Here is the complete syllabus as Mentioned in the official site.

Instrumentation Engineering

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.

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

Hello,

Here is the link to detailed syllabus for instrumentaion engineering for GATE

https://engineering.careers360.com/articles/gate-syllabus-for-instrumentation-engineering

I would suggest you to go through with the given below link to check the sections and topics that need to be studied to prepare for Instrumentation Engineering programme.

https://engineering.careers360.com/articles/gate-syllabus-for-instrumentation-engineering

Good Luck!