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Circuit analysis

J E Whitehouse, University of Reading, UK

This text presents the fundamentals of circuit analysis in a way suitable for first and second year undergraduate courses in electronic or electrical engineering. It is very much a ‘theme text’ and not a work book. The author is at pains to follow the logical thread of the subject, showing that the development of topics, one from the other, is not ad hoc as it can sometimes appear. A case in point is the application of graph theory to justify the derivation of the Node- and Mesh-equations from the more extensive set of Kirchhoff current and voltage equations. The topology of networks is stressed, again with the aid of graph theory.

The Fourier series is discussed at an early stage in regard to time-varying voltages to pave the way for sinusoidal analysis, and then dealt with in a later chapter. The complex frequency is presented at the earliest opportunity with ‘steady a.c.’ subsequently seen as a special case. The use of Laplace transformation appears as an operational method for the solution of differential equations which govern the behaviour of all physical systems. However, more emphasis is laid on the use of impedances as a means of bypassing the need to solve, or indeed even having to write down, differential equations.

The author discusses the role of network duals in circuit analysis, and clarifies the duality of Thevenin’s and Norton’s equations, and also exploits time/frequency duality of the Fourier transform in his treatment of the convolution of functions in time and frequency.

Worked examples are given throughout the book, together with chapter problems for which the author has provided solutions and guidance.

ISBN 1 898563 40 3
ISBN-13: 978 1 898563 40 2
December 1997
200 pages  234 x 173mm  hardback  
£35.00 / US$60.00 / €45.00

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About the author

John E Whitehouse, University of Reading, UK

Contents

Fundamentals
 - The Electronic Engineer
 - The Electronic System
 - The Linear System
 - Passive and Active Circuits
 - Ideal Sources and Practical Sources
 - Stability and Causality
 - Summary
 - Problems

Network equations
 - Kirchhoff’s Laws
 - The Node and Loop Equations
 - Tellegen’s Theorem
 - The State Equations
 - Summary
 - Problems

Network theorems
 - Superposition in Network Analysis
 - Thevenin’s and Norton’s Theorems
 - Power Transfer between Systems
 - Network Duals
 - Summary
 - Problems

Networks with inductors and capacitors
 - General n-terminal and Two-port Networks
 - The Free Response of Systems
 - The Role of the Sine Function
 - Response to a Simple Harmonic Input
 - 5 Mutual Inductance: Networks with Transformers
 - Summary
 - Problems

Network analysis using phasors
 - Complex Exponential Representation of Simple Harmonic Motion
 - A General Solution for the Free Response
 - The Complex Frequency
 - Response to a Complex Exponential input
 - The nth Order System
 - The Complex Impedance
 - Networks with Transformers
 - Summary
 - Problems

The Laplace transform in network analysis
 - Operational Calculus
 - The Laplace Transform
 - Application to Network Equations
 - The General Interpretation of the System Function
 - The Laplacian Impedance
 - Finding the Time Domain Response
 - The Impulse Response of Networks
 - Non-zero Initial Stored Energy
 - The Bilateral Laplace Transform
 - Summary
 - Problems

The Fourier series and Fourier transform
 - Time and Frequency Domains
 - Fourier’s Theorem
 - The Fourier Transform
 - Impulses in Time and Frequency: Duality and Convolution
 - Time-shifted Impulses and Impulse Sequences
 - Rectangular Pulses in Time and Frequency
 - Summary
 - Problems

The Frequency response of networks
 - The Response to Steady a.c
 - The Steady a.c. Impedance
 - Driving-point Impedance and Admittance
 - Reflected impedance in Networks with Transformers
 - Logarithmic Scales, Decibels and Bode Plots
 - First-order Filters
 - Second-order Band-pass Filters
 - The Quality Factor, Q
 - Second-order Notch, Low-pass and High-pass Filters
 - Summary
 - Problems

Power dissipation and energy storage in networks
 - Power Dissipation in Resistive Networks
 - Power Dissipation in Networks with Reactive Components
 - The Complex Power
 - Stored Energy in an LCR Circuit
 - Summary
 - Problems

Appendices
 - Coefficients in the Fourier series
 - General solution of first-order linear differential equation
 - Laplace operational transforms
 - Recommended reading
 - Answers and guidance to problems