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2021

      Abdullah Eroglu received his PhD degree in electrical engineering from the Electrical Engineering & Computer Science Department at Syracuse University, in 2004. He was a Senior RF Design Engineer with MKS Instruments, from 2000 to 2008, where he was involved in the design of RF amplifier systems. He joined Purdue University Fort Wayne in 2008 and worked as Professor and Chair of the Electrical and Computer Engineering Department until 2018. Since then, he has been Emeritus Professor at Purdue University and Professor and Chair at the Electrical and Computer Engineering Department, North Carolina A&T State University. He was a Faculty Fellow with the Fusion Energy Division, Oak Ridge National Laboratory, in 2009. His current research interests include RF/microwave/THz circuit design and applications, RF amplifiers and topologies, antennas, RF metrology, wave propagation, and radiation characteristics of anisotropic, gyrotropic, and metamaterials. He has published over 140 journal and conference publications, and has several patents in his area of expertise. He is the author of five books and co‐editor of one book. He is a reviewer and on the editorial board of several journals.

      Spending a lifetime with a researcher sometimes can be challenging. My wife and my children do just that, and they are always with me at every step along the way. They support me for every project – and gave me the encouragement I needed to complete this book, too.

      I would also like to thank my editor, Juliet Booker, for her patience and support of this book. She was very understanding and gave me the time I needed to complete the book.

      RF/Microwave Engineering and Applications in Energy Systems is accompanied by a companion website:

       www.wiley.com/go/eroglu/rfmicrowave

      The website includes:

       Solutions to End of Chapter Problems

      1.1 Introduction

      The fundamentals of electromagnetics constitute steps toward the advancement of technology in communication, radar, and energy and power applications. In this chapter, some important theorems and mathematical concepts are discussed with examples.

      1.2.1 Vector Analysis

      In Figure 1.1, the magnitude of the vector is given by |A|. The unit vector which defines the direction of the vector is given by

      (1.2)

      You may consider falling snowflakes as an example for a vector which has direction and magnitude.

      1.2.1.1 Unit Vector Relationship

      (1.4a)

      (1.4b)

      (1.4c)

      In Cartesian coordinate system, unit vectors are defined as

      (1.5)

      So

      (1.6a)

      (1.6b)ModifyingAbove y With ampersand c period circ semicolon times ModifyingAbove z With ampersand c period circ semicolon equals ModifyingAbove x With ampersand 
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