Modern Printed Circuit Antennas

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Modern Printed-Circuit Antennas

Author : Hussain Al-Rizzo
Publisher : BoD – Books on Demand
ISBN 13 : 1838808574
Total Pages : 178 pages
Book Rating : 4.8/5 (388 download)

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Book Synopsis Modern Printed-Circuit Antennas by : Hussain Al-Rizzo

Download or read book Modern Printed-Circuit Antennas written by Hussain Al-Rizzo and published by BoD – Books on Demand. This book was released on 2020-10-28 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents in-depth information on a variety of the latest developments in modern printed-circuit antennas written by several prominent authors in the field. This book consists of nine chapters covering a wide range of recent research topics. The topics covered include low-profile metamaterial-based adaptive beamforming techniques, high performance meta-surface antennas, fractal antennas, reconfigurable antennas for 5G systems operating at 60 GHz, radiation pattern synthesis of planar arrays using parasitic patches fed by a small number of active elements, decoupled and de-scattered monopole MIMO antenna arrays with orthogonal radiation patterns, ultra-wide band antennas with defected ground plane and microstrip line fed for Wi-Fi/Wi-Max/DCS/5G/satellite communications, and design, fabrication, and characterization of wearable textile antennas with high body-antenna isolation.

Millimeter-wave Microstrip and Printed Circuit Antennas

Author : P. Bhartia
Publisher : Artech House Publishers
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Millimeter-wave Microstrip and Printed Circuit Antennas by : P. Bhartia

Download or read book Millimeter-wave Microstrip and Printed Circuit Antennas written by P. Bhartia and published by Artech House Publishers. This book was released on 1991 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides information needed to design millimeter-wave microstrip and printed circuit antennas from analysis methods and materials selection to antennas for particular applications. Special focus is given to the issues that impact the ability to scale microwave frequency designs to the millimeter-wav

Advanced Radio Frequency Antennas for Modern Communication and Medical Systems

Author : Albert Sabban
Publisher : BoD – Books on Demand
ISBN 13 : 1839683457
Total Pages : 282 pages
Book Rating : 4.8/5 (396 download)

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Book Synopsis Advanced Radio Frequency Antennas for Modern Communication and Medical Systems by : Albert Sabban

Download or read book Advanced Radio Frequency Antennas for Modern Communication and Medical Systems written by Albert Sabban and published by BoD – Books on Demand. This book was released on 2020-09-23 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this book is to present novel radio frequency (RF) antennas for 5G, IOT, and medical applications. The book is divided into four sections that present the main topics of radio frequency antennas. The rapid growth in development of cellular wireless communication systems over the last twenty years has resulted in most of world population owning smartphones, smart watches, I-pads, and other RF communication devices. Efficient compact wideband antennas are crucial in RF communication devices. This book presents information on planar antennas, cavity antennas, Vivaldi antennas, phased arrays, MIMO antennas, beamforming phased array reconfigurable Pabry-Perot cavity antennas, and time modulated linear array.

Modern Antenna Design

Author : Thomas A. Milligan
Publisher : John Wiley & Sons
ISBN 13 : 0471457760
Total Pages : 646 pages
Book Rating : 4.4/5 (714 download)

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Book Synopsis Modern Antenna Design by : Thomas A. Milligan

Download or read book Modern Antenna Design written by Thomas A. Milligan and published by John Wiley & Sons. This book was released on 2005-07-11 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical book written for engineers who design and use antennas The author has many years of hands on experience designing antennas that were used in such applications as the Venus and Mars missions of NASA The book covers all important topics of modern antenna design for communications Numerical methods will be included but only as much as are needed for practical applications

Modern Antenna Handbook

Author : Constantine A. Balanis
Publisher : John Wiley & Sons
ISBN 13 : 1118209753
Total Pages : 1617 pages
Book Rating : 4.1/5 (182 download)

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Book Synopsis Modern Antenna Handbook by : Constantine A. Balanis

Download or read book Modern Antenna Handbook written by Constantine A. Balanis and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 1617 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most up-to-date, comprehensive treatment of classical and modern antennas and their related technologies Modern Antenna Handbook represents the most current and complete thinking in the field of antennas. The handbook is edited by one of the most recognizable, prominent, and prolific authors, educators, and researchers on antennas and electromagnetics. Each chapter is authored by one or more leading international experts and includes cover-age of current and future antenna-related technology. The information is of a practical nature and is intended to be useful for researchers as well as practicing engineers. From the fundamental parameters of antennas to antennas for mobile wireless communications and medical applications, Modern Antenna Handbook covers everything professional engineers, consultants, researchers, and students need to know about the recent developments and the future direction of this fast-paced field. In addition to antenna topics, the handbook also covers modern technologies such as metamaterials, microelectromechanical systems (MEMS), frequency selective surfaces (FSS), and radar cross sections (RCS) and their applications to antennas, while five chapters are devoted to advanced numerical/computational methods targeted primarily for the analysis and design of antennas.

Microstrip and Printed Antennas: Applications-Based Designs

Author : Anil Pandey
Publisher : Artech House
ISBN 13 : 1630816701
Total Pages : 480 pages
Book Rating : 4.6/5 (38 download)

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Book Synopsis Microstrip and Printed Antennas: Applications-Based Designs by : Anil Pandey

Download or read book Microstrip and Printed Antennas: Applications-Based Designs written by Anil Pandey and published by Artech House. This book was released on 2019-03-31 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive resource presents antenna fundamentals balanced with the design of printed antennas. Over 70 antenna projects, along with design dimensions, design flows and antenna performance results are discussed, including antennas for wireless communication, 5G antennas and beamforming. Examples of smartphone antennas, MIMO antennas, aerospace and satellite remote sensing array antennas, automotive antennas and radar systems and many more printed antennas for various applications are also included. These projects include design dimensions and parameters that incorporate the various techniques used by industries and academia. This book is intended to serve as a practical microstrip and printed antenna design guide to cover various real-world applications. All Antenna projects discussed in this book are designed, analyzed and simulated using full-wave electromagnetic solvers. Based on several years of the author’s research in antenna design and development for RF and microwave applications, this book offers an in-depth coverage of practical printed antenna design methodology for modern applications.

Wearable and Neuronic Antennas for Medical and Wireless Applications

Author : Arun Kumar
Publisher : John Wiley & Sons
ISBN 13 : 1119791804
Total Pages : 276 pages
Book Rating : 4.1/5 (197 download)

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Book Synopsis Wearable and Neuronic Antennas for Medical and Wireless Applications by : Arun Kumar

Download or read book Wearable and Neuronic Antennas for Medical and Wireless Applications written by Arun Kumar and published by John Wiley & Sons. This book was released on 2022-05-24 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: WEARABLE AND NEURONIC ANTENNAS FOR MEDICAL AND WIRELESS APPLICATIONS This new volume in this exciting new series, written and edited by a group of international experts in the field, covers the latest advances and challenges in wearable and neuronic antennas for medical and wireless applications. Antenna development and engineering is changing at a rapid pace, and it is incredibly important that engineers, scientists, and students in the field have a valuable reference work to consult. Students are able to use this book as a learning tool, and professors and industrial short courses are able to use it as a textbook. Covering all of the advances and developments of wearable and neuronic antennas for medical and wireless applications, this outstanding new volume offers information not available anywhere else in any other format. Covering new research and development of antenna designs never seen before, this volume, written and edited by a team of experts in the field, breaks new ground, offering new solutions to engineering and scientific problems to experts in the field, while providing the full theoretical and conceptual background for the practical applications. Whether for the veteran engineer or scientist, the student, or a manager or other technician working in the field, this volume is a must-have for any library.

Advanced Sensing in Image Processing and IoT

Author : Rashmi Gupta
Publisher : CRC Press
ISBN 13 : 1000543021
Total Pages : 380 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Advanced Sensing in Image Processing and IoT by : Rashmi Gupta

Download or read book Advanced Sensing in Image Processing and IoT written by Rashmi Gupta and published by CRC Press. This book was released on 2021-03-26 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides future research directions in IoT and image processing based Energy, Industry, and Healthcare domain and explores the different applications of its associated technologies. However, the Internet of Things and image processing is a very big field with a lot of subfields, which are very important such as Smart Homes to improve our daily life, Smart Cities to improve the citizens' life, Smart Towns to recover the livability and traditions, Smart Earth to protect our world, and Industrial Internet of Things to create safer and easier jobs. This book considers very important research areas in Energy, Industry, and Healthcare domain with IoT and image processing applications.The aim of the book to highlights future directions of optimization methods in various engineering and science applications in various IoT and image processing applications. Emphasis is given to deep learning and similar models of neural network-based learning techniques employed in solving optimization problems of different engineering and science applications. The role of AI in mechatronics is also highlighted using suitable optimization methods. This book considers very important research areas in Energy, Industry, and Healthcare. It addresses major issues and challenges in Energy, Industry, and Healthcare and solutions proposed for IoT-enabled cellular/computer networks, routing/communication protocols, surveillances applications, secured data management, and positioning approaches. It focuses mainly on smart and context-aware implementations. Key sailing Features: The impact of the proposed book is to provide a major area of concern to develop a foundation for the implementation process of new image processing and IoT devices based on Energy, Industry, and Healthcare related technology. The researchers working on image processing and IoT devices can correlate their work with other requirements of advanced technology in Energy, Industry, and Healthcare domain. To make aware of the latest technology like AI and Machine learning in Energy, Industry, and Healthcare related technology. Useful for the researcher to explore new things like Security, cryptography, and privacy in Energy, Industry, and Healthcare related technology. People who want to start in Energy, Industry, and Healthcare related technology with image processing and IoT world.

IMDC-IST 2021

Author : Abd-Alhameed Raed
Publisher : European Alliance for Innovation
ISBN 13 : 1631903403
Total Pages : 1790 pages
Book Rating : 4.6/5 (319 download)

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Book Synopsis IMDC-IST 2021 by : Abd-Alhameed Raed

Download or read book IMDC-IST 2021 written by Abd-Alhameed Raed and published by European Alliance for Innovation. This book was released on 2022-01-26 with total page 1790 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the Second International Conference on Integrated Sciences and Technologies (IMDC-IST-2021). Where held on 7th–9th Sep 2021 in Sakarya, Turkey. This conference was organized by University of Bradford, UK and Southern Technical University, Iraq. The papers in this conference were collected in a proceedings book entitled: Proceedings of the second edition of the International Multi-Disciplinary Conference Theme: “Integrated Sciences and Technologies” (IMDC-IST-2021). The presentation of such a multi-discipline conference provides a lot of exciting insights and new understanding on recent issues in terms of Green Energy, Digital Health, Blended Learning, Big Data, Meta-material, Artificial-Intelligence powered applications, Cognitive Communications, Image Processing, Health Technologies, 5G Communications. Referring to the argument, this conference would serve as a valuable reference for future relevant research activities. The committee acknowledges that the success of this conference are closely intertwined by the contributions from various stakeholders. As being such, we would like to express our heartfelt appreciation to the keynote speakers, invited speakers, paper presenters, and participants for their enthusiastic support in joining the second edition of the International Multi-Disciplinary Conference Theme: “Integrated Sciences and Technologies” (IMDC-IST-2021). We are convinced that the contents of the study from various papers are not only encouraged productive discussion among presenters and participants but also motivate further research in the relevant subject. We appreciate for your enthusiasm to attend our conference and share your knowledge and experience. Your input was important in ensuring the success of our conference. Finally, we hope that this conference serves as a forum for learning in building togetherness and academic networks. Therefore, we expect to see you all at the next IMDC-IST.

IMDC-SDSP 2020

Author : Raed Abd-Alhameed
Publisher : European Alliance for Innovation
ISBN 13 : 163190261X
Total Pages : 1619 pages
Book Rating : 4.6/5 (319 download)

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Book Synopsis IMDC-SDSP 2020 by : Raed Abd-Alhameed

Download or read book IMDC-SDSP 2020 written by Raed Abd-Alhameed and published by European Alliance for Innovation. This book was released on 2020-09-09 with total page 1619 pages. Available in PDF, EPUB and Kindle. Book excerpt: IMDC-SDSP conference offers an exceptional platform and opportunity for practitioners, industry experts, technocrats, academics, information scientists, innovators, postgraduate students, and research scholars to share their experiences for the advancement of knowledge and obtain critical feedback on their work. The timing of this conference coincides with the rise of Big Data, Artificial Intelligence powered applications, Cognitive Communications, Green Energy, Adaptive Control and Mobile Robotics towards maintaining the Sustainable Development and Smart Planning and management of the future technologies. It is aimed at the knowledge generated from the integration of the different data sources related to a number of active real-time applications in supporting the smart planning and enhance and sustain a healthy environment. The conference also covers the rise of the digital health, well-being, home care, and patient-centred era for the benefit of patients and healthcare providers; in addition to how supporting the development of a platform of smart Dynamic Health Systems and self-management.

Fostering Cross-Industry Sustainability With Intelligent Technologies

Author : Mishra, Brojo Kishore
Publisher : IGI Global
ISBN 13 :
Total Pages : 633 pages
Book Rating : 4.3/5 (693 download)

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Book Synopsis Fostering Cross-Industry Sustainability With Intelligent Technologies by : Mishra, Brojo Kishore

Download or read book Fostering Cross-Industry Sustainability With Intelligent Technologies written by Mishra, Brojo Kishore and published by IGI Global. This book was released on 2024-01-22 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: In today's context of intricate global challenges, encompassing climate crises, resource scarcity, and social disparities, the imperative for sustainable development has never been more pressing. While academic scholars and researchers are instrumental in crafting solutions, they often grapple with the intricate balance between theoretical concepts and practical implementation. This gap impedes the transformation of innovative ideas into tangible societal progress, leaving a void where effective real-world strategies for cross-industry sustainability should flourish. "Fostering Cross-Industry Sustainability With Intelligent Technologies" seeks to bridge this divide. This book is more than just a collection of pages; it serves as a roadmap for those determined to make a tangible impact. It brings together a diverse group of esteemed experts from various disciplines, offering a comprehensive spectrum of actionable insights, all grounded in the ethical imperatives of inclusivity and environmental responsibility. Anchored in the United Nations Sustainable Development Goals (SDGs), this volume serves as a guiding star, channeling theoretical expertise into practical solutions. For academic scholars, scientists, innovators, and students alike, Fostering Cross-Industry Sustainability With Intelligent Technologies is the definitive guidepost. It fosters a profound understanding of the real-world implications of research, promoting interdisciplinary collaborations that transcend conventional boundaries. This comprehensive book presents a wealth of sustainable science and intelligent technology applications, all while emphasizing the importance of ethics and societal impact. With visionary insights woven throughout its pages, it calls upon humanity to envision a future where challenges transform into opportunities, and sustainable development becomes an attainable reality.

Microwave/RF Components for 5G Front-End Systems

Author : Naser Ojaroudi Parchin
Publisher : AVID SCIENCE
ISBN 13 : 9388170822
Total Pages : 207 pages
Book Rating : 4.3/5 (881 download)

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Book Synopsis Microwave/RF Components for 5G Front-End Systems by : Naser Ojaroudi Parchin

Download or read book Microwave/RF Components for 5G Front-End Systems written by Naser Ojaroudi Parchin and published by AVID SCIENCE. This book was released on 2019-12-16 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the development of mobile 4G communication system, people’s requirements for the speed of wireless communication are rapidly increasing. In order to meet this need, the research and development of the fifth generation (5G) wireless systems has been carried out. Compared with previous generation (1G~4G), 5G will have significant improvements in transmission rate, latency, mobility and so on. The book “Microwave/RF Components for 5G Front-End Systems” is outlines the simulation, design, and fabrication of microwave components including Antennas, Filters, and Power Amplifiers for 5G wireless communications. In addition, exhaustive reviews have been presented, classifying the various types and applications of reconfigurable antennas, Filters and amplifiers for current and future wireless networks.

Advances in Communication, Devices and Networking

Author : Sourav Dhar
Publisher : Springer Nature
ISBN 13 : 9811629110
Total Pages : 501 pages
Book Rating : 4.8/5 (116 download)

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Book Synopsis Advances in Communication, Devices and Networking by : Sourav Dhar

Download or read book Advances in Communication, Devices and Networking written by Sourav Dhar and published by Springer Nature. This book was released on 2021-08-30 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers recent trends in the field of devices, wireless communication and networking. It gathers selected papers presented at the International Conference on Communication, Devices and Networking (ICCDN 2020), which was organized by the Department of Electronics and Communication Engineering, Sikkim Manipal Institute of Technology, Sikkim, India, on 19–20 December 2020. Gathering cutting-edge research papers prepared by researchers, engineers and industry professionals, it helps young and experienced scientists and developers alike to explore new perspectives, and offer them inspirations on how to address real-world problems in the areas of electronics, communication, devices and networking.

Smart Antennas: Recent Trends in Design and Applications

Author : Praveen Kumar Malik
Publisher : Bentham Science Publishers
ISBN 13 : 1681088606
Total Pages : 108 pages
Book Rating : 4.6/5 (81 download)

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Book Synopsis Smart Antennas: Recent Trends in Design and Applications by : Praveen Kumar Malik

Download or read book Smart Antennas: Recent Trends in Design and Applications written by Praveen Kumar Malik and published by Bentham Science Publishers. This book was released on 2021-07-30 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference provides the reader with focused information about microstrip antenna design and applications. Readers are first introduced to the basic design of microstrip antennas. Subsequent chapters explain how microstrip antennas are suitable for practical applications. These chapters cover topics such as fractal and defected ground structure antennas, microstrip antenna evaluation, and the use of microstrip antennas in mobile communications and IoT applications. Scholars, researchers, and industrial professionals involved in the fields of electronics and electrical engineering as well as instrumentation will benefit from the information given in this book.

Antennas

Author : Yi Huang
Publisher : John Wiley & Sons
ISBN 13 : 1119092329
Total Pages : 548 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Antennas by : Yi Huang

Download or read book Antennas written by Yi Huang and published by John Wiley & Sons. This book was released on 2021-09-14 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Antennas From Theory to Practice Comprehensive coverage of the fundamentals and latest developments in antennas and antenna design In the newly revised Second Edition of Antennas: From Theory to Practice, renowned researcher, engineer, and author Professor Yi Huang delivers comprehensive and timely coverage of issues in modern antenna design and theory. Practical and accessible, the book is written for engineers, researchers, and students who work with radio frequency/microwave engineering, radar, and radio communications. The book details the basics of transmission lines, radiowaves and propagation, antenna theory, antenna analysis and design using industrial standard design software tools and the theory of characteristic modes, antenna measurement equipment, facilities, and techniques. It also covers the latest developments in special topics, like small and mobile antennas, wide- and multi-band antennas, automotive antennas, RFID, UWB, metamaterials, reconfigurable and MIMO antennas, and more. The new edition includes up to date information on a wide variety of newly relevant topics and trends, like adaptive impedance matching, the theory of characteristic modes, antenna materials and fabrication processes, and over-the-air (OTA) antenna system measurements. Many questions and examples are provided which enhances the learning experience. The book covers: An introduction to circuit concepts and transmission lines, including lumped and distributed element systems, transmission line theory, and the Smith Chart An exploration of field concepts and radiowaves, including wave equations and solutions and radiowave propagation mechanisms, characteristics, and models Discussions of antenna basics and popular antennas, including wire-type antennas, aperture-type antennas, and antenna arrays Information about antenna manufacturing and measurements, including antenna measurement facilities and methods The use of industrial standard simulation tools for antenna design and analysis Perfect for engineers and researchers who work in RF engineering or radar and radio communications, Antennas: From Theory to Practice, Second Edition will also earn a place on the bookshelves of university students seeking a concise and practical introduction to the basics of antennas and antenna design.

RF/Microwave Engineering and Applications in Energy Systems

Author : Abdullah Eroglu
Publisher : John Wiley & Sons
ISBN 13 : 1119268818
Total Pages : 644 pages
Book Rating : 4.1/5 (192 download)

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Book Synopsis RF/Microwave Engineering and Applications in Energy Systems by : Abdullah Eroglu

Download or read book RF/Microwave Engineering and Applications in Energy Systems written by Abdullah Eroglu and published by John Wiley & Sons. This book was released on 2022-04-07 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: RF/MICROWAVE ENGINEERING AND APPLICATIONS IN ENERGY SYSTEMS An essential text with a unique focus on RF and microwave engineering theory and its applications In RF/Microwave Engineering and Applications in Energy Systems, accomplished researcher Abdullah Eroglu delivers a detailed treatment of key theoretical aspects of radio-frequency and microwave engineering concepts along with parallel presentations of their practical applications. The text includes coverage of recent advances in the subject, including energy harvesting methods, RFID antenna designs, HVAC system controls, and smart grids. The distinguished author provides step-by-step solutions to common engineering problems by way of numerous examples and offers end-of-chapter problems and solutions on each topic. These practical applications of theoretical subjects aid the reader with retention and recall and demonstrate a solid connection between theory and practice. The author also applies common simulation tools in several chapters, illustrating the use and implementation of time domain circuit simulators in conjunction with electromagnetic simulators, as well as Matlab for design, simulation, and implementation at the component and system levels. Readers will also benefit from: A thorough introduction to the foundations of electromagnetics, including line, surface, and volume integrals, vector operation and theorems, and Maxwell’s equations Comprehensive explorations of passive and active components in RF and microwave engineering, including resistors, capacitors, inductors, and semiconductor materials and active devices Practical discussions of transmission lines, including transmission line analysis, Smith charts, microstrip lines, and striplines In-depth examinations of network parameters, including impedance parameters, ABCD parameters, h-Hybrid parameters, and network connections Perfect for senior-level undergraduates and graduate students studying RF or Microwave engineering, RF/Microwave Engineering and Applications in Energy Systems is also an indispensable resource for professionals whose work touches on radio-frequency and microwave technologies.

Planar Spiral Inductors, Planar Antennas and Embedded Planar Transformers

Author : Amal Banerjee
Publisher : Springer Nature
ISBN 13 : 303108778X
Total Pages : 197 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Planar Spiral Inductors, Planar Antennas and Embedded Planar Transformers by : Amal Banerjee

Download or read book Planar Spiral Inductors, Planar Antennas and Embedded Planar Transformers written by Amal Banerjee and published by Springer Nature. This book was released on 2022-08-26 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a novel, automated, accurate and unified scheme to design and determine the performance characteristics of standalone planar, spiral inductors and multiple coupled planar spiral inductors (as in embedded transformers), for RF/microwave MMIC designers. The author demonstrates with a set of analysis/design examples a novel scheme that exploits judiciously the existing transmission theory and concepts, organizing and condensing available, scattered information/knowledge about planar spiral inductor, embedded planar transformer and planar antenna design and performance evaluation, into one coherent and unified electronic circuit model easily used by radio frequency electronic circuit engineers. A dedicated chapter contains an exhaustive (19) set of design examples. Presents a bottom-up scheme, starting with Maxwell's equations of classical electrodynamics and transmission line theory (Telegrapher's equation), specifically microstrips; Demonstrates design of standalone planar, spiral inductors and multiple coupled planar spiral inductors; Includes a set of ready-to-use, C executables (for both Linux and Windows) , that accept predefined input parameters for each of the sub-circuits discussed and generate SPICE netlists for the equivalent electrical circuit; Automates execution of multi-step design calculations to guarantee their accuracy and reliability.