## GATE Syllabus for Instrumentation Engineering

### ENGINEERING MATHEMATICS

**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
analysis.

**Numerical Methods**: Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.

**Transform Theory:** Fourier transform, Laplace transform, Z-transform.

### INSTRUMENTATION ENGINEERING

**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 signal
generators.

**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.