Vectors: Representation and Dot products, Norms, Matrices: The Four Fundamental Spaces of a Matrix, The Matrix as a Linear Operator, The Geometry associated with matrix operations, Inverses and Generalized Inverses, Matrix factorization/Decompositions, rank of a matrix, Matrix Norms.

Module 1: Role of Interface Electronics, Analog Electronic Blocks, OPAMP – internal structure, Open- loop gain, Input R, Output R, DC noise sources and their drifts, CMRR, PSRR, Bandwidth and stability, Slew rate, Noise – general introduction, OPAMP Circuits and Analysis - Difference and Instrumentation Amplifiers (3-opamp and 2-opamp), Effect of cable capacitance and wire-resistance on CMRR, IA with guards, Biomedical application, Current-mode IA (Howland), Current-input IA, filters, Filters with underdamped response, state-variable filters, All- pass filters, Current Sources (floating and

Introduction and Background of state-of-art sensing and measurement techniques. Contactless potentiometer (resistance-capacitance scheme) – Methodology, Interface Circuits, Overview of Flight Instrumentation. Analog Electronic Blocks, CMRR Analysis (Non-ideal opamps) of an Instrumentation Amplifier, Linearization circuits for single- element wheatstone bridges (application to strain gauge), Direct Digital Converter for Strain gauges, Signal conditioning for Remote-connected sensor elements.

Introduction to high speed links. Review of PCB trace behavior at high frequencies. Concepts of cross-talk, dispersion, inter-symbol interference (ISI). Transceiver schemes. Design of transmitter, output impedance matching, multiplexing techniques, clocking, signaling techniques. Pre-distortion and equalization. Link budgets. Design of receivers – continuous time linear equalizers, slicers, DFE techniques, clocking, critical paths, IIR/FIR implementations. PLLs, clock and data recovery circuits and schemes.

Power-speed-noise trade-off. Ultra-lower power VLSI design. Leakage power vs dynamic power. Minimum energy point concept. Low voltage analog, mixed-signal design. VLSI design for IoT applications. Low voltage memories.

Designing for high speed/performance. Dynamic voltage and frequency scaling. Selected topics on clock skew, clock routing, power routing. Selected topics on layout techniques in mixed-signal circuits – guard rings, etc. Role of calibration in modern ICs.

Analysis of LTI system: Phase and Magnitude response of the system, Minimum phase, maximum phase, Allpass. Multirate Signal Processing: Interpolation, Decimation, sampling rate conversion, Filter bank design, Polyphase structures. Time-frequency representation; frequency scale and resolution; uncertainty principle, short-time Fourier transform. Multi- resolution concept and analysis, Wavelet transform (CWT, DWT). Optimum Linear Filters: Innovations Representation of a Stationary Random Process, Forward and Backward linear prediction, Solution of the Normal Equations.

Electronic integrated circuits, Scaling of electronic devices, Electrical interconnects, issues with electrical interconnection, Optical interconnects-advantages-similarities with electrical interconnects Integration-Photonic Integrated Circuits (PIC)-brief history of PIC-Features- Materials for PIC platform-Si, Silica, SOI, III-V, LiNbO3 Basic theory of Planar and channel waveguide-effective index method-guided modes Types of waveguides-Optical losses in waveguides-(side wall scattering, bending, losses due to metal layer)-waveguide fabrication (LiNbO3 and III-V based)

Fundamentals of Semiconductors: Carrier concentration of semiconductor, Transport Equations, P-N Junction Diode, Schottky Junction Diode and MOSFET. Fundamentals of Compound Semiconductors: Introduction of Compound Semiconductors, Properties of Compound semiconductors, Synthesis of Compound Semiconductors.

Introduction to Power Semiconductor devices, Device Basic Structure and Characteristics, High current effects in diodes, Breakdown considerations for various devices, Schottky rectifiers. - P- i-N rectifiers Power BJTs, Parasitics in Power Transistors, Power MOSFETs, Thyristors, Power Insulated Gate Transistors, Heat transfer in power devices, device packaging

Introduction to Digital Signal Processing; Need of VLSI DSP algorithms. main DSP Blocks and typical DSP Algorithms. Number Representation: Fixed point Representation Floating point Representation; Binary Adders; Binary Multiplier; Binary Dividers; Floating point Arithmetic Implementation: CORDIC architectures; Multiply Accumulator unit; Computation of Special functions using MAC cells. Redundant arithmetic, redundant number representations, carry free radix 2 addition and subtraction. Hybrid radix 4 addition. Radix 2 hybrid redundant multiplication architectures, data format conversion.