GATE syllabus for Instrumentation Engineeringconsists of:
Engineering Mathematics.
Electrical Circuits.
Signals and Systems.
Control Systems.
Analog Electronics.
Digital Electronics.
Measurements.
Sensors and Industrial Instrumentation.
Communication and Optical Instrumentation.

Engineering Mathematics

• Linear Algebra
• Matrix algebra
• Systems of linear equations
• Eigen values and Eigen vectors

Ordinary Differential Equation ( ODE )

• First order ( linear and non  linear )equations
• higher order linear equations with constant coefficients
• Euler  Cauchy equations
• Laplace transform and its application in solving linear ODEs
• Initial and boundary value problems.

Analysis of complex variables

• Analytic functions
• Cauchy's integral theorem and integral formula
• Taylor's and Laurent's series
• residue theorem
• solution of integrals.

Calculus

• Functions of single variableLimit, continuity and differentiability
• Mean value theorems
• local maxima and minima
• Taylor and Maclaurin series
• Evaluation of definite and indefinite integrals
• application of definite integral to obtain area and volume
• Partial derivatives
• Total derivative
• Gradient
• Divergence and Curl, Vector identities
• Directional derivatives
• Line, Surface and Volume integrals
• Stokes
• Gauss and Green's theorems.

Probability and Statistics

• Sampling theorem
• conditional probability
• meanmedianmode and standard deviation
• random variable
• discrete and continuous distributions
• normalPoisson and binomial distributions

Numerical Methods

• Matrix inversionsolutions of non-linear algebraic equations
• Iterative methods for solving differential equations
• numerical integration
• Regression and correlation analysis

Electrical Circuits

• Voltage and current sources
• Independent dependentideal and practical v  i relationships of resistorinductormutual inductor and capacitor
• transient analysis of RLC circuits with dc excitation.
• Kirchoff's laws
• mesh and nodal analysis
• superpositionThevenin, Norton, maximum power transfer and reciprocity theorems
• Peak-, average- and rms values of ac quantities
• apparentactive- and reactive powerphasor analysis
• impedance and admittance
• series and parallel resonance
• locus diagramsrealization of basic filters with R, L and C elements.One  port and two  port networks,driving point impedance and admittanceopen-, and short circuit parameters.

Signals and Systems

• Periodic, aperiodic and impulse signals
• LaplaceFourier 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 responsefrequency responsepulse
• transfer function
• DFT and FFT
• basics of IIR and FIR filters.

Control Systems

• Feedback principles
• signal flow graph
• transient respons
• steady  state  errors
• Bode plot
• phase and gain margin
• 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 valveson-off, P, P  I, P  I  Dcascade, feedforward, and ratio controllers.

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.

Digital Electronics

• Combinational logic circuits
• minimization of Boolean functions
• IC families
• TTL and CMOS
• Arithmetic circuits
• Comparators
• Schmitt trigger
• multi  vibrators
• sequential circuits
• flipflopshift registers
• timers and countersample  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.

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 voltagecurrent and power in single and three phase circuitac and dc current probes
• True rms meters
• voltage and current scalinginstrument
• transformers
• timer / countertimephase and frequency measurements
• digital voltmeter
• digital multimeter
• Oscilloscope
• shielding and grounding.

Sensors and Industrial Instrumentation

• Resistive -, capacitive -, inductive -, piezoelectric -,
• Hall effect sensors and associated signal conditioning circuits
• transducers for industrial instrumentation
• displacement ( linear and angular )velocityacceleration,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 levelpH, conductivity and viscosity measurement.

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 detectorsLEDlaser, photo  diode
• light dependent resistor and their characteristics
• Interferometer
• applications in metrology
• basics of fiber optic

All the best dear

Gate examination is for admission for masters in IITs. Since you have bachelor's in electronics and instrumentation engineering. It's based on your field of interest..you don't prepare for both. It's not easily to secure high rank in gate. Mainly it's concerned with instrumentation.so opt for instrumentation and prepare for it.

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