Copyright 20 13 Dorling Kindersley (India) Pvt. Ltd

13. Analysis of Dynamic Circuits by Laplace Transforms 
13.1
13.1 Circuit Response to Complex Exponential Input 
13.3
13.2 Expansion of a Signal in terms of Complex Exponential Functions 
13.4
13.2.1 Interpretation of Laplace Transform 
13.5
13.3 Laplace Transforms of Some Common Right-Sided Functions 
13.7
13.4 The s-Domain System Function H(s) 
13.9
13.5 Poles and Zeros of System Function and Excitation Function 
13.11
13.6 method of Partial Fractions for Inverting Laplace Transforms 
13.13
13.7 Some Theorems on Laplace Transforms 
13.19
13.7.1 Time-Shifting Theorem 
13.19
13.7.2 Frequency-Shifting Theorem 
13.21
13.7.3 Time-Differentiation Theorem 
13.21
13.7.4 Time-Integration Theorem 
13.22
13.7.5 s-Domain-Differentiation Theorem 
13.23
13.7.6 s-Domain-Integration Theorem 
13.23
13.7.7 Convolution Theorem 
13.24
13.7.8 Initial Value Theorem 
13.24
13.7.9 Final Value Theorem 
13.25
13.8 Solution of Differential Equations by Using Laplace Transforms 
13.25
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Contents
13.9 The s-Domain Equivalent Circuit 
13.28
13.9.1 s-Domain Equivalents of Circuit Elements 
13.28
13.9.2 Is s-domain Equivalent Circuit Completely Equivalent 
to Original Circuit? 
13.30
13.10 Total Response of Circuits Using s-Domain Equivalent Circuit 
13.31
13.11 Network Functions and Pole-Zero Plots 
13.43
13.11.1 Driving-Point Functions and Transfer Functions 
13.43
13.11.2 The Three Interpretations for a Network Function H(s) 
13.44
13.11.3 Poles and Zeros of H(s) and Natural Frequencies of the Circuit 
13.45
13.11.4 Specifying a Network Function 
13.47
13.12 Impulse Response of Network Functions from Pole-Zero Plots 
13.49
13.13 Sinusoidal Steady-State Frequency Response from Pole-Zero Plots 
13.53
13.13.1 Three Interpretations for H( j
w
) 
13.54
13.13.2 Frequency Response from Pole-Zero Plot 
13.55
13.14 Summary 
13.58
13.15 Problems 
13.60