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Instrumentation and Measurement

Introduction to measurement and instrumentation, Static characteristics of instruments; Types of Errors, Statistical Error Analysis, Propagation of Errors; Dynamic Characteristics of Instrumentation Systems, Sensor Reliability; Basic analog measuring instruments (PMMC, electrodynamometer, rectifier) and its use as electronic voltmeter and ammeter. Wattmeter and Energy meters; High Current/Voltage Measurement – C. T., P. T., C. V. T; Null-Based Measurement - D.C. and A.C.

Quantum Mechanics

Mathematical Introduction: Linear vector spaces, inner products, linear operators, eigenvalue problem, generalization to infinite dimensions.

Towards quantum mechanics: relevant experiments, wave particle duality, uncertainty principle, postulates of quantum mechanics, Schrodinger equation, probability current and conservation.

Simple one-dimensional potential problems: Free particle, particle in a box; scattering in step-potentials, transmission and reflection coefficients.

Integral Transform, PDE and Calculus of Variations

Integral Transforms: The Fourier transform pair - algebraic properties of Fourier transform – convolution, modulation, and translation – transforms of derivatives and derivatives of transform – inversion theory. Laplace transforms of elementary functions – inverse Laplace transforms – linearity property – first and second shifting theorem – Laplace transforms of derivatives and integrals – Laplace transform of Dirac delta function – applications of Laplace transform in solving ordinary differential equations.

Semiconductor Devices

Semiconductor fundamentals, crystal structure, concept of effective-mass, Fermi level, energy‐band diagram, concept of holes, intrinsic and extrinsic semiconductors, carrier concentration, carrier transport, scattering and drift of electrons and holes, drift and diffusion, generation and recombination, quasi-Fermi levels.

Semiconductor junctions, Physical description of p‐n junction, p-n junction under forward and reverse bias, current – voltage characteristics and temperature dependence, tunneling current and tunnel diode, small signal ac analysis.