In 1864, James Clerk Maxwell predicted that electric and magnetic fields could propagate in the form of electromagnetic waves. Experiments performed in 1885–1887 by physicist Heinrich Rudolf Hertz confirmed the existence of radio waves. Hertz developed equipment to produce, radiate, and detect very short electromagnetic waves and observed the reflection of microwave energy from solids [1]. In 1922, Marchese Guglielmo Marconi proposed the use of short waves for radio detection of objects [1]. In 1934, the first experimental radar station was developed and led to the British “Chain Home” air defense system [1].
The need for radar equipment, especially during World War II, stimulated development of microwave technology. Powerful generators and amplifiers were necessary for radar. Scientists and engineers successfully solved problems using it. Albert Hull invented the magnetron in 1920. Brothers Russell and Sigurd Varian developed klystron in 1936. Andrew V. Haeff proposed the idea of traveling-wave devices in 1933 [2]. In 1942 and 1943, Rudolf Kompfner developed a traveling-wave tube. Later, Kompfner and Pierce refined it at Bell Labs.
Interaction of electromagnetic oscillations and electrons of electron beams is used in microwave electrovacuum devices. Traveling-wave devices are based on interaction of traveling electromagnetic waves and the beams. The velocity of the traveling wave must be matched with the velocity of the electrons, and the velocity of the electrons is less than the velocity of electromagnetic waves in free space. Thus, retarded waves are necessary in traveling-wave devices. Slow-wave structures are used for retardation of electromagnetic waves.
Researchers have developed many types of slow-wave devices [3]. Because of the dependence of properties of active microwave devices on properties of used slow waves, many efforts have been made in the development of theory, experimental investigations, and improvement of slow-wave devices. Results of investigations have been presented in Silin and Sazonov [4] and Taranenko and Trohimenko [5], as well as in many other publications.
As a result of such investigations, new fields for application of slow-wave devices were discovered. At the same time, requirements for special properties of the devices appeared.
Slow-wave devices with super-wide pass-bands are necessary for electromagnetic delay lines (DLs) and traveling-wave cathode-ray tubes (TW CRTs). TW CRTs have been developed for traveling-wave oscilloscopes used for investigation of single high-speed processes. Traveling-wave deflection systems must ensure the pass-band of tubes and oscilloscopes from 0 to some gigahertz.
In 1965, Professor Zenonas Vainoris initiated research in the field of electrodynamic slow-wave devices at Vilnius Gediminas Technical University in Lithuania. As a result of research in the following 30 years, important problems related to investigation and design of super-wide band delay lines and traveling-wave deflecting systems have been solved and a generalized theory of super-wide band helical and meander systems developed. Processes in traveling-wave deflecting systems have been revealed and the theory of TW CRTs developed. New technical solutions in the field of super-wide-band delay lines and traveling-wave deflecting systems have been proposed; the main results of these investigations are presented in references 6,7,8,9.
Approximately since 1990, intensive investigations in the field of electromagnetics have taken place. They are based on wide application of numerical methods for investigation of electromagnetic fields and microwave and other electrodynamic devices. The main problems and their solutions are discussed in references 10,11,12,13,14 and other overviews. The principles of numerical methods are described in references 15,16,17,18,19,20,21,22,23,24,25,26,27.
Numerical methods are used for solution of Maxwell, Poisson, and Laplace equations. Differential and integral forms of Maxwell equations are used. For this reason, two groups of numerical methods were developed. Methods of one group are based on solution of differential equations with partial derivatives. Finite difference method (FDM), finite element method (FEM), and finite difference time domain method (FDTD) are the methods of this group. Methods of the other group (integral equation methods) are used for solution of integral equations. The most important method of this group is the method of moments (MoM).
In addition to these methods, new modifications of numerical methods were developed. On the basis of FDTD and MoM, the very effective finite integration method (FIM) was created. It is used for software systems MAFIA and Microwave Studio developed by the Computer Simulation Technology (CST) Company for analysis of electromagnetic fields and simulation and design of microwave devices.
The authors have used electrodynamic, multiconductor line, and numerical methods for modeling, simulation, analysis, and design of super-wide-band slow-wave structures. Because of reasons related to the history of Lithuania, a significant quantity of results of research in the period since 1990 has been published in Russian and Lithuanian. In order to make the results better available, the decision to prepare this book in English was made.
In the general case, the main goal of analysis of a slow-wave structure is to determine its frequency characteristics—the retardation factor and characteristic impedance versus frequency.
The retardation factor kR shows how many times the phase velocity vph in the slow-wave system is less than c0, which is the velocity of light in the free space (in vacuum). According to transmission line theory,
(0.1) |
where L1 and C1 are inductance and capacitance per unit length.
Characteristic impedance of the system is given by
(0.2) |
Characteristic impedance of a homogeneous structure can be found using the following equation:
(0.3) |
where U(x) and I(x) are voltage and current at the section of the system with coordinate x. In the case of a nonhomogeneous structure, the ratio U(x)/I(x) is complex and means input impedance.
Usually, the retardation factor, characteristic impedance, input impedance, and other characteristics of slow-wave structures are determined as a result of the solution of the dispersion equation, which can be relatively easily derived for a homogeneous system. In the case of complex inhomogeneous slow-wave structures, derivation of the equation is complicated. For this reason, numerical methods are used for analysis. Numerical methods allow avoiding many difficulties, and they save time and mental labor resources.
At application of slow-wave systems, a lot of other characteristics are used. In the case of delay lines, delay time versus frequency, transfer function, amplitude-frequency response, phase-frequency response, and transient response are the most important characteristics. If the retardation factor is determined, the delay time of the delay line is given by
(0.4) |
where lL is the length of the line.
In TW CRTs, the incident wave in the traveling deflecting system acts on electrons of the electron beam and causes its deflection [8,9]. In this case, two groups of characteristics must be considered: characteristics of the traveling-wave deflection system and characteristics of the cathode-ray tube that characterize restoration of the signal form on the screen. It is important that characteristics of the cathode-ray tube characterizing restoration of the signal form on the screen differ from characteristics of the deflecting system characterizing transmission of the signal to the load of the signal path in the tube.
The book consists of this introduction and nine chapters.
Inhomogeneous helical slow-wave systems are considered in Chapter 1. The generalized models of the systems with rectangular cross section are proposed. The electrodynamical method is applied for analysis. The expressions for retardation factor and input impedance are derived. Simulation of the systems revealed ways for reduction of dispersion and widening of the pass-band.
The fundamentals of the multiconductor line method are presented in Chapter 2. The method is applied for investigation of complex meander and helical structures. The numerical methods and algorithms based on iterations, and applications of scattering transmission-line matrices are developed.
At application of the multiconductor line method, values of characteristic impedances of the multiconductor lines are necessary. Methods of calculation of characteristic impedances are described in Chapter 3. The fundamentals of finite difference, finite element, and integral equation numerical methods are presented. The moment method is applied for calculation of parameters of microstrip multiconductor lines consisting of a finite number of conductors.
The twined helical, quasi-symmetrical, and gutter-type helical and meander systems are considered in Chapter 4. Models of the systems based on the multiconductor line method are proposed. Frequency properties of the systems are revealed and described. In addition to the multiconductor line method, the CST Microwave Studio software system is used for simulation of the quasi-symmetrical and gutter-type systems. The rejecting properties of slow-wave systems containing periodical inhomogeneities are revealed. The hybrid method is proposed for simulation of the microstrip meander line with finite length. The influence of the end effects is taken into account in the calculation of the delay time of the microstrip meander lines.
Many commercial software packages have been developed for simulation of electromagnetic fields, research, and design of microwave devices. Possibilities of application of the Applied Wave Research (AWR) software package, Microwave Office, and CST MicroWave Studio software system for investigation of super-wide-band periodical structures are considered in Chapter 5. The Microwave Office package is used for investigation of the helical system, twined helical system properties, and research and elimination of resonances in the system of shields in helical systems. The MicroWave Studio system is used for three-dimensional modeling of helical delay lines and traveling-wave deflection systems. Properties of helical systems containing anisotropical shields, systems containing periodical inhomogeneities, and asymmetrical and symmetrical meander systems (with plane and axial symmetry) are investigated.
Using the multiconductor line method, we can reveal general properties of the super-wide band slow-wave structures and relatively easily find solutions for improving properties of the systems. On the other hand, the multiconductor line method generally allows investigation of infinitely long structures. Using software packages like Microwave Studio, we can simulate systems with finite length and take into account finite conductances of metallic parts, losses in dielectric elements, reflections from inhomogeneities in the signal path, etc. Unfortunately, calculated characteristics depend on the total influence of various factors and it is difficult to evaluate the influence of a separate factor in order to improve properties of the structure in this instance. For these reasons, the idea using the synergy of various methods is proposed and used for investigation of slow-wave systems in Chapter 6. The multiconductor line method and Microwave Studio software system are used for research of inhomogeneous meander systems, H-profile meander systems, symmetrically and asymmetrically shielded helical systems, and the helical system with axial symmetry.
Specific problems related to application of the slow-wave structures for deflection of electron beams in TW CRTs are solved in Chapter 7. Here, frequency responses (amplitude frequency and phase frequency characteristics) and transient responses of traveling-wave deflecting systems and cathode-ray tubes are considered. Possibilities of compensation of phase-frequency distortions are discovered and distribution of the electric field in various types of deflection systems analyzed. Nonlinear frequency distortions of harmonic signals and electrical pulses are estimated. The model of the signal path of TW CRTs is proposed and applied to estimate the influence of transitions to slow-wave deflecting systems on characteristics of deflecting systems and cathode-ray tubes. Finally, methods that allow improving dynamic properties of TW CRTs are discovered.
Various types of microstrip meander lines for delay of wide-band electrical signals are considered in Chapter 8. Proposed models and methods allow estimating the influence of variations of conductor steps, shields, and properties of dielectric materials on frequency characteristics of meander DLs. Additionally, models of complex meander DLs containing additional shields among the conductors of the lines are proposed and methods for calculation of frequency characteristics developed. The best results can be achieved using modified, gutter-type meander DLs.
Problems related to automatization of design and optimal design of meander and helical slow-wave systems and delay lines are considered and solved in Chapter 9.
The results of research presented in this book can be used for analysis, synthesis, and design of slow-wave structures for modern electronic devices with super-wide pass-bands.
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