Table Of ContentLecture Notes in Electrical Engineering 689
Mikhail V. Nesterenko ·
Victor A. Katrich · Yuriy M. Penkin ·
Sergey L. Berdnik · Oleksandr M. Dumin
Combined
Vibrator-Slot
Structures:
Theory and
Applications
Theoretical Aspects and Applications
Lecture Notes in Electrical Engineering
Volume 689
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Mikhail V. Nesterenko
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Victor A. Katrich Yuriy M. Penkin
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Sergey L. Berdnik Oleksandr M. Dumin
(cid:129)
Combined Vibrator-Slot
Structures: Theory
and Applications
Theoretical Aspects and Applications
123
Mikhail V.Nesterenko Victor A.Katrich
V.N.KarazinKharkivNational University V.N.Karazin KharkivNational University
Kharkiv, Ukraine Kharkiv, Ukraine
YuriyM. Penkin Sergey L.Berdnik
V.N.KarazinKharkivNational University V.N.KarazinKharkivNational University
Kharkiv, Ukraine Kharkiv, Ukraine
Oleksandr M.Dumin
V.N.KarazinKharkivNational University
Kharkiv, Ukraine
ISSN 1876-1100 ISSN 1876-1119 (electronic)
Lecture Notesin Electrical Engineering
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It is impossible to solve the problem at the
same level at which it arose. You need to get
higher than this problem by rising to the next
level.
Albert Einstein
Preface
At present, linear vibrator and slot radiators and coupling slots between electrody-
namic volumes are widely used in variety of radio-electronic devices which are
structural elements of antennas and antenna-feeder devices. Their multifunctional
and extensive applications have become an objective prerequisite for developing
theoretical methods aimed at studying electrodynamic characteristics of such devi-
ces. A special attention is paid to combined vibrator–slot structures significantly
expanding possibilities for formatting electromagnetic fields with predefined
spatial-frequency characteristics. Over the past decades, many authors, particularly
authors of this book, have developed a modern theory of thin vibrator, slot, and
combined vibrator–slot radiators. This theory combines fundamental asymptotic
methodsandthenumerical–analyticalapproachesbasedonthemwhichareintended
fordeterminingcharacteristics ofstandalongvibratorandslotelements.However,
the electrodynamics theory of linear vibrator and slot radiators is far from being
completed. First of all, this is related to further developing modern technology of
transceiver antennas and antenna-feeder devices characterized by the following
features: multifunctionality, multi-element applications, integration and modifica-
tion of structural components to minimize weight and size parameters, electro-
magnetic compatibility of devices, usage of composites and metamaterials, and
formation of required spatial-energy, spatial-polarization, and frequency–energy
distributions ofelectromagnetic fields, including fields indissipative media.
Multiparameter optimization of complex electrodynamic problems requires
effective computing and software resources for mathematical modeling. Therefore,
despite the rapid growth of the computing potential of modern computer technol-
ogy, there is a need to develop new, more efficient methods of electrodynamic
problemsolutionsconcerningthedesignofantenna-feedersystemsbasedonlinear
vibratorandslotstructureswitharbitrarygeometricandelectrophysicalparameters.
Theeffectivenessofmathematical modelingisdeterminedbyrigorousformulation
andsolutionofcorrespondingboundary-valueproblems,theruntimeofalgorithms
under condition that the minimum possible amount of RAM is used. The solution
effectivenessdirectlydependsonthedegreeofanalyticaldevelopmentalworkspent
duringitsderivation.Thatis,themoresignificantistheanalyticalcomponentofthe
vii
viii Preface
method,thehigheristheoveralleffectivenessofitsimplementation.Inthisregard,
the development of rigorous numerical–analytical methods of electrodynamic
analysisexpandingthepossibilitiesofphysicallycorrectmathematicalmodelingto
new classes of boundary-value problems has been and remains an important
problem for researchers in the field of theoretical and applied radio physics.
Known numerical–analytical methods for analyzing single and multi-element
structures of linear radiators and antenna-feeder devices created on their basis can
be divided into two types. The first type includes analytical solution of integral
equations for electric and magnetic currents in separate structural elements. The
second type refers to the method of moments in which the expressions for matrix
elements in the final system of linear algebraic equations (SLAE) can be solved
analytically. Of course, methods of the first type are preferable due to their effec-
tiveness and easiness of physical realization. However, their implementation is
limited by the complexity of constructing asymptotic solutions of boundary-value
problems for systems with large number of different constructive elements.
Characteristic property of electrodynamic problems concerning the linear
vibrator and slot radiators is longitudinal dimensions of their elements which are
comparable with the operating wavelength in the medium. Therefore, asymptotic
long-wave or short-wave (quasi-optical) approximations cannot be applied. In
resonant regions, asymptotic solutions of boundary-value problems for perfectly
conducting rectilinear vibrators in free space were previously obtained by various
methods,namelybythe successive iteration method, weight function expansionin
a series in powers of a small parameter, variational method, and key equation
method.Similarly,theequivalentmagnetic currentfor aslot cutinathin perfectly
conducting infinite screen was determined by using the small parameter method,
variational method, and method of successive iterations. The electrodynamic
characteristicsofmulti-elementvibrator–slotsystemswereobtainedbythemethods
of induced electromotive forces (EMF) and magnetomotive forces (MMF).
However, within the framework of numerical–analytical methods of boundary-
value problem, solutions for a class of linear radiators promising for practical
applications were not proposed. This primarily concerns impedance vibrator radi-
ators(scatterers)withirregulargeometricandelectrophysicalparameterslocatedin
free space and other electrodynamic volumes, slot radiators cut in walls of various
waveguide and resonator sections with perfectly conducting and impedance
boundaries, and combined multi-element vibrator–slot structures. Beside the prin-
ciplesofasymptoticsolutionsofequationforelectricandmagneticcurrentsbythe
methods of induced EMF, MMF or the hybrid method of electro-magneto-motive
forces (EMMF) for analyzing combined vibrator–slot structures have not been
generalized.
The problem solutions concerning the electrodynamic characteristics of impe-
dance vibrator and slot radiators with arbitrary geometric and electrophysical
parameters were obtained within a framework of unified methodological approach
toconstructingasymptoticsolutionsofintegralequations.Thisapproachallowedus
to investigate several combined vibrator–slot structures. The research results have
revealed the possibilities of using these structures as basic elements of modern
Preface ix
antenna-waveguide devices with advanced technical characteristics and function-
alities operating in the ranges from meter to millimeter wavelengths.
Investigatingtransientnearfieldsofelectricallyshortradiatorsisusuallycarried
outbythemethodofvectorpotentialintimedomainbasedonthesmallparameter
approach.Thefeaturesofelectromagnetic fieldsinthenearzoneareappliedtothe
study of interaction between elements of ultrawideband vibrator–slot structures
similar to the Clavin element.
The monograph consists of nine chapters and five appendixes. For the conve-
nienceofworkingwiththematerialofthebook,alistofauthors’literarysourcesis
highlighted in a separate list (Authors’ Publications List (APL)).
Chapter 1 is introductory in nature. Basic equations of macroscopic electrody-
namics and methods for constructing Green’s functions are presented. Besides
issues related to surface impedances of various metal–dielectric structures are
discussed. Asymptotic formulas for determining complex surface impedances of
vibratorsarepresentedinSubsection 1.3.2.6.Theseformulasallowustocalculate
impedances for following metal–dielectric structures: a solid lossy cylindrical
conductor, periodically corrugated or ribbed cylindrical conductor, cylindrical
conductor coated by a magnetodielectric, cylindrical conductor with periodic
dielectrictransverseinserts,anddielectriccylinder.Formulasdefiningrelationships
between vibrator structural parameters and its surface impedance were used in
mathematical models for various radiators. The information presented in this sec-
tion allows the reader to perceive the information in further sections of the book
without searching for special hard-to-reach literature.
In Chap. 2, a problem of the excitation (scattering or radiation) of electromag-
netic fields by material bodies of finite dimensions in presence of coupling holes
between two electrodynamic volumes is formulated in most general form. Initial
systems of integral equations relative to densities of surface electric currents on
vibratorandequivalentmagneticcurrentsoncouplingholeswerederivedbasedon
the impedance boundary conditions on the vibrator surfaces and the continuity
conditions of tangential components of magnetic fields at coupling holes. It was
shown that the problem solution should be better based on integral equations with
Green’s function kernels for Hertz vector potentials. The asymptotic solutions
of the equations in various electrodynamic volumes were obtained by using a
generalapproachconsistinginisolationofirregularpartoftheGreen’spresentedby
the Green’s function of the free space. A physically correct transition from the
derivedintegralequationstoone-dimensionalequationsismadeforcurrentsonthin
linear impedancevibratorswith irregular geometricandelectrophysicalparameters
along their length, in narrow slots arbitrary located relative to boundaries of cor-
respondingelectrodynamicvolumes,andincombinedvibrator–slotstructures.The
fundamentals of the method of moments are presented, the advantages and disad-
vantages of various approximate analytical methods for solving the integral equa-
tions for currents are analyzed, and the application of the generalized method of
induced EMF for studying multi-element vibrator–slot structures is considered.
New aspects of thin impedance vibrator theory proposed by the authors are
considered.
x Preface
In Chap. 3, solutions of integral equations for currents in waveguide structures
with single vibrator and slot elements are obtained by the averaging method and
generalized methods of induced EMF and MMF. The choice of approximating
functionsforcurrentsisjustifiedbytheresultsofcomparativeanalysisofcalculated
andexperimentaldata.Aproblemofelectromagneticwavescatteringbyavibrator
systeminrectangularwaveguidesisalsosolvedtodemonstratehowtransitionfrom
single to multi-element structures can be made.
Chapter4,entitled“CombinedRadiatingVibrator-SlotStructuresinRectangular
Waveguides”, is devoted to developing mathematical models and studying elec-
trodynamic characteristics of structures consisting of transverse slot in a wide wall
of a rectangular waveguide with impedance vibrators. Structures with or without
vibrator–slotfieldinteractionswereconsidered;thesecondvariantcorrespondstoa
casewhenvibrator–slotfieldinteractionsareabsentduetopolarizationdecoupling.
The possibility of controlling over a wide range reflection and transmission coef-
ficients in waveguides with vibrator–slot structures by using passive vibrators of
constant length with various distribution function of surface impedance is con-
firmed. It is also shown that the slot radiation coefficient in such structures can be
close to unity.
In Chap. 5, T-shaped E-plane junctions consisting of infinite and semi-infinite
waveguides coupling through a transverse slot cut in a wide wall of the infinite
waveguide are considered. One or two impedance monopoles are located near the
slot inside the main infinite waveguide. A characteristic feature of the T-junction
structure model is simultaneous application of monopoles with variable surface
impedance and the end wall of the semi-infinite waveguide with constant impe-
dance distributed over its surface. Multiparameter studies of energy characteristics
ofT-junctionswerecarriedoutinsingle-moderegimeofthecouplingwaveguides.
The main motive for the complicating the T-junction design is defined by the
authors’ desire to investigate conditions allowing its two-resonant operating mode
by using two impedance vibrators inside the main waveguide. This possibility has
been successfully confirmed by numerical modeling. Conditions necessary for
transmittingthemainpartofinputpowerfromtheT-junctionmainarmtotheside
waveguide at two resonant frequencies were determined. It was shown that impe-
dancecoatingsofvibratorsandendwallofsidewaveguidecanbeusedaseffective
control elements for dividing the power between the T-junction output arms. It is
also established that such a coating with frequency-dependent heterogeneous
impedancecanprovideathree-resonantmodeofpowertransmissionfromthemain
to side arm of T-junction.
In Chap. 6, a problem concerning of electromagnetic wave radiated by a
Clavin-typeelementintoahalfspaceaboveaninfiniteperfectlyconductingspaceis
solved. A Clavin element consists of a longitudinal or transverse slot cut in a
waveguidebroadwallandtwopassiveimpedancevibratorslocatedonbothsidesof
slot longitudinal axis. The influence of vibrator length and distances between
vibrators on the directional characteristics of the Clavin-type elements is analyzed
under conditions that the relative level of E-plane lateral radiation and difference
oftheRPmainlobewidthsinthemainpolarizationplanesatthelevelof–3 dBare
