Power Electronic Systems : Walsh Analysis with MATLAB® book cover
1st Edition

Power Electronic Systems
Walsh Analysis with MATLAB®

ISBN 9781138075023
Published March 30, 2017 by CRC Press
297 Pages 76 B/W Illustrations

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Book Description

A Totally Different Outlook on Power Electronic System Analysis

Power Electronic Systems: Walsh Analysis with MATLAB® builds a case for Walsh analysis as a powerful tool in the study of power electronic systems. It considers the application of Walsh functions in analyzing power electronic systems, and the advantages offered by Walsh domain analysis of power electronic systems.

Solves Power Electronic Systems in an Unconventional Way

This book successfully integrates power electronics as well as systems and control. Incorporating a complete orthonormal function set very much unlike the sine–cosine functions, it introduces a blending between piecewise constant orthogonal functions and power electronic systems. It explores the background and evolution of power electronics, and discusses Walsh and related orthogonal basis functions. It develops the mathematical foundation of Walsh analysis, and first- and second-order system analyses by Walsh technique. It also describes the Walsh domain operational method and how it is applied to linear system analysis.

Introduces Theories Step by Step

While presenting the underlying principles of Walsh analysis, the authors incorporate many illustrative examples, and include a basic introduction to linear algebra and MATLAB® programs. They also examine different orthogonal piecewise constant basis functions like Haar, Walsh, slant, block pulse functions, and other related orthogonal functions along with their time scale evolution.

• Analyzes pulse–fed single input single output (SISO) first- and second-order systems

• Considers stepwise and continuously pulse width modulated chopper systems

• Describes a detailed analysis of controlled rectifier circuits

• Addresses inverter circuits

Power Electronic Systems: Walsh Analysis with MATLAB® is written for postgraduate students, researchers, and academicians in the area of power electronics as well as systems and control.

Table of Contents


Evolution of Power Electronics

Analysis of Power Electronic Circuits

Search for a New Method of Analysis


An Alternative Class of Orthogonal Functions

Orthogonal Functions and Their Properties

Haar Functions

Rademacher and Walsh Functions

Block Pulse Functions and Their Applications

Slant Functions

Delayed Unit Step Functions

General Hybrid Orthogonal Functions

Sample-and-Hold Functions

Triangular Functions

Hybrid Function: A Combination of SHF and TF

Applications of Walsh Functions


Walsh Domain Operational Method of System Analysis

Introduction to Operational Matrices

Time Scaling of Operational Matrices

Philosophy of the Proposed Walsh Domain Operational Technique

Analysis of a First-Order System with Step Input

Analysis of a Second-Order System with Step Input

Oscillatory Phenomenon in Walsh Domain System Analysis



Analysis of Pulse-Fed Single-Input Single-Output Systems

Analysis of a First-Order System

Analysis of a Second-Order System

Pulse-Width Modulated Chopper System



Analysis of Controlled Rectifier Circuits

Representation of a Sine Wave by Walsh Functions

Conventional Analysis of Half-Wave Controlled Rectifier

Walsh Domain Analysis of Half-Wave Controlled Rectifier

Walsh Domain Analysis of Full-Wave Controlled Rectifier



Analysis of Inverter Circuits

Voltage Control of a Single-Phase Inverter

Analysis of an RL Load Fed from a Typical Three-Phase Inverter Line-to-Neutral Voltage





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Anish Deb obtained his BTech in 1974 (recipient of Calcutta University silver medal), MTech in 1976 (recipient of Calcutta University gold medal and P. N. Ghosh memorial gold medal), and PhD (Tech) in 1990 from the Department of Applied Physics, University of Calcutta, India. In 1978, he joined the Department of Applied Physics, University of Calcutta, as Lecturer in 1983. In 1990, he became Reader (associate professor) in the same department. He has been holding the post of Professor since 1998. His research interest includes automatic control in general and application of "alternative" orthogonal functions in power electronics and systems and control. He has authored one book entitled "Triangular orthogonal functions for the analysis of continuous time systems" and published more than 65 research papers in different national and international journals and conferences.

Suchismita Ghosh obtained her BTech (2008) from the Calcutta Institute of Engineering and Management, West Bengal University of Technology, India, and MTech (2010) from the Department of Applied Physics, University of Calcutta, India. She is currently an assistant professor in the Department of Electrical Engineering, MCKV Institute of Engineering, West Bengal University of Technology, India. She has taught courses on power electronics, basic electrical engineering, control systems, and electrical machines. Her research area includes automatic control in general and application of "alternative" orthogonal functions in systems and control. She is presently involved in research with Anish Deb and has published five research papers in international journals and national conferences.


"One of the salient features of power electronic dynamics is the switching of the waveforms involved in the phenomenon. However, time domain analysis of power electronics often uses Fourier series to represent waveforms despite its smooth nature and its difficulties to compactly represent switching signals. This book uses Walsh Series, a switching orthogonal set of functions, to more effectively represent waveforms in power electronics. The book may be the only one in the market with this philosophy."
––J Jesus Rico-Melgoza, Universidad Michoacana de San Nicolas de Hidalgo, Morelia, Mexico

"… a remarkable job of presenting the subject in a clear and coherent manner. … My recommendation to anyone who is interested in the analysis any other system with such discontinuous phenomena: This book may guide you to the use of appropriate tools."
—Ganti Prasada Rao, Member, UNESCO-EOLSS Joint Committee

"… an authoritative reference for researchers and engineering professionals with an interest in the area of power electronic systems, their optimization and practical applications."
—Radomir S. Stanković, Dept. of Computer science, Faculty of Electronic Engineering, Niš, Serbia

"… a refreshing approach based on Walsh analysis and presents an alternate approach to Fourier series approach that is usually followed. The material presented is quite systematic. Even if one does not have any prior knowledge on the topics, the book is still very much readable. It presents a detail bottom-to-top tutorial approach in each chapter, with adequate background material in first two chapters, which I am sure will make it quite easier for the students and practicing engineers to follow the concepts effortlessly."
—Radhakant Padhi, Indian Institute of Science, Bangalore