Tunability and bandwidth of microstrip filters fabricated on magnetized ferrites

The method of moments in the spectral domain is applied to the rigorous full-wave analysis of coupled line microstrip filters fabricated on magnetized ferrites. The results show that the center frequency of the filters can be tuned over a wide range by adjusting the magnitude of the bias magnetic field of the ferrite substrates. However, the filters bandwidth is reduced as the tuning frequency increases. This bandwidth reduction is explained in terms of the behavior of the resonant frequencies and quality factors of the resonators included in the filters.     

An alternative approach to FD-TD analysis of magnetized ferrites

This paper presents a new approach to the finite difference-time domain (FD-TD) analysis of magnetized ferrites. An equivalent lumped circuit of an FD-TD cell filled with such a medium is developed. Then the lumped circuit is used to propose a new FD-TD algorithm. This algorithm is verified on canonical examples and is shown to be simple, accurate, robust and computationally more effective than the previously published approaches.     

Analysis of shielded striplines and finlines with finitemetallization thickness containing magnetized ferrites

The applicability of the spectral domain approach is extended to analyze various types of shielded planar transmission lines, taking the anisotropy of the magnetized ferrites and the finite metallization thickness into consideration. The numerical computations include the propagation characteristics of finlines and striplines and the metallization thickness effect in these lines. Numerical data of simpler structures are compared with the available exact solution as well as with published data     

FDTD treatment of partially magnetized ferrites with a newpermeability tensor model

This paper outlines the finite-difference time-domain (FDTD) treatment of partially magnetized ferrites characterized by a permeability tensor model, which was recently published. Its causal aspect makes this tensor well adapted to time-domain simulations. Validation is demonstrated for a resonant ferrite structure, Numerical and analytical results are compared, showing good agreement     

Experimental validation of analysis software for tunable microstrip filters on magnetized ferrites

Measurements are presented for microstrip filters on layered media containing magnetized ferrites. The measurements show that the filters can be tuned by adjusting the magnitude of the magnetic-bias field. The measured results are compared with full-wave numerical results obtained by the authors via the method of moments in the spectral domain. The agreement between experimental and numerical results is reasonably good. The results show that the bandwidth of the filters appreciably decreases as the tuning frequency increases for frequencies located above the magnetostatic waves range (MWR). However, tuning is achieved without substantial bandwidth reduction for frequencies located below the MWR.     

Static Green's functions with conformal mapping and MATLAB

In this paper, conformal mapping was combined with Matlab. An application of the theory was showed in examples showing its ability to provide analytical expressions for two-dimensional Green's functions associated with Poisson's equation, i.e., electrostatic potentials created by infinite line sources parallel to metallic infinite cylinders of the various shapes. The solution is naturally expressed in the transformed domain, but usually a direct expression in the original (x,y) coordinates is easily obtained. In most cases, the proposed solutions are an order of magnitude simpler than those obtained by other approaches.     

Multilayered media Green's functions in integral equationformulations

A compact representation is given of the electric- and magnetic-type dyadic Green's functions for plane-stratified, multilayered, uniaxial media based on the transmission-line network analog along the aids normal to the stratification. Furthermore, mixed-potential integral equations are derived within the framework of this transmission-line formalism for arbitrarily shaped, conducting or penetrable objects embedded in the multilayered medium. The development emphasizes laterally unbounded environments, but an extension to the case of a medium enclosed by a rectangular shield is also included     

Closed-form Green's functions for cylindrically stratified media

A numerically efficient technique is developed to obtain the spatial-domain closed-form Green's functions of the electric and magnetic fields due to z- and φ-oriented electric and magnetic sources embedded in an arbitrary layer of a cylindrical stratified medium. First, the electric- and magnetic-field components representing the coupled TM and TE modes are derived in the spectral domain for an arbitrary observation layer. The spectral-domain Green's functions are then obtained and approximated in terms of complex exponentials in two consecutive steps by using the generalized pencil of function method. For the Green's functions approximated in the first step, the large argument behavior of the zeroth-order Hankel functions is used for the transformation into the spatial domain with the use of the Sommerfeld identity. In the second step, the remaining part of the Green's functions are approximated on two complementary parts of a proposed deformed path and transformed into the spatial domain, analytically. The results obtained in the two consecutive steps are combined to yield the spatial-domain Green's functions in closed forms     

Dyadic Green's functions for a coaxial line

The eigenfunction expansions of the dyadic Green's functions for a coaxial line have been derived based on the method ofbarbar{G}_{m}, whereby the irrotational vector wave functionbar{L}is not needed. A dyadic boundary condition for the discontinuity of the tangential component ofbarbar{G}_{m}has been used to facilitate the derivation of the expression for the electric dyadic Green's function.     

One- and two-dimensional dyadic Green's functions in chiral media

The one-dimensional and two-dimensional dyadic Green's functions are calculated for 1D and 2D electric sources in an unbounded, lossless, reciprocal chiral medium which is electromagnetically described by a set of symmetric constitutive relations. It is shown that in two- and one-dimensional cases, similar to the three-dimensional case, the medium supports two eigenmodes of propagation with two different wavenumbers. One of them corresponds to the right-circularly polarized wave and the other one to the left-circularly polarized wave. The eigenmode amplitudes a and b are similar to those of the three-dimensional case     

Nonreciprocal cell for the broadband measurement of tensorialpermeability of magnetized ferrites: direct problem

In this paper, a broad-band characterization method for measuring the complex permeability tensor components and complex scalar permittivity of magnetized ferrites is described. The technique is based on the reflection/transmission measurement of a rectangular waveguide partly filled with the ferrite that is to be characterized. The fundamental principle of the measurement consists in using the anisotropy of the material to lead to the nonreciprocity of the device in order to have the same number of measurable parameters (the S-parameters of the cell) for the characteristics we want to determine. Here, we will recall the principle of the mode-matching method used for the electromagnetic analysis of the cell (direct problem). We will bring to the fore the difficulties linked to the determination of the complex propagation constants of the different modes and will present a calculation procedure that makes this determination in a wide-frequency range easier. We will then compare at X-band frequencies (8-12 GHz) the theoretical S-parameters with those measured for ferrites of well-known properties in order to validate the direct problem. The determination of the permittivity and permeability values from the measured parameters (inverse problem) is not addressed here     

The eigenfunction expansion of dyadic Green's functions forchirowaveguides

A general method of formulating eigenfunction expansion of dyadic Green's functions in lossless, reciprocal and homogeneous chirowaveguides is presented. Bohren's decomposition of the electromagnetic field is used to obtain the vector wave functions. The method of G¯¯_m is used to rigorously derive the magnetic and electric dyadic Green's functions. A specific application to the cylindrical chirowaveguide illustrates the method     

On the eigenfunction expansion of dyadic Green's functions

As a result of an error, the singular behavior of the eigenfunction expansion of the dyadic Green's function is not correctly formulated in my book (C. T. Tai, Dyadic Green's Functions in Electromagnetic Theory, Scranton, Pa.: International Textbook, 1971). The correct expressions are given here and an improved method for deriving the residue series is presented.     

Electric dyadic Green's functions in the source region

A straightforward approach that does not involve delta-function techniques is used to rigorously derive a generalized electric dyadic Green's function which defines uniquely the electric field inside as well as outside the source region. The electric dyadic Green's function, unlike the magnetic Green's function and the impulse functions of linear circuit theory, requires the specification of two dyadics: the conventional dyadic G^-eoutside its singularity and a source dyadic L^-which is determined solely from the geometry of the "principal volume" chosen to exclude the singularity of G^-e. The source dyadic L^-is characterized mathematically, interpreted physically as a generalized depolarizing dyadic, and evaluated for a number of principal volumes (self-cells) which are commonly used in numerical integration or solution schemes. Discrepancies at the source point among electric dyadic Green's functions derived by a number of authors are shown to be explainable and reconcilable merely through the proper choice of the principal volume. Moreover, the ordinary delta-function method, which by itself is shown to be inadequate to extract uniquely the proper electric dyadic Green's function in the source region, can be supplemented by a simple procedure to yield unambiguously the correct Green's function representation and associated fields.     

Time-dependent dyadic Green's functions for rectangular andcircular waveguides

Closed-form expressions for the time-dependent dyadic Green's functions of electric and magnetic types for rectangular and circular waveguides are derived from the dyadic Maxwell equations in the time domain. These functions can be used to obtain the time-dependent electric and magnetic fields propagating in those guides due to any arbitrary time-dependent current distribution inside the guide. Stationary vector wave functions are introduced that separate the space-dependent parts from the time-dependent parts of the Green's functions. Comparison of the results for the rectangular and circular guides reveals that the time-dependent parts are identical. Thus the results can be easily extended to some other cylindrical pipes such as elliptical waveguides and also to coaxial cables     

Two-dimensional Green's functions for a rotationally invariantanisotropic medium

A coordinate transformation is introduced to map the anisotropic region into a fictitious isotropic region of finite angular extent where the field equations can be easily solved. This results in an infinite series representation which is not convenient for numerical calculations. An alternative representation is found by introduction of an apparently new integral form for the product of two-cylinder functions. The new representation provides physical insight as to the nature of the solution and is attractive from the computational standpoint. The results are analyzed, and a new corner-reflector-type effect is found for certain kinds of materials, which is in agreement with independent calculations. The analysis is of special importance for the derivation of a mathematical statement of a Huygen's principle for this type of material     

On the dyadic Green's functions for Beltrami fields

A simple derivation of the Green's functions for Beltrami fields is presented for use with time-harmonic electromagnetism in homogeneous biisotropic media.     

Time domain Green's functions for lossy and dispersive multilayered media

We have introduced a fast method of calculating the time domain Green's functions for multilayered media. In this paper, we demonstrate the use of this method to compute the scalar potential Green's function for a multilayer lossy dispersive medium on a PEC ground. The strength of the method lies in obtaining the Green's function for many source-to-field distances /spl rho/ and time instances t simultaneously. It only takes 6 min 28 s to compute 100/spl times/336=33 600 space time Green's function points in Matlab on a Pentium III 867 MHz processor with 1 GB of RAM for a multilayered lossy dispersive medium.     

New closed-form Green's functions for microstrip structures theory and results

This paper presents an efficient technique to evaluate the Green's functions of single-layer and multilayer structures. Using the generalized pencil of function method, a Green's function in the spectral domain is accurately approximated by a short series of exponentials, which represent images in spatial domain. New compact closed-form spatial-domain Green's functions are found from these images using several semi-infinite integrals of Bessel functions. With the numerical integration of the Sommerfeld integrals avoided, this method has the advantages of speed and simplicity over numerical techniques, and it leads to closed-form expressions for the method-of-moments matrix coefficients. Numerical examples are given and compared with those from numerical integration     

FDTD analysis of magnetized ferrites: application to thecalculation of dispersion characteristics of ferrite-loaded waveguides

The finite-difference time-domain (FDTD) method is extended to include magnetized ferrites. The treatment of the ferrite material is based on the equation of motion of the magnetization vector. Magnetic losses are also included in the equation of motion by means of Gilbert's approximation of the phenomenological Landau-Lifschitz damping term. The discretization scheme is based on central finite-differences and linear interpolation. This scheme allows the fully explicit nature of the FDTD method to be maintained. This extension of the FDTD method to magnetized ferrites is applied to the full-wave analysis of ferrite-loaded waveguides. The dispersion curves are calculated by using a recently proposed 2D-FDTD formulation for dispersion analysis which has been adapted to the present problem. The results for both the phase and attenuation constants of various transversely and longitudinally magnetized ferrite-loaded waveguides are compared with the exact values and with those obtained by means of Schelkunoff's method