i SYLLABUS osmania university UNIT - I CHAPTER - 1 : TRANSIENT RESPONSE Initial Conditions in Zero-Input Response of RC, RL and RLC Networks, Definitions of Unit Impulse, Unit Step and Ramp Functions, Zero State Response with Impulse and Step Inputs. Complete Response of Circuits with Initial Conditions and Forcing Functions such as Step, Exponential and Sinusoidal Functions. UNIT - II CHAPTER - 2 : LAPLACE TRANSFORM OF SIGNALS Laplace Transform Pair, Evaluation of Laplace Transforms of Common Time Functions in Particular Delta, Unit Step, Ramp, Sinusoids and Exponential Functions and Building of Laplace Transform Tables, Laplace Transform Theorems Relating Time Shifting Differentiation, Integration and Convolution of Time Functions, Initial and Final Value Theorems, Waveform Synthesis, Partial Fraction Expansion Method of Obtaining Inverse Transforms. UNIT - III CHAPTER - 3 : APPLICATION OF LAPLACE TRANSFORM FOR CIRCUIT ANALYSIS Application of Laplace Transform for Circuit Analysis, Concept of Transfer Function, Pole, Zero Plots. UNIT - IV CHAPTER - 4 : FOURIER SERIES Fourier Series Representation of Periodic Functions using both Trigonometric and Exponential Functions, Symmetry Conditions.
iii electrical circuits ii ii FOR b.e. (o.u) Ii year ii semester (ELECTRICAL AND ELECTRONICS ENGINEERING) CONTENTS UNIT - I [CH. H. - 1] ] [TRANSIENT RESPONSE]... 1.1-1.128 1.1 INTRODUCTION... METHODS OF TRANSIENT ANALYSIS YSIS....1 Finding the Solution of Differential Equations....1.1 Solution for a First Order System with DC Input.... Solution for a First Order System with AC Input... 1.4.1.3 Solution for a Second Order System with AC (or) DC Input... 1.5 1.3 INITIAL CONDITIONS... 1.7 1.3.1 Initial Conditions in Elements... 1.7 1.3.2 Final Steady State Conditions... 1.10 1.3.3 Procedure for Finding the Initial Conditions... 1.11 1.3.4 Solved Problems... 1.11 1.4 DC TRANSIENTS... 6 1.4.1 Transient Response of Series RL Circuit for DC Excitation... 7 1.4.1.1 Transient Response of Driven Series RL Circuit... 7 1.4. Transient Response of Undriven Series RL Circuit... 1.31 1.4.1.3 Solved Problems... 1.34
v 1.6.1.4 Rectangular Pulse... 1.100 1.6.1.5 Unit Area Triangular Function... 1.100 1.6.1.6 Exponential Function... 1.101 1.6.1.7 Sinusoidal Signals... 1.102 1.6.1.8 Exponential Damped Sinusoidal Signal... 1.103 1.6.1.9 Signum Function... 1.103 1.6.1.9.1 Relation Between u(t) and sgn(t)... 1.104 1.6.1.10 Sinc Function... 1.105 1.7 ZERO STATE TE RESPONSE WITH IMPULSE FUNCTION... 1.107 1.7.1 RL Circuit... 1.107 1.7.2 RC Circuit... 1.108 1.7.3 RLC Circuit... 1.109 1.8 COMPLETE RESPONSE OF CIRCUITS WITH INITIAL CONDITIONS AND STEP FORCING FUNCTION... 1.109 1.9 COMPLETE RESPONSE OF CIRCUITS WITH INITIAL CONDITIONS AND EXPONENTIAL FORCING FUNCTION... 1.110 1.10 COMPLETE RESPONSE OF CIRCUIT WITH CONDITIONS AND SINUSOIDAL FORCING FUNCTIONS... 1.110 Short Questions and Answers... 1.111-1.122 Expected University Questions with Answers... 1.123-1.128 UNIT - II [CH. - 2] ] [LAPLACE TRANSFORM OF SIGNALS]... 2.1-2.106 2.1 INTRODUCTION... 2.2 2.2 DEFINITION OF LAPLACE TRANSFORM... 2.3 2.2.1 Existence of Laplace Transform... 2.4 2.2.2 Concept of Region of Convergence (ROC) for Laplace Transforms... 2.4 2.2.2.1 Properties of ROC... 2.6 2.2.3 Advantages of Laplace Transform... 2.6 2.2.4 Disadvantages of Laplace Transform... 2.7
vii 2.4.16 Periodicity Property roperty... 2.32 2.4.17 First Shifting Theorem... 2.33 2.4.18 Second Shifting Theorem... 2.33 2.4.19 Solved Problems using Properties of Laplace Transform ransform... 2.34 2.5 LAPLACE TRANSFORM TABLE... 2.47 2.6 WAVEFORM SYNTHESIS... 2.48 2.7 PARTIAL FRACTION EXPANSION METHOD OF OBTAINING INVERSE LAPLACE TRANSFORM... 2.65 2.7.1 Simple and Real Roots... 2.66 2.7.2 Multiple Roots... 2.67 2.7.3 Complex Roots... 2.67 2.7.4 Solved Problems... 2.67 Short Questions and Answers... 2.93-2.102 Expected University Questions with Answers... 2.103-2.106 UNIT - III [CH.. - 3] ] [APPLICA APPLICATION OF LAPLACE TRANSFORM FOR CIRCUIT ANALYSIS YSIS]... 3.1-3.88 3.1 INTRODUCTION... 3.2 3.2 CONCEPT OF COMPLEX FREQUENCY... 3.2 3.3 APPLICATION OF LAPLACE CE TRANSFORM TO O ELECTRIC NETWORKS... 3.4 3.3.1 Transforms of Basic R, L and C Components... 3.4 3.3.2 Transforms of RL,, RC and RLC Networks... 3.10 3.3.2.1 RL Circuit... 3.11 3.3.2.2 RC Circuit... 3.12 3.3.2.3 RLC Circuit... 3.14 3.3.3 Solved Problems... 3.18
ix 4.5 RELATION BETWEEN TRIGONOMETRIC AND EXPONENTIAL FOURIER SERIES... 4.25 4.6 SYMMETRY CONDITIONS... 4.27 4.6.1 Even Symmetry... 4.27 4.6.2 Odd Symmetry... 4.30 4.6.3 Half-Wave ave Symmetry... 4.32 4.6.4 Quarter-Wave ave Symmetry... 4.33 4.6.5 Summary of Waveform Symmetry... 4.34 4.7 PROPERTIES OF CONTINUOUS TIME FOURIER SERIES... 4.34 4.7.1 Linearity... 4.35 4.7.2 Time Shifting... 4.35 4.7.3 Frequency Shifting... 4.37 4.7.4 Time Scaling... 4.37 4.7.5 Time Reversal... 4.38 4.7.6 Time-Differentiation... 4.39 4.7.7 Time-Integration... 4.40 4.7.8 Multiplication in Time-Domain... 4.41 4.7.9 Conjugation and Conjugate Symmetry... 4.42 4.7.10 Parseval s Theorem... 4.43 4.8 COMPLETE RESPONSE TO O PERIODIC FORCING FUNCTIONS... 4.44 4.8.1 Solved Problems... 4.44 Short Questions and Answers... 4.49-4.58 Expected University Questions with Answers... 4.59-4.62 UNIT - IV [CH. - 5] ] [FOURIER TRANSFORM]... 4.63-4.140 5.1 INTRODUCTION... 4.64 5.2 DERIVING FOURIER TRANSFORM FROM FOURIER SERIES... 4.64 5.2.1 Definition of Fourier Transform... 4.67 5.2.2 Existence of Fourier Transform... 4.67
xi 5.5 FOURIER TRANSFORM REPRESENTATION TION OF PERIODIC SIGNAL... 4.108 5.6 SPECTRAL CONTENT OF A SIGNAL... 4.109 5.7 AMPLITUDE AND PHASE SPECTRA... 4.110 5.8 ENERGY DENSITY SPECTRUM... 4.111 5.8.1 Parseval s Theorem for Energy Signals... 4.111 5.8.2 Energy Spectral Density (ESD)... 4.113 5.8.3 Energy Spectral Densities of Input and Output... 4.115 5.8.4 Properties of Energy Spectral Density... 4.115 5.9 BANDWIDTH OF A SIGNAL... 4.118 5.10 POWER DENSITY SPECTRUM... 4.120 5.10.1 Parseval s Theorem for Power Signals... 4.120 5.10.2 Power Spectral Density (PSD)... 4.122 5.10.3 Properties of PSD... 4.124 5.11 SYSTEM FUNCTION AND ITS APPLICATION IN DETERMINING STEADY-ST STATE TE RESPONSE... 4.125 5.11.1 Solved Problem... 4.126 Short Questions and Answers... 4.129-4.137 Expected University Questions with Answers... 4.138-4.140 UNIT - V [CH. - 6] ] [NETWORK SYNTHESIS]... 5.1-5.66 6.1 INTRODUCTION... 5.2 6.2 HURWITZ POLYNOMIAL... 5.2 6.2.1 Properties of Hurwitz Polynomial olynomial... 5.2 6.2.2 Routh-Hurwitz Method (or) Routh outh s Criterion... 5.3 6.2.3 Solved Problems... 5.4 6.3 POSITIVE REAL FUNCTIONS... 5.12 6.3.1 Proof for Z(s) to be Positive Real Function unction... 5.12 6.3.2 Properties of Positive Real Functions... 5.13
xiii 6.7 SYNTHESIS OF DRIVING POINT IMMITTANCE FUNCTION OF RL NETWORK... 5.51 6.7.1 Properties of RL Driving Point Immittance Function unction... 5.52 6.7.2 Realization of Immittance Functions of RL Networks... 5.52 6.7.2.1 Foster I Form... 5.52 6.7.2.2 Foster II Form... 5.53 6.7.2.3 Cauer I Form... 5.53 6.7.2.4 Cauer II Form... 5.54 6.7.2.5 Solved Problems... 5.54 Short Questions and Answers... 5.59-5.64 Expected University Questions with Answers... 5.65-5.66 LATEST UNIVERSITY QUESTION PAPER WITH ANSWERS [April/May - 2013] [New] [Main]... QP.1 - QP.8