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Effect of the Permittivity of Isotropic Load on the Area of Phase Shifter Operation of a Circular Ferrite-Dielectric Waveguide with Azimuthal Magnetization: Analysis in Terms of the L3±Numbers 25

Effect of the Permittivity of Isotropic Load on the Area of ...

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25th International Conference on Electromagnetics in Advanced Applications, ICEAA 2023

作者： Georgiev, Georgi Nikolov Georgieva-Grosse, Mariana Nikolova Consulting and Researcher in Physics Mathematics and Computer Sciences BG-5229 Slomer PolikraishteBG-5138 Bulgaria Consulting and Researcher in Physics and Computer Sciences BG-5138 Polikraishte SlomerBG-5229 Bulgaria

ISBN: (纸本)9798350320589

A circular waveguide, entirely filled with a coaxially positioned azimuthally magnetized ferrite cylinder and a dielectric toroid, which sustains normal TE01 mode, is considered. If ϵd and ϵr are the relative permittivities of the isotropic and anisotropic medium, resp., the impact of ϵd on the width of the area in which the structure provides differential phase shift is studied, on condition that ϵd> ϵr and ϵd grows, while ϵr is kept unchanged. The approach employs the characteristic equation of the configuration, derived previously by means of complex Kummer confluent hypergeometric and real ordinary Bessel and Neumann functions. In it the permittivities of the two strata participate through their ratio ϵ=ϵd/ϵr. That's why it is chosen as a parameter in the investigation with a value, larger than 1 (ϵ>1), which increases, rather than ϵd and ϵr. Using the definite purely imaginary roots of the equation mentioned in its independent variable, and certain new real positive numbers (L3± numbers), introduced by the authors earlier, the lower and upper cut-off frequencies of transmission line are computed. They allow to deduce the criterion, whose fulfillment guarantees its work as a phase shifter, and to reckon the width of the area in that this is observed. The dielectric region is assumed thin. Calculations are performed for several equidistant values of the off-diagonal ferrite Polder permeability tensor element, corresponding to strong anisotropy. The results are debated in detail. © 2023 IEEE.

关键词： Ferrite

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Some Features of the Circular Ferrite-Dielectric Waveguide Phase Shifter of Azimuthal Magnetization 23

Some Features of the Circular Ferrite-Dielectric Waveguide P...

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23rd International Conference on Electromagnetics in Advanced Applications, ICEAA 2022

作者： Georgieva-Grosse, Mariana Nikolova Georgiev, Georgi Nikolov Consulting and Researcher in Physics Mathematics and Computer Sciences PolikraishteBG-5138 Bulgaria Consulting and Researcher in Physics Mathematics and Computer Sciences SlomerBG-5229 Bulgaria

ISBN: (数字)9781665481113

ISBN: (纸本)9781665481113

The lower and upper cut-off frequencies and the width of the work area of a digital phase shifter, built on a circular waveguide, containing a co-axially positioned azimuthally magnetized latching ferrite cylinder and a dielectric toroid, under normal TE01 mode excitation, are investigated. The size of anisotropic region is assumed large and the relative permittivities of both strata-equal. The off-diagonal element of ferrite permeability tensor changes in the whole interval in which it has sense. The analysis is based on the characteristic equation of the structure, derived earlier in terms of complex Kummer confluent hypergeometric and real ordinary Bessel and Neumann functions, and on its phase curves, plotted before, too. It indicates that for any set of parameters the transmission line has one lower and two upper cut-off frequencies. They specify the condition for phase shifter operation of the device and the width of the area in that it is fulfilled. The lower frequencies are determined with the help of the roots xi0, n(c) of the equation mentioned in its purely imaginary independent variable, computed for a zero value of the imaginary part of the complex first parameter of Kummer functions. The upperby means of the real positive L3± numbers, advanced recently by the authors, calculated, using the same roots, but for infinitely large positive and negative numerical equivalents of the imaginary part referred to. Detailed computations of xi0, n(c) and L3±, of the cut-off frequencies and of the width of the area in question are performed. The effect of off-diagonal tensor element on all results is studied. It is established that in certain cases the configuration does not provide phase shift at all. © 2022 IEEE.

关键词： Boundary value problems

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An Application of the L4±Numbers in the Theory of Azimuthally Magnetized Ferrite-Dielectric Circular Waveguides 23

An Application of the L4±Numbers in the Theory of Azimuthal...

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23rd International Conference on Electromagnetics in Advanced Applications, ICEAA 2022

作者： Georgiev, Georgi Nikolov Georgieva-Grosse, Mariana Nikolova Consulting and Researcher in Physics Mathematics and Computer Sciences SlomerBG-5229 Bulgaria Consulting and Researcher in Physics Mathematics and Computer Sciences PolikraishteBG-5138 Bulgaria

The real positive L4±=L4±(c,ρ,α ±,n) numbers (c=3,quad ρ, α ±-real, >1, 00,k-0, z>0, y=ρ qz, q= q(α,k),q>0, m=0,1). The values of L4± are found, using a special iterative techni... 详细信息

ISBN: (数字)9781665481113

ISBN: (纸本)9781665481113

The real positive L4±=L4±(c,ρ,α ±,n) numbers (c=3,quad ρ, α ±-real, >1, 00,k-0, z>0, y=ρ qz, q= q(α,k),q>0, m=0,1). The values of L4± are found, using a special iterative technique. The effect of parameters and ρ on them is studied for fixed |α ±|, assuming n=1. The identity F4(a,c;x,ϵ,ρ,α)=0 is interpreted as characteristic equation of the circular waveguide, comprising a coaxial dielectric cylinder and a ferrite toroid with azimuthal bias that sustains normal TE 0n modes, and η k ±,n(c)(ϵ,ρ,α ±) (the roots of equation) as portrait of its eigenvalue spectrum. The L4± numbers are regarded as mathematical image of the upper cut-off frequencies of configuration, η0,n(c)(ϵ,ρ,α ±)-of its lower ones (ϵ-dielectric ϵ d to ferrite ϵ r relative permittivity ratio, ρ-factor of filling with dielectric, α ±-off-diagonal ferrite permeability tensor element, n-order of the mode, k,y,z-functions of the phase constant, structure parameters and frequency). The subscripts '±' show the direction of magnetization of anisotropic load (sgnk=sgnα). The condition ϵ>1(ϵ d >ϵ r) is essential. In general, L4+≠L4-and L4±>η0,n(c). For each |α ±|there are two upper and one lower cut-off frequency that differ, except the first in some isolated cases. The criterion for phase shifter operation of the geometry is derived. The upper and lower cut-off frequencies and the width of the area where it exhibits phase shifting properties are reckoned in normalized form for the TE01 mode, depending on ϵ,φ ±mid and ρ. © 2022 IEEE.

关键词： Boundary value problems

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Contribution to the Theory of the Two-Layered Ferrite-Dielectric Circular Waveguide

Contribution to the Theory of the Two-Layered Ferrite-Dielec...

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International Conference on Electromagnetics in Advanced Applications (ICEAA)

作者： Mariana Nikolova Georgieva-Grosse Georgi Nikolov Georgiev Consulting and Researcher in Physics Mathematics and Computer Sciences BG-5229 Slomer / BG-5138 Polikraishte Bulgaria Consulting and Researcher in Physics Mathematics and Computer Sciences BG-5138 Polikraishte / BG-5229 Slomer Bulgaria

ISBN: (数字)9798350360974

ISBN: (纸本)9798350360981

The effect of the material and geometry parameters on some traits of the circular waveguide, which contains a co-axially positioned dielectric cylinder and a ferrite toroid of azimuthal magnetization, and supports normal $T E_{01}$ mode, is examined. The method uses definite roots of its characteristic equation, deduced earlier in terms of complex Kummer and Tricomi confluent hypergeometric and real ordinary Bessel functions, and certain new real positive numbers ($\bar{L}_{4 \pm}$ and $\bar{L}_{4 \pm}$ numbers), advanced recently by the authors. With their help the lower and upper cut-off frequencies of configuration are calculated. Knowing them permits to find the width of the area in which it operates as a phase shifter. Assuming the anisotropy of the ferrite medium weak, a numerical study of the dependence of the quantities said is done on: i) the size of the section, occupied by dielectric, stipulating that the relative permittivities of the two layers are equal; i i) the dielectric to ferrite relative permittivities ratio, provided the first is larger than the second one and the axial isotropic cylinder is thin. A profound discussion of the outcomes is presented.

关键词： Ferrites Circular waveguides Geometry Anisotropic magnetoresistance Phase shifters Cutoff frequency Toroidal magnetic fields Mathematical models Dielectrics Permittivity

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Effect of the Permittivity of Isotropic Load on the Area of Phase Shifter Operation of a Circular Ferrite-Dielectric Waveguide with Azimuthal Magnetization: Analysis in Terms of the L3 ± Numbers

Effect of the Permittivity of Isotropic Load on the Area of ...

引用

International Conference on Electromagnetics in Advanced Applications (ICEAA)

作者： Georgi Nikolov Georgiev Mariana Nikolova Georgieva-Grosse Consulting and Researcher in Physics Mathematics and Computer Sciences BG-5138 Polikraishte / BG-5229 Slomer Bulgaria Consulting and Researcher in Physics and Computer Sciences BG-5229 Slomer / BG-5138 Polikraishte Bulgaria

A circular waveguide, entirely filled with a coaxially positioned azimuthally magnetized ferrite cylinder and a dielectric toroid, which sustains normal $TE_{01}$ mode, is considered. If $\varepsilon_{d}$ and $\varepsilon_{r}$ are the relative permittivities of the isotropic and anisotropic medium, resp., the impact of $\varepsilon_{d}$ on the width of the area in which the structure provides differential phase shift is studied, on condition that $\varepsilon_{d}\gt \varepsilon_{r}$ and $\varepsilon_{d}$ grows, while $\varepsilon_{r}$ is kept unchanged. The approach employs the characteristic equation of the configuration, derived previously by means of complex Kummer confluent hypergeometric and real ordinary Bessel and Neumann functions. In it the permittivities of the two strata participate through their ratio $\overline{\bar{\varepsilon}}=\varepsilon_{d}/\varepsilon_{r}$. That’s why it is chosen as a parameter in the investigation with a value, larger than 1 $(\overline{\bar{\varepsilon}}\gt 1)$, which increases, rather than $\varepsilon_{d}$ and $\varepsilon_{r}$. Using the definite purely imaginary roots of the equation mentioned in its independent variable, and certain new real positive numbers ($\overline{\bar{L}}_{3\pm}$ numbers), introduced by the authors earlier, the lower and upper cut-off frequencies of transmission line are computed. They allow to deduce the criterion, whose fulfillment guarantees its work as a phase shifter, and to reckon the width of the area in that this is observed. The dielectric region is assumed thin. Calculations are performed for several equidistant values of the off-diagonal ferrite Polder permeability tensor element, corresponding to strong anisotropy. The results are debated in detail.

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Numerical Analysis of the Azimuthally Magnetized Ferrite-Dielectric Circular Waveguide

Numerical Analysis of the Azimuthally Magnetized Ferrite-Die...

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European Conference on Antennas and Propagation, EuCAP

作者： Mariana Nikolova Georgieva-Grosse Georgi Nikolov Georgiev Consulting and Researcher in Physics and Computer Sciences SlomerBulgaria Faculty of Mathematics and Informatics University of Veliko Tirnovo “St. St. Cyril and Methodius” Veliko Tirnovo Bulgaria

An original numerical approach for investigation of a circular waveguide, containing a co-axially positioned ferrite cylinder of azimuthal magnetization and a dielectric toroid and that propagates normal $TE_{01}$ mode, is developed. It utilizes certain positive purely imaginary roots in the independent variable of the characteristic equation of the structure, derived in terms of the complex Kummer confluent hypergeometric and real zeroth and first order Bessel and Neumann functions and specific real numbers ( $\bar{L}_{3\pm}$ numbers). The latter are linked with the same roots of the equation mentioned, computed at other assumptions and have been defined and discussed by the authors in earlier studies. Tables of the roots in question and of the $\bar{L}_{3\pm}$ numbers for selected values of parameters of the configuration are given. Using them the lower and upper cut-off frequencies which specify the boundaries of the area of phase shifter operation of the transmission line are determined. The width of this area is also calculated. The discussion is confined to the case of a thick ferrite and a thin dielectric layers. It is assumed, as well that the relative permittivities of the two layers are equal.

关键词： Ferrites Circular waveguides Magnetic resonance imaging Magnetic confinement Phase shifters Cutoff frequency Toroidal magnetic fields

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Theorem for the Relation between the L1(c,n) and T1(L,n) Numbers

Theorem for the Relation between the L1(c,n) and T1(L,n) Num...

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URSI International Symposium on Electromagnetic Theory (EMTS)

作者： Georgi Nikolov Georgiev Mariana Nikolova Georgieva-Grosse Faculty of Mathematics and Informatics University of Veliko Tirnovo "St. St. Cyril and Methodius" Veliko Tirnovo Bulgaria Consulting and Researcher in Physics and Computer Sciences Polikraishte BG Bulgaria

The definitions of the finite real positive numbers L 1 (c,n) and T 1 (L,n) for c and L - restricted arbitrary real and n - a natural number, are brought forward. When c ≠ l, l = 0,-1,-2,..., the first are advanced through the positive purely imaginary zeros $\zeta _{k,n}^{(c)}$ in the independent variable x (z) of the complex Kummer confluent hypergeometric function Φ(a,c; x) (a = c / 2 - jk - complex, c = 2Rea - real, k - real, -∞ 0 ), corresponding to k → -∞ . Provided L ≠ l / 2 -1, the second are determined by the positive zeros $o_{\eta ,n}^L$ in the independent variable ρ of the generalized in keeping with the Thompson and Barnett's interpretation real regular Coulomb wave function F L (η,ρ) (ρ, η and L - all real, ρ > 0, -∞ 1(l,n)= L 1 (2 - l,n) and T 1 (l / 2 -1,n)=T 1 (-l / 2,n), resp. Numerical values of numbers are given as a function of their parameters. It is proved numerically that if c = 2L + 2 ( L = c / 2 -1 ) for identical n, it is fulfilled L 1 (c,n)= 2T 1 (L,n) [T 1 (L,n)=L 1 (c,n)/ 2]. This statement is called Theorem for the relation between the L 1 (c,n) and T 1 (L,n) numbers. An application of the mathematical result obtained in the analysis of guided-wave propagation along an anisotropic configuration is presented.

关键词： Wave functions Magnetic resonance imaging Ferrites Magnetization Phase shifters Mathematics Informatics

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Advanced Computational Method for Analysis of the Circular Waveguide, Loaded with an Azimuthally Magnetized Ferrite Toroid and a Dielectric Cylinder 20

Advanced Computational Method for Analysis of the Circular W...

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20th International Conference on Electromagnetics in Advanced Applications, ICEAA 2018

作者： Georgiev, Georgi Nikolov Nikolova Georgieva-Grosse, Mariana Faculty of Mathematics and Informatics University of Veliko Tirnovo 'St. St. Cyril and Methodius' Veliko Tirnovo Bulgaria Consulting and Researcher in Physics and Computer Sciences Gerlingen Germany

ISBN: (纸本)9781538667620

A sophisticated method is developed for investigation of the dependence of the phase constant of the normal TE01 mode, supported by a circular waveguide, containing an azimuthally magnetized ferrite toroid and a dielectric cylinder on its geometry and material parameters, and the frequency. The debate is focused on the case in which the relative permittivity of the isotropic region is smaller than that of the anisotropic one. This necessitates the employment of three forms of the structure's characteristic equation, written with the help of complex Kummer and Tricomi confluent hypergeometric Φ(a, c;x) and Ψ(a, c;x) and real ordinary or modified Bessel functions J0(y) and J1(y) and I1(u) and I0(u), resp. Each of them is responsible for the calculation of a definite portion of the phase portrait of transmission line. The propagation problem needs to use in the equation referred to the logarithmic representation of Ψ(a, c;x) functions. This calls for in addition elaboration of special schemes for numerical evaluation of the involved in the power series, defining them complex Euler gamma function Γ(a)and logarithmic derivative of the latter of complex ψ(a)and of integer variable ψ(n). Procedures for reckoning up Φ(a, c;x), J0(y), J1(y), I0(u) and I1(u), and for ferreting out the purely imaginary roots of the equation spoken of in the independent variable of Tricomi functions, worked out, constitute an integral part of the method, being the object of the study, as well. A sample of the results obtained for selected parameters is presented in numerical form. The analysis shows that the area of wave propagation is restricted. A numerical technique for tracing its upper border is brought forward. It requires the introduction and tabulation of certain real positive numbers (e L-4pm numbers), proportional to some roots of the aforesaid equation. © 2018 IEEE.

关键词： Boundary value problems

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Criterion for Phase Shifter Operation of the Circular Waveguide with Azimuthally Magnetized Ferrite and Dielectric 20

Criterion for Phase Shifter Operation of the Circular Wavegu...

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20th International Conference on Electromagnetics in Advanced Applications, ICEAA 2018

作者： Georgieva-Grosse, Mariana Nikolova Nikolov Georgiev, Georgi Consulting and Researcher in Physics and Computer Sciences PolikraishteBG-5138 Bulgaria Faculty of Mathematics and Informatics University of Veliko Tirnovo 'St. St. Cyril and Methodius' Veliko TirnovoBG-5000 Bulgaria

ISBN: (纸本)9781538667620

The criterion under which the circular waveguide, containing a co-axially positioned dielectric cylinder and latching ferrite toroid of azimuthal magnetization, acts as a nonreciprocal digital phase shifter for the normal TE01 mode, is ferreted out. Employing it, a numerical method is elaborated that enables to reveal the impact of the material and geometry parameters of the transmission line considered on the width of the area in which it provides differential phase shift. The approach uses definite set of roots of the structure's characteristic equation, derived earlier by means of complex Kummer and Tricomi confluent hypergeometric and real zeroth and first order Bessel functions, and the real positive bar L-4 pm numbers, connected with other set of roots of the equation spoken of. For simplification it is assumed that the relative permittivities of the two layers are equal. Results are presented for a fixed value of the dielectric cylinder to guide radius ratio and a varying off-diagonal ferrite permeability tensor element. © 2018 IEEE.

关键词： Boundary value problems

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Advanced Computational Method for Analysis of the Circular Waveguide, Loaded with an Azimuthally Magnetized Ferrite Toroid and a Dielectric Cylinder

Advanced Computational Method for Analysis of the Circular W...

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International Conference on Electromagnetics in Advanced Applications (ICEAA)

作者： Georgi Nikolov Georgiev Mariana Nikolova Georgieva-Grosse Faculty of Mathematics and Informatics University of Veliko Tirnovo “St. St. Cyril and Methodius” Veliko Tirnovo Bulgaria Consulting and Researcher in Physics and Computer Sciences Gerlingen Germany

ISBN: (纸本)9781538667637

A sophisticated method is developed for investigation of the dependence of the phase constant of the normal TE 01 mode, supported by a circular waveguide, containing an azimuthally magnetized ferrite toroid and a dielectric cylinder on its geometry and material parameters, and the frequency. The debate is focused on the case in which the relative permittivity of the isotropic region is smaller than that of the anisotropic one. This necessitates the employment of three forms of the structure's characteristic equation, written with the help of complex Kummer and Tricomi confluent hypergeometric Φ(a, c; x) and Ψ(a, c; x) and real ordinary or modified Bessel functions J 0 (y) and J 1 (y) and I 1 (u) and I 0 (u), resp. Each of them is responsible for the calculation of a definite portion of the phase portrait of transmission line. The propagation problem needs to use in the equation referred to the logarithmic representation of Ψ(a, c; x) functions. This calls for in addition elaboration of special schemes for numerical evaluation of the involved in the power series, defining them complex Euler gamma function Γ(a)and logarithmic derivative of the latter of complex ψ(a)and of integer variable ψ(n). Procedures for reckoning up Φ(a, c; x), J 0 (y), J 1 (y), I 0 (u) and I 1 (u), and for ferreting out the purely imaginary roots of the equation spoken of in the independent variable of Tricomi functions, worked out, constitute an integral part of the method, being the object of the study, as well. A sample of the results obtained for selected parameters is presented in numerical form. The analysis shows that the area of wave propagation is restricted. A numerical technique for tracing its upper border is brought forward. It requires the introduction and tabulation of certain real positive numbers (L̃ 4± ), proportional to some roots of the aforesaid equation.

关键词： Ferrites Mathematical model Dielectrics Perpendicular magnetic anisotropy Permittivity Geometry

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