Author: Venceslav F. Kroupa
Publisher: John Wiley & Sons
ISBN: 111831011X
Category : Technology & Engineering
Languages : en
Pages : 330
Book Description
An in-depth look at the theory and applications of frequency stability An understanding of the acquisition of stable frequency is essential for anyone who needs to solve noise problems in wireless communications. This book offers a thorough introduction to the principles and applications of frequency stability, arming practicing engineers with the tools they need to minimize noise in systems and devices that affect everyday communications for millions of people. With an emphasis on both practical and scientific points of view, Frequency Stability: Introduction and Applications examines frequency and time fluctuations in resonators, as well as the stability of both standard and practical microwave oscillators. It explains noise properties of building circuit blocks, introducing time domain properties and how they relate to noise spectral densities. Including a special chapter devoted to the design and properties of phase locked loops—a crucial topic for frequency synthesizers—the book also: Examines in detail L/F noise, showing how power losses in the propagation material extend over a long period of time Covers sapphire, optoelectronics, MW, and ring oscillators with the discussion of noise in delay-line oscillators with lasers Offers an extended treatment of phase noise in semiconductors and amplifiers based on Van der Ziel investigations Emphasizes the modified Allan variance in the time domain, including exact computations Outlines the relationship between resonator frequency and output phase noises via the feedback theory Featuring numerous tables with actual data, Frequency Stability: Introduction and Applications is an invaluable guide for engineers wishing to rein in acoustic and electromagnetic interference in modern communications.
Frequency Stability
Author: Venceslav F. Kroupa
Publisher: John Wiley & Sons
ISBN: 111831011X
Category : Technology & Engineering
Languages : en
Pages : 330
Book Description
An in-depth look at the theory and applications of frequency stability An understanding of the acquisition of stable frequency is essential for anyone who needs to solve noise problems in wireless communications. This book offers a thorough introduction to the principles and applications of frequency stability, arming practicing engineers with the tools they need to minimize noise in systems and devices that affect everyday communications for millions of people. With an emphasis on both practical and scientific points of view, Frequency Stability: Introduction and Applications examines frequency and time fluctuations in resonators, as well as the stability of both standard and practical microwave oscillators. It explains noise properties of building circuit blocks, introducing time domain properties and how they relate to noise spectral densities. Including a special chapter devoted to the design and properties of phase locked loops—a crucial topic for frequency synthesizers—the book also: Examines in detail L/F noise, showing how power losses in the propagation material extend over a long period of time Covers sapphire, optoelectronics, MW, and ring oscillators with the discussion of noise in delay-line oscillators with lasers Offers an extended treatment of phase noise in semiconductors and amplifiers based on Van der Ziel investigations Emphasizes the modified Allan variance in the time domain, including exact computations Outlines the relationship between resonator frequency and output phase noises via the feedback theory Featuring numerous tables with actual data, Frequency Stability: Introduction and Applications is an invaluable guide for engineers wishing to rein in acoustic and electromagnetic interference in modern communications.
Publisher: John Wiley & Sons
ISBN: 111831011X
Category : Technology & Engineering
Languages : en
Pages : 330
Book Description
An in-depth look at the theory and applications of frequency stability An understanding of the acquisition of stable frequency is essential for anyone who needs to solve noise problems in wireless communications. This book offers a thorough introduction to the principles and applications of frequency stability, arming practicing engineers with the tools they need to minimize noise in systems and devices that affect everyday communications for millions of people. With an emphasis on both practical and scientific points of view, Frequency Stability: Introduction and Applications examines frequency and time fluctuations in resonators, as well as the stability of both standard and practical microwave oscillators. It explains noise properties of building circuit blocks, introducing time domain properties and how they relate to noise spectral densities. Including a special chapter devoted to the design and properties of phase locked loops—a crucial topic for frequency synthesizers—the book also: Examines in detail L/F noise, showing how power losses in the propagation material extend over a long period of time Covers sapphire, optoelectronics, MW, and ring oscillators with the discussion of noise in delay-line oscillators with lasers Offers an extended treatment of phase noise in semiconductors and amplifiers based on Van der Ziel investigations Emphasizes the modified Allan variance in the time domain, including exact computations Outlines the relationship between resonator frequency and output phase noises via the feedback theory Featuring numerous tables with actual data, Frequency Stability: Introduction and Applications is an invaluable guide for engineers wishing to rein in acoustic and electromagnetic interference in modern communications.
Proceedings of the 6th International Conference on Electrical, Control and Computer Engineering
Author: Zainah Md. Zain
Publisher: Springer Nature
ISBN: 9811686904
Category : Technology & Engineering
Languages : en
Pages : 1148
Book Description
This book presents the proceedings of the 6th International Conference on Electrical, Control and Computer Engineering (InECCE 2021), held in Kuantan, Pahang, Malaysia, on 23 August 2021. The topics covered are sustainable energy, power electronics and drives and power engineering including distributed/renewable generation, power system optimization, artificial/computational intelligence, smart grid, power system protection and machine learning energy management and conservation. The book showcases some of the latest technologies and applications developed to solve local energy and power problems in order to ensure continuity, reliability and security of electricity for future generations. It also links topics covered the sustainable developed goals (SDGs) areas outlined by the United Nation for global sustainability. The book will appeal to professionals, scientists and researchers with experience in industry.
Publisher: Springer Nature
ISBN: 9811686904
Category : Technology & Engineering
Languages : en
Pages : 1148
Book Description
This book presents the proceedings of the 6th International Conference on Electrical, Control and Computer Engineering (InECCE 2021), held in Kuantan, Pahang, Malaysia, on 23 August 2021. The topics covered are sustainable energy, power electronics and drives and power engineering including distributed/renewable generation, power system optimization, artificial/computational intelligence, smart grid, power system protection and machine learning energy management and conservation. The book showcases some of the latest technologies and applications developed to solve local energy and power problems in order to ensure continuity, reliability and security of electricity for future generations. It also links topics covered the sustainable developed goals (SDGs) areas outlined by the United Nation for global sustainability. The book will appeal to professionals, scientists and researchers with experience in industry.
Frequency Standards And Metrology, Procs Of The 6th Symposium
Author: Patrick Gill
Publisher: World Scientific
ISBN: 9814488860
Category : Science
Languages : en
Pages : 679
Book Description
This book discusses the latest research ideas with application to frequency standards (e.g. optical clocks) and assesses ideas from previous symposia which have undergone critical analysis.
Publisher: World Scientific
ISBN: 9814488860
Category : Science
Languages : en
Pages : 679
Book Description
This book discusses the latest research ideas with application to frequency standards (e.g. optical clocks) and assesses ideas from previous symposia which have undergone critical analysis.
Piezoelectric MEMS Resonators
Author: Harmeet Bhugra
Publisher: Springer
ISBN: 3319286889
Category : Technology & Engineering
Languages : en
Pages : 423
Book Description
This book introduces piezoelectric microelectromechanical (pMEMS) resonators to a broad audience by reviewing design techniques including use of finite element modeling, testing and qualification of resonators, and fabrication and large scale manufacturing techniques to help inspire future research and entrepreneurial activities in pMEMS. The authors discuss the most exciting developments in the area of materials and devices for the making of piezoelectric MEMS resonators, and offer direct examples of the technical challenges that need to be overcome in order to commercialize these types of devices. Some of the topics covered include: Widely-used piezoelectric materials, as well as materials in which there is emerging interest Principle of operation and design approaches for the making of flexural, contour-mode, thickness-mode, and shear-mode piezoelectric resonators, and examples of practical implementation of these devices Large scale manufacturing approaches, with a focus on the practical aspects associated with testing and qualification Examples of commercialization paths for piezoelectric MEMS resonators in the timing and the filter markets ...and more! The authors present industry and academic perspectives, making this book ideal for engineers, graduate students, and researchers.
Publisher: Springer
ISBN: 3319286889
Category : Technology & Engineering
Languages : en
Pages : 423
Book Description
This book introduces piezoelectric microelectromechanical (pMEMS) resonators to a broad audience by reviewing design techniques including use of finite element modeling, testing and qualification of resonators, and fabrication and large scale manufacturing techniques to help inspire future research and entrepreneurial activities in pMEMS. The authors discuss the most exciting developments in the area of materials and devices for the making of piezoelectric MEMS resonators, and offer direct examples of the technical challenges that need to be overcome in order to commercialize these types of devices. Some of the topics covered include: Widely-used piezoelectric materials, as well as materials in which there is emerging interest Principle of operation and design approaches for the making of flexural, contour-mode, thickness-mode, and shear-mode piezoelectric resonators, and examples of practical implementation of these devices Large scale manufacturing approaches, with a focus on the practical aspects associated with testing and qualification Examples of commercialization paths for piezoelectric MEMS resonators in the timing and the filter markets ...and more! The authors present industry and academic perspectives, making this book ideal for engineers, graduate students, and researchers.
MEMS Sensors and Resonators
Author: Frederic Nabki
Publisher: MDPI
ISBN: 3039288652
Category : Technology & Engineering
Languages : en
Pages : 164
Book Description
Microelectromechanical systems (MEMS) have had a profound impact on a wide range of applications. The degree of miniaturization made possible by MEMS technology has significantly improved the functionalities of many systems, and the performance of MEMS has steadily improved as its uses augment. Notably, MEMS sensors have been prevalent in motion sensing applications for decades, and the sensing mechanisms leveraged by MEMS have been continuously extended to applications spanning the detection of gases, magnetic fields, electromagnetic radiation, and more. In parallel, MEMS resonators have become an emerging field of MEMS and affected subfields such as electronic timing and filtering, and energy harvesting. They have, in addition, enabled a wide range of resonant sensors. For many years now, MEMS have been the basis of various industrial successes, often building on novel academic research. Accordingly, this Special Issue explores many research innovations in MEMS sensors and resonators, from biomedical applications to energy harvesting, gas sensing, resonant sensing, and timing.
Publisher: MDPI
ISBN: 3039288652
Category : Technology & Engineering
Languages : en
Pages : 164
Book Description
Microelectromechanical systems (MEMS) have had a profound impact on a wide range of applications. The degree of miniaturization made possible by MEMS technology has significantly improved the functionalities of many systems, and the performance of MEMS has steadily improved as its uses augment. Notably, MEMS sensors have been prevalent in motion sensing applications for decades, and the sensing mechanisms leveraged by MEMS have been continuously extended to applications spanning the detection of gases, magnetic fields, electromagnetic radiation, and more. In parallel, MEMS resonators have become an emerging field of MEMS and affected subfields such as electronic timing and filtering, and energy harvesting. They have, in addition, enabled a wide range of resonant sensors. For many years now, MEMS have been the basis of various industrial successes, often building on novel academic research. Accordingly, this Special Issue explores many research innovations in MEMS sensors and resonators, from biomedical applications to energy harvesting, gas sensing, resonant sensing, and timing.
MEMS Silicon Oscillating Accelerometers and Readout Circuits
Author: Yong Ping Xu
Publisher: CRC Press
ISBN: 1000793737
Category : Technology & Engineering
Languages : en
Pages : 312
Book Description
Most MEMS accelerometers on the market today are capacitive accelerometers that are based on the displacement sensing mechanism. This book is intended to cover recent developments of MEMS silicon oscillating accelerometers (SOA), also referred to as MEMS resonant accelerometer. As contrast to the capacitive accelerometer, the MEMS SOA is based on the force sensing mechanism, where the input acceleration is converted to a frequency output. MEMS Silicon Oscillating Accelerometers and Readout Circuits consists of six chapters and covers both MEMS sensor and readout circuit, and provides an in-depth coverage on the design and modelling of the MEMS SOA with several recently reported prototypes. The book is not only useful to researchers and engineers who are familiar with the topic, but also appeals to those who have general interests in MEMS inertial sensors. The book includes extensive references that provide further information on this topic.
Publisher: CRC Press
ISBN: 1000793737
Category : Technology & Engineering
Languages : en
Pages : 312
Book Description
Most MEMS accelerometers on the market today are capacitive accelerometers that are based on the displacement sensing mechanism. This book is intended to cover recent developments of MEMS silicon oscillating accelerometers (SOA), also referred to as MEMS resonant accelerometer. As contrast to the capacitive accelerometer, the MEMS SOA is based on the force sensing mechanism, where the input acceleration is converted to a frequency output. MEMS Silicon Oscillating Accelerometers and Readout Circuits consists of six chapters and covers both MEMS sensor and readout circuit, and provides an in-depth coverage on the design and modelling of the MEMS SOA with several recently reported prototypes. The book is not only useful to researchers and engineers who are familiar with the topic, but also appeals to those who have general interests in MEMS inertial sensors. The book includes extensive references that provide further information on this topic.
Microwave and Wireless Synthesizers
Author: Ulrich L. Rohde
Publisher: John Wiley & Sons
ISBN: 1119666007
Category : Technology & Engineering
Languages : en
Pages : 818
Book Description
The new edition of the leading resource on designing digital frequency synthesizers from microwave and wireless applications, fully updated to reflect the most modern integrated circuits and semiconductors Microwave and Wireless Synthesizers: Theory and Design, Second Edition, remains the standard text on the subject by providing complete and up-to-date coverage of both practical and theoretical aspects of modern frequency synthesizers and their components. Featuring contributions from leading experts in the field, this classic volume describes loop fundamentals, noise and spurious responses, special loops, loop components, multiloop synthesizers, and more. Practical synthesizer examples illustrate the design of a high-performance hybrid synthesizer and performance measurement techniques—offering readers clear instruction on the various design steps and design rules. The second edition includes extensively revised content throughout, including a modern approach to dealing with the noise and spurious response of loops and updated material on digital signal processing and architectures. Reflecting today's technology, new practical and validated examples cover a combination of analog and digital synthesizers and hybrid systems. Enhanced and expanded chapters discuss implementations of direct digital synthesis (DDS) architectures, the voltage-controlled oscillator (VCO), crystal and other high-Q based oscillators, arbitrary waveform generation, vector signal generation, and other current tools and techniques. Now requiring no additional literature to be useful, this comprehensive, one-stop resource: Provides a fully reviewed, updated, and enhanced presentation of microwave and wireless synthesizers Presents a clear mathematical method for designing oscillators for best noise performance at both RF and microwave frequencies Contains new illustrations, figures, diagrams, and examples Includes extensive appendices to aid in calculating phase noise in free-running oscillators, designing VHF and UHF oscillators with CAD software, using state-of-the-art synthesizer chips, and generating millimeter wave frequencies using the delay line principle Containing numerous designs of proven circuits and more than 500 relevant citations from scientific journal and papers, Microwave and Wireless Synthesizers: Theory and Design, Second Edition, is a must-have reference for engineers working in the field of radio communication, and the perfect textbook for advanced electrical engineering students.
Publisher: John Wiley & Sons
ISBN: 1119666007
Category : Technology & Engineering
Languages : en
Pages : 818
Book Description
The new edition of the leading resource on designing digital frequency synthesizers from microwave and wireless applications, fully updated to reflect the most modern integrated circuits and semiconductors Microwave and Wireless Synthesizers: Theory and Design, Second Edition, remains the standard text on the subject by providing complete and up-to-date coverage of both practical and theoretical aspects of modern frequency synthesizers and their components. Featuring contributions from leading experts in the field, this classic volume describes loop fundamentals, noise and spurious responses, special loops, loop components, multiloop synthesizers, and more. Practical synthesizer examples illustrate the design of a high-performance hybrid synthesizer and performance measurement techniques—offering readers clear instruction on the various design steps and design rules. The second edition includes extensively revised content throughout, including a modern approach to dealing with the noise and spurious response of loops and updated material on digital signal processing and architectures. Reflecting today's technology, new practical and validated examples cover a combination of analog and digital synthesizers and hybrid systems. Enhanced and expanded chapters discuss implementations of direct digital synthesis (DDS) architectures, the voltage-controlled oscillator (VCO), crystal and other high-Q based oscillators, arbitrary waveform generation, vector signal generation, and other current tools and techniques. Now requiring no additional literature to be useful, this comprehensive, one-stop resource: Provides a fully reviewed, updated, and enhanced presentation of microwave and wireless synthesizers Presents a clear mathematical method for designing oscillators for best noise performance at both RF and microwave frequencies Contains new illustrations, figures, diagrams, and examples Includes extensive appendices to aid in calculating phase noise in free-running oscillators, designing VHF and UHF oscillators with CAD software, using state-of-the-art synthesizer chips, and generating millimeter wave frequencies using the delay line principle Containing numerous designs of proven circuits and more than 500 relevant citations from scientific journal and papers, Microwave and Wireless Synthesizers: Theory and Design, Second Edition, is a must-have reference for engineers working in the field of radio communication, and the perfect textbook for advanced electrical engineering students.
Microelectronics to Nanoelectronics
Author: Anupama B. Kaul
Publisher: CRC Press
ISBN: 1466509554
Category : Science
Languages : en
Pages : 464
Book Description
Composed of contributions from top experts, Microelectronics to Nanoelectronics: Materials, Devices and Manufacturability offers a detailed overview of important recent scientific and technological developments in the rapidly evolving nanoelectronics arena. Under the editorial guidance and technical expertise of noted materials scientist Anupama B. Kaul of California Institute of Technology’s Jet Propulsion Lab, this book captures the ascent of microelectronics into the nanoscale realm. It addresses a wide variety of important scientific and technological issues in nanoelectronics research and development. The book also showcases some key application areas of micro-electro-mechanical-systems (MEMS) that have reached the commercial realm. Capitalizing on Dr. Kaul’s considerable technical experience with micro- and nanotechnologies and her extensive research in prestigious academic and industrial labs, the book offers a fresh perspective on application-driven research in micro- and nanoelectronics, including MEMS. Chapters explore how rapid developments in this area are transitioning from the lab to the market, where new and exciting materials, devices, and manufacturing technologies are revolutionizing the electronics industry. Although many micro- and nanotechnologies still face major scientific and technological challenges and remain within the realm of academic research labs, rapid advances in this area have led to the recent emergence of new applications and markets. This handbook encapsulates that exciting recent progress by providing high-quality content contributed by international experts from academia, leading industrial institutions—such as Hewlett-Packard—and government laboratories including the U.S. Department of Energy’s Sandia National Laboratory. Offering something for everyone, from students to scientists to entrepreneurs, this book showcases the broad spectrum of cutting-edge technologies that show significant promise for electronics and related applications in which nanotechnology plays a key role.
Publisher: CRC Press
ISBN: 1466509554
Category : Science
Languages : en
Pages : 464
Book Description
Composed of contributions from top experts, Microelectronics to Nanoelectronics: Materials, Devices and Manufacturability offers a detailed overview of important recent scientific and technological developments in the rapidly evolving nanoelectronics arena. Under the editorial guidance and technical expertise of noted materials scientist Anupama B. Kaul of California Institute of Technology’s Jet Propulsion Lab, this book captures the ascent of microelectronics into the nanoscale realm. It addresses a wide variety of important scientific and technological issues in nanoelectronics research and development. The book also showcases some key application areas of micro-electro-mechanical-systems (MEMS) that have reached the commercial realm. Capitalizing on Dr. Kaul’s considerable technical experience with micro- and nanotechnologies and her extensive research in prestigious academic and industrial labs, the book offers a fresh perspective on application-driven research in micro- and nanoelectronics, including MEMS. Chapters explore how rapid developments in this area are transitioning from the lab to the market, where new and exciting materials, devices, and manufacturing technologies are revolutionizing the electronics industry. Although many micro- and nanotechnologies still face major scientific and technological challenges and remain within the realm of academic research labs, rapid advances in this area have led to the recent emergence of new applications and markets. This handbook encapsulates that exciting recent progress by providing high-quality content contributed by international experts from academia, leading industrial institutions—such as Hewlett-Packard—and government laboratories including the U.S. Department of Energy’s Sandia National Laboratory. Offering something for everyone, from students to scientists to entrepreneurs, this book showcases the broad spectrum of cutting-edge technologies that show significant promise for electronics and related applications in which nanotechnology plays a key role.
Metrology and Physical Constants
Author: A. Di Giuseppe
Publisher: IOS Press
ISBN: 1614993262
Category : Science
Languages : en
Pages : 567
Book Description
The reliability and accuracy of systems of measurement continue to advance. We are about to enter a period of the most stable measurement system we can imagine with the anticipated new definitions of the SI units of measurement; a direct link between fundamental physics and metrology which will eliminate the current definition of the kilogram, until now based upon an artifact. This book presents selected papers from Course 185 of the Enrico Fermi International School of Physics, held in Varenna, Italy, in July 2012 and jointly organized with the Bureau International des Poids et Mesures (BIPM). The papers delivered at the school covered some of the most advanced topics in the discipline of metrology, including nano-technologies; quantum information and quantum devices; biology and medicine; food; surface quality; ionising radiation for health, environment, art and archaeology; and climate. The continuous and striking advances in basic research concerning atomic frequency standards operating both in the visible range and at microwave levels and the applications to satellite systems are also considered, in the framework of a historical review of the international organization of metrology, as are the problems inherent in uncertainty statements and definitions. This book will be of interest to all those whose work involves scientific measurement at the highest levels of accuracy.
Publisher: IOS Press
ISBN: 1614993262
Category : Science
Languages : en
Pages : 567
Book Description
The reliability and accuracy of systems of measurement continue to advance. We are about to enter a period of the most stable measurement system we can imagine with the anticipated new definitions of the SI units of measurement; a direct link between fundamental physics and metrology which will eliminate the current definition of the kilogram, until now based upon an artifact. This book presents selected papers from Course 185 of the Enrico Fermi International School of Physics, held in Varenna, Italy, in July 2012 and jointly organized with the Bureau International des Poids et Mesures (BIPM). The papers delivered at the school covered some of the most advanced topics in the discipline of metrology, including nano-technologies; quantum information and quantum devices; biology and medicine; food; surface quality; ionising radiation for health, environment, art and archaeology; and climate. The continuous and striking advances in basic research concerning atomic frequency standards operating both in the visible range and at microwave levels and the applications to satellite systems are also considered, in the framework of a historical review of the international organization of metrology, as are the problems inherent in uncertainty statements and definitions. This book will be of interest to all those whose work involves scientific measurement at the highest levels of accuracy.
MEMS-based Circuits and Systems for Wireless Communication
Author: Christian C Enz
Publisher: Springer Science & Business Media
ISBN: 1441987983
Category : Technology & Engineering
Languages : en
Pages : 334
Book Description
MEMS-based Circuits and Systems for Wireless Communications provides comprehensive coverage of RF-MEMS technology from device to system level. This edited volume places emphasis on how system performance for radio frequency applications can be leveraged by Micro-Electro-Mechanical Systems (MEMS). Coverage also extends to innovative MEMS-aware radio architectures that push the potential of MEMS technology further ahead. This work presents a broad overview of the technology from MEMS devices (mainly BAW and Si MEMS resonators) to basic circuits, such as oscillators and filters, and finally complete systems such as ultra-low-power MEMS-based radios. Contributions from leading experts around the world are organized in three parts. Part I introduces RF-MEMS technology, devices and modeling and includes a prospective outlook on ongoing developments towards Nano-Electro-Mechanical Systems (NEMS) and phononic crystals. Device properties and models are presented in a circuit oriented perspective. Part II focusses on design of electronic circuits incorporating MEMS. Circuit design techniques specific to MEMS resonators are applied to oscillators and active filters. In Part III contributors discuss how MEMS can advantageously be used in radios to increase their miniaturization and reduce their power consumption. RF systems built around MEMS components such as MEMS-based frequency synthesis including all-digital PLLs, ultra-low power MEMS-based communication systems and a MEMS-based automotive wireless sensor node are described.
Publisher: Springer Science & Business Media
ISBN: 1441987983
Category : Technology & Engineering
Languages : en
Pages : 334
Book Description
MEMS-based Circuits and Systems for Wireless Communications provides comprehensive coverage of RF-MEMS technology from device to system level. This edited volume places emphasis on how system performance for radio frequency applications can be leveraged by Micro-Electro-Mechanical Systems (MEMS). Coverage also extends to innovative MEMS-aware radio architectures that push the potential of MEMS technology further ahead. This work presents a broad overview of the technology from MEMS devices (mainly BAW and Si MEMS resonators) to basic circuits, such as oscillators and filters, and finally complete systems such as ultra-low-power MEMS-based radios. Contributions from leading experts around the world are organized in three parts. Part I introduces RF-MEMS technology, devices and modeling and includes a prospective outlook on ongoing developments towards Nano-Electro-Mechanical Systems (NEMS) and phononic crystals. Device properties and models are presented in a circuit oriented perspective. Part II focusses on design of electronic circuits incorporating MEMS. Circuit design techniques specific to MEMS resonators are applied to oscillators and active filters. In Part III contributors discuss how MEMS can advantageously be used in radios to increase their miniaturization and reduce their power consumption. RF systems built around MEMS components such as MEMS-based frequency synthesis including all-digital PLLs, ultra-low power MEMS-based communication systems and a MEMS-based automotive wireless sensor node are described.