JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Prerequisite

Mathematics – II & Network Theory

Course Objectives:

• To develop ability to analyze linear systems and signals
• To develop critical understanding of mathematical methods to analyze linear systems and signals

Course Outcomes

After successfully completing this course, students will be able to:

• 1. Use mathematical modeling tools to represent linear systems
• 2. Use mathematical modeling tools to analyze linear systems

UNIT - I

State Variable Analysis: Choice of state variables in Electrical networks-Formulation of state equations for Electrical networks Equivalent source method. Network topological method - Solution of state equations-Analysis of simple networks with state variable approach.

UNIT - II

Fourier Series and Fourier Transform Representation: Introduction, Trigonometric form of Fourier series, Exponential form of Fourier series, Wave symmetry, Fourier integrals and transforms, Fourier transform of a periodic function , Properties of Fourier Transform , Parseval’s theorem , Fourier transform of some common signals, Fourier transform relationship with Laplace Transform. Applications of Fourier series and Fourier Transform Representation: Introduction, Effective value, and average values of non sinusoidal periodic waves, currents, Power Factor, Effects of harmonics, Application in Circuit Analysis, Circuit Analysis using Fourier Series.

UNIT - III

Laplace Transform Applications: Application of Laplace transform Methods of Ananlysis – Response of RL, RC, RLC Networks to Step, Ramp, and impulse functions, Shifting Theorem – Convolution Integral – Applications Testing of Polynomials: Elements of realisability - Hurwitz polynomials-positive real functions-Properties-Testing-Sturm’s Test, examples. Network Synthesis: Network synthesis: Synthesis of one port LC networks-Foster and Cauer methods-Synthesis of RL and RC one port networks-Foster and Cauer methods

R16 B.TECH EEE.

UNIT - IV

Sampling: Sampling theorem – Graphical and Analytical proof for Band Limited Signal impulse sampling, natural and Flat top Sampling, Reconstruction of signal from its samples, effect of under sampling – Aliasing, introduction to Band Pass sampling, Cross correlation and auto correlation of functions, properties of correlation function, Energy density spectrum, Power density spectrum, Relation between auto correlation function and Energy / Power spectral density function.

UNIT - V

Z-Transforms: Fundamental difference between continuous and discrete time signals, discrete time complex, exponential and sinusoidal signals, periodicity of discrete time complex exponential, concept of Z Transform of a discrete sequence. Distinction between Laplace, Fourier, and Z-Transforms. Region of convergence in Z-Transforms, constraints on ROC for various classes of signals, Inverse Z-Transform properties of Z-Transforms.

Text Books:

• 1. “B. P. Lathi”, “Signals, Systems and Communications”, BS Publications 2003.
• 2. “Umesh Sinha” “Network Analysis and Synthesis”, Satya Prakashan Publications, 2013.

Reference Books:

• 1. “A. N. Tripathi”, “Linear System Analysis”, New Age International, 2nd Edition 1987.
• 2. “D. Roy Chowdhary”, “Network and Systems”, New Age International, 2005.
• 3. “Gopal G Bhise, Prem R. Chadha”, Engineering Network Analysis and Filter Design, Umesh Publications 2009.
• 4. “A. Cheng”, linear system analysis, Oxford publishers, 1999. R16 B.TECH EEE.