. Oscillators and
Digital Electronics: Combinational logic circuits, minimization of Boolean functions. IC families, TTL, MOS and CMOS.
Arithmetic circuits. Comparators, Schmitt trigger, timers and mono-stable multi-vibrator. Sequential circuits, flip-flops,
counters, shift registers. Multiplexer, S/H circuit. Analog-to-Digital and Digital-to-Analog converters. Basics of number
system. Microprocessor applications, memory and input-output interfacing. Microcontrollers.
Signals, Systems and Communications: Periodic and aperiodic signals. Impulse response, transfer function and frequency
response of first- and second order systems. Convolution, correlation and characteristics of linear time invariant systems.
Discrete time system, impulse and frequency response. Pulse transfer function. IIR and FIR filters. Amplitude and frequency
modulation and demodulation. Sampling theorem, pulse code modulation. Frequency and time division multiplexing. Amplitude
shift keying, frequency shift keying and pulse shift keying for digital modulation.
Electrical and Electronic Measurements: Bridges and potentiometers, measurement of R,L and C. Measurements of voltage,
current, power, power factor and energy. A.C & D.C current probes. Extension of instrument ranges. Q-meter and waveform
analyzer. Digital voltmeter and multi-meter. Time, phase and frequency measurements. Cathode ray oscilloscope. Serial and
parallel communication. Shielding and grounding.
Control Systems and Process Control: Feedback principles. Signal flow graphs. Transient Response, steady-state-errors. Routh
and Nyquist criteria. Bode plot, root loci. Time delay systems. Phase and gain margin. State space representation of systems.
Mechanical, hydraulic and pneumatic system components. Synchro pair, servo and step motors. On-off, cascade, P, P-I, P-I-D,
feed forward and derivative controller, Fuzzy controllers.
Analytical, Optical and Biomedical Instrumentation: Mass spectrometry. UV, visible and IR spectrometry. X-ray and nuclear
radiation measurements. Optical sources and detectors, LED, laser, Photo-diode, photo-resistor and their characteristics.
Interferometers, applications in metrology. Basics of fiber optics. Biomedical instruments, EEG, ECG and EMG. Clinical
measurements. Ultrasonic transducers and Ultrasonography. Principles of Computer Assisted Tomography.
For more information refer: http://gate.iitk.ac.in/