Complex Analytic functions and conformal mapping: curves and regions in the complex plane, complex functions, limit, derivative, analytic function, Cauchy - Riemann equations, Elementary complex functions such as powers, exponential function,logarithmic, trigonometric and hyperbolic functions. Conformal mapping: Linear fractional transformations, mapping by elementary functions like Z2, ez, sin z, cos z, sin hz, and Cos hz, Z+1/Z.
Complex integration: Line integral, Cauchy's integral theorem, Cauchy's integral formula, Taylor's series, Laurent's series, residue theorem, evaluation of real integrals using integration around unit circle, around the semi circle, integrating contours having poles, on the real axis.
Partial differential equations:Formation of partial differential equations. Solutions of equations of the form F(p, q) = 0, F(x,p,q)=0, F(y,p,q)=0, F(z,p,q)=0, F1(x,p) = F2 (y,q),Lagrange’s form Pp+Qq = R. Linear homogeneous partial differential equations with constant co-effients.
Vibrating string : one dimensional wave equation, D’Alembert’s solution, solution by the method of separation of variables. One dimensional heat equation, solution of the equation by the method of separation of variables, Solutions of Laplace’s equation over a rectangular region and a circular region by the method of separation of variables.
1. R.K.Jain, S.R.K.Iyengar: Advanced Engineering Mathematics, Narosa Publishers.19912. C.R.Wilie & L.C.Barrett: Advanced Engineering Mathematics, MGH Co.
1. Ervin Kreyszig, Wiley Eastern - Advanced Engineering Mathematics2. Churchill R.V- Complex Variables & Applications: MGH Publishers.3. M.C.Potter - Advanced Engineering Mathematics, , J.L.Goldberg Oxford University Press
Introduction to microprocessors: Microcomputers and microprocessors, 8/ 16/ 32/ 64-bit microprocessor families.Internal architecture of Intel 8086 microprocessor: Block diagram, Registers, Internal Bus Organization, Functional details of pins, Control signals, External Address / Data bus multiplexing, De-multiplexing, Memory Address space and data organisation, Memory segmentation and segment registers, IO Address space. Basic 8086/8088 configuration, Minimum mode and maximum mode. Comparison of 8086 and 8088.
Instruction set and Assembly language Programming of 8086: Instruction set, Instruction Classifications, addressing modes, Assembler Directives, Strings, Procedures and Macros Assembly language Program development tools: editor, assembler, linker, locator, debugger and emulator.
Interfacing concepts and devices: Memory interface: Concept of memory chip/ chips interface to 8086 with examples Direct Memory Access (DMA) data transfer Programmable interfacing devices: - Programmable peripheral interface (Intel 8255), Programmable timer interface (Intel 8253/ 54) -Block diagram and modes of operation .Hardware and Software aspects of Interfacing these peripherals to 8086. 8087 Numeric coprocessor interface.
Multiuser /Multitasking operating system concepts and the need for protection.Introduction to 80386: Architecture of 80386, Real and protected modes of operation, Virtual memory, Address translation with Segmentation and Paging, Virtual 8086mode.RISC architecture, Instruction Level Parallelism- concept and limitations-Pipelining and Superscalar architecture, Branch Prediction, Intel MMX architecture, VLIW architecture, NetBurst microarchitecture, Multicore Processing, Hyper threading technology, Trusted Execution Technology(TXT) - concepts
Differential Amplifiers - BJT differential pair, large signal and small signal analysis of differential amplifiers, Input resistance, voltage gain, CMRR, non-ideal characteristics of differential amplifier. Frequency response of differential amplifiers, MOS differential amplifiers.Current sources, Active load, cascode load, current mirror circuits, Wilson current mirror circuits. Small signal equivalent circuits, multistage differential amplifiers.
Feedback amplifiers - Properties of negative feedback. The four basic feedback topologies-Series-shunt, series-series, shunt-shunt, shunt-series. Analysis and design of discrete circuits in each feedback topologies - Voltage, Current, Tran conductance and Tran resistance amplifiers, its loop gain, input and output impedance., Stability of feedback circuits. Effect of feedback on amplifier poles, frequency compensation-Dominant pole and Pole-zero.
Low frequency Oscillators: Barkhausen criterion, RC phase shift and Wien bridge oscillators - analysis. High frequency oscillators- Hartley, Colpitts, Crystal oscillators and UJT Oscillators.Astable, Monostable and Bistable multivibrators, Schmitt trigger - analysis. Sweep circuits- Bootstrap, Miller sweep and current sweep circuits - analysis.
Internal block schematic of analog IC (op amp) -Biasing used in IC- Constant current source- Current mirror Circuits- Active Load – Level Shifters- Power amplifier stages. Open loop gain input- output impedance & bandwidth calculation using small signal equivalents. Frequency compensation and slew rate.
Continuous time (CT) and Discrete time (DT) Signals -Transformations of the independent variable- exponential and sinusoidal - unit step and impulse functions / sequences – Classification of signals - CT and DT Systems - Properties of systems - Linear time-invariant (LTI) systems – The representation of signals in terms of impulses - convolution - Properties of LTI systems - Singularity functions – LTI Systems described by differential and difference equations and calculation of impulse responses.
Sampling – Introduction - Representation of a continuous-time signal by its samples - the sampling theorem -The effect of under sampling: aliasing - Sampling with a zero-order hold - Reconstruction of a signal from its samples using interpolation - Sampling of discrete-time signals - Discrete-time decimation and interpolation – Laplace transform - The region of convergence for Laplace transforms - The inverse Laplace transform - Properties of the Laplace transform - Analysis and characterization of First-order and second-order LTI systems using the Laplace transform.
Fourier Series and Transforms - The response of continuous-time LTI systems to complex exponentials - Fourier series representation of Continuous time periodic signals - Convergence of Fourier series – Properties - Continuous-time Fourier transform representation of Aperiodic signals – Fourier transform of periodic signals - Properties - Fourier transform and Fourier series pairs - the discrete-time Fourier series - Properties - Discrete-time Fourier transform - Properties of Discrete-time Fourier transform - Properties .
The z-transform- The region of convergence – Pole zero plot - Properties of the z-transform - Inverse z-transform ( partial fraction method ) - Analysis and characterization of LTI systems using z-transforms - System function – Introduction to Linear feedback systems - Some applications and consequences of feedback - Root - locus analysis of linear feedback systems.
Introduction to continuous wave modulation - needs of modulation - Amplitude modulation - modulators, spectrum, Demodulation. DSBSC signals - spectrum, modulators, demodulators. SSB signals-spectrum, modulators demodulators - VSB – AM receivers – TRF receivers, Super heterodyne receiver, Double Super heterodyne receiver – SSB receiver.
Angle modulation-FM &PM - mathematical analysis, principles, waveforms, frequency deviation, frequency analysis, bandwidth requirement, phasor representation, Transmission bandwidth. Generation of FM. FM receivers-block diagram– demodulators – Tuned circuit frequency discriminators, slope detector, balanced slope detector
Noise: White noise, Narrow band noise, effective noise temperature and noise figure representation Sine wave contaminated with narrow band noise. Effect of noise in Systems; eg: Linear and angle modulation systems, threshold effect and threshold extension, pre-emphasis and de-emphasis filtering.
Sampling Process: Sampling theorem, Interpolation Formula, Quadrature sampling of band pass signals, Reconstruction of a message process from its samples, signal distortion in sampling, practical aspects. PAM, PPM, PWM, Multiplexing- TDM, FDM. Frequency domain analysis Waveform Coding Techniques: PCM, Quantization Noise & Signal to noise ratio, effect of sampling on quantization noise, uniform and nonuniform quantization companding- A Law and μ Law characteristics DPCM, Delta Modulation.
Standard Combinational Modules: Binary Decoders – decoder networks, Binary Encoders, Priority Encoders, Multiplexers – multiplexer trees, Demultiplexers, Shifters – barrel shifter, Programmable Modules- PLA, PAL, ROM, Network of ROMs. Implementation of combinational systems with decoder, multiplexers, ROMs and PLAs.
Synchronous sequential systems- state description of finite state system – Mealy and Moore Machines, representation of the state transition and output functions, time behavior of finite sate machines, finite memory sequential systems, equivalent sequential systems and minimization of the number of states, Binary specification of sequential systems, Different types of sequential systems- modulo-p counter – pattern recognizer – block pattern recognizer – sequential decoders.
Sequential Networks: Canonical form of Sequential Networks, Timing characteristics of sequential networks – setup time – hold time – propagation delay – maximum clock frequency, analysis of canonical sequential networks, Design of canonical sequential networks, Flip flop modules, Analysis of network with flip flops, Design of networks with flip flops
Standard Sequential Modules: Registers, Shift registers, Counters, Multimodule implementation of sequential systems – array of registers – Networks of shift registers - cascade counters – parallel counters, Design of sequential systems with standard sequential modules. Multimodule systems.