A PRACTICAL APPROACH TO MODELING DOUBLY CURVED CONFORMAL MICROSTRIP ANTENNAS - ABSTRACT

Designers are increasingly integrating conformal microstrip antennas into the curved structures of either air or land vehicles. Quite often, these structures are doubly curved (e.g. curved along two orthogonal surface directions). This practice necessitates the development of accurate codes versatile enough to model conformal antennas with arbitrarily shaped apertures radiating from doubly curved surfaces. Traditional planar-structure-based design techniques are not well suited for this application. A hybrid finite element-boundary integral formulation appropriate for the high-frequency analysis and design of doubly curved conformal antennas is introduced in this paper. The novelty of this approach lies in its use of an asymptotic prolate spheroidal dyadic Green’s function to model the physics of curved surface diffraction. To demonstrate the utility of this approach, the effects of curvature on the resonant frequency and input impedance of both a doubly curved conformal square and circular patch antenna are investigated. Different feed positions are also considered. Due to a paucity of published experimental data, the numerical results are benchmarked by comparison with the results for planar square and circular patch antennas. The planar results are obtained by using an experimentally validated planar finite element-boundary integral code. 296 Macon, Trott, and Kempel

Feasibility of a 434 MHz microwave intracavitary applicator with conformal patch antennas is presented for hyperthermia treatment of gynaecological cancers. 3D numerical modelling was used to design a 434 MHz resonant conformal rectangular patch on a cylindrical alumina substrate. A conformal array applicator designed using four conformal patch antennas was evaluated in muscle tissue phantom. Applicator measurements indicated that the conformal patch resonated at 434 MHz with power reflection coefficient ρ < −35 dB, penetration depth of 12 mm at 434 MHz and −10 dB bandwidth >40 MHz. Normalised power deposition in the applicator transverse (XY) plane yielded 25% Effective Field Size (EFS) of 180 and 175 mm2 in simulation and measurement, respectively, for excitation of single conformal patch. The 25% EFS for excitation of two antennas was 500 and 510 mm2 in simulation and measurement, respectively. Simulations and measurements suggest that the 434 MHz intracavitary microwave applicator with conformal patch antennas could be used to deliver adjustable and localised power deposition at the target sparing the surrounding healthy tissues.

Over the last decade, several methods [1–8] have been developed to obtain the dyadic Green's functions (DGFs) of layered anisotropic media. The most commonly used methods to find the DGFs are the Fourier transform method with differential formulation [6], the method of eigen-function expansion [7], the matrix formulation [8], and the dyadic decomposition techniques [5, 9–11]. In [8], the dyadic Green's function is formulated based on the tangential electric field and current at the interface, which is not suitable for the problem with z-directed current. The dyadic decomposition techniques as discussed in [5, 9–11] are more general and can provide the complete set of the dyadic Green's functions but only the case when the source is in the free space has been considered. If the source is located in a biaxial slab, then reciprocity theorem for the Green's function can be invoked to obtain the DGFs as in [12]. However, the reciprocity holds true only when the slab is filled with reciprocal medium such as uniaxial medium, biaxial medium, etc. For non-reciprocal medium such as the gyroelectric or gyromagnetic medium, the reciprocity relation for the Green's function no longer holds. The DGFs for source located in a non-reciprocal slab cannot be obtained using the reciprocity theorem.

An efficient closed-form asymptotic representation for the Dyadic Green's function for the grounded double-layered anisotropic uniaxial geometry is developed. In the present asymptotic development the large parameter is directly proportional to the lateral separation between the source and observation point. The asymptotic solution developed remains accurate even for very small lateral separation of the source and field points. The asymptotic closed-form Dyadic Green's function has been cast in such a form that the physical behavior of the electromagnetic fields due to anisotropy of the medium reveals itself through simple mathematical parameters. Thus, the physical understanding of the interaction of the spatially confined source with a grounded anisotropic (uniaxial) double-layered material slab is greatly enhanced through the new representation. Also, this representation is very useful in the moment method solution of the current excited on the microstrip antennas and arrays in a grounded double-layered uniaxial geometry, as well as the volumetric current excited within a dielectric scatterer buried in a ground double-layered anisotropic uniaxial slab. >

Recent formulations of the dyadic (or generalized) Green's function describe the relationship between sources (both mechanical stresses and electrical charge) and waves (both mechanical displacements and acoustic potential) on the surface of a substrate. The sixteen elements of the function intrinsically describe all propagation modes, whether Rayleigh or leaky, and are therefore extremely useful in the design of surface acoustic wave devices. While requiring little additional computational effort, the dyadic Green's function thus provides much more information than the traditional effective permittivity function. In this paper, we extend the calculation of the dyadic Green's function to multi-layer substrates. We show that its computation involves a simple cascaded matrix multiplication. The resulting function fully contains the substrate characteristics and, once obtained, can be used to describe the surface behavior with no further regard to the substrate's composition. The dyadic Green's function for a sample multi-layer substrate is presented.

The electric field within a source region is derived by use of a vector form of Green's second identity. The expression obtained is identical to that previously derived1 by a less direct method, but the present approach exposes the need to assume continuity of current density and electric field. The analysis gives the extra dyadic which must be added to the customary superposition integral to take account of the source-point singularity of the electric dyadic Green's function.

The dyadic Green's functions for a parallel-plate chirowaveguide are formulated by using the method of eigenfunction expansion. The eigenfunctions of the chirowaveguide are derived first in terms of two transformed fields. The purely solenoidal magnetic type dyadic Green's function is then expanded by these eigenfunctions. The electric type dyadic Green's function, which is solenoidal as well as longitudinal, is subsequently obtained from the magnetic dyadic Green's function through a simple relationship. It is found that the singular term in the electric dyadic Green's function accounting for the electric field in the source point is established through this latter procedure. The dyadic Green's functions obtained can be used to examine the electric and magnetic fields inside the chirowaveguide and to construct other dyadic Green's functions.

The use of a dyadic layered-medium Green's function as the kernel in a method of moments (MoM) modeling problem greatly reduces the complexity of modeling a stratified medium. Compared to the free-space Green's function, there is an additional cost of having to compute a semi-infinite Sommerfeld integral for each call to calculate the dyadic layered-medium Green's function. This letter discusses a method to tabulate and interpolate the Green's function as a method of reducing the impedance matrix filling time. This method can be used in conjunction with existing methods for increasing the computational speed of the Green's functions.

A conformal differentially fed antenna at 915 MHz industrial, scientific, and medical (902–928 MHz) band for monitoring in body core temperature is presented in this paper. In virtue of its characteristics of ultrathin and flexible substrate, the peculiarity that proposed antenna can be wrapped around the capsule inner wall demonstrates the satisfactory performance of occupying a little space. The volume of the conformal patch antenna only measures 30 mm3 by notching meandering slots to achieve miniaturization. The simulated impedance bandwidth ( $\vert S_{11}\vert dB) covers from 861 to 942 MHz. The integrated capsule system, inserted in a cubic homogeneous muscle phantom for initial parametric studies and optimization, occupies the dimensions of 22 mm (length) $\times11$ mm (diameter). Meanwhile, the performance on the sensitivity to surrounding environment and specific absorption rate distribution are studied. In the measurements, the conformal antenna is rolled around a 3-D-printed capsule inside minced pork. The pork temperature data are monitored in time and transferred wirelessly. To confirm the system reliability, hardware circuits are designed with differential concept and a data logger is also realized to record in-time temperature data. Finally, the feasibility of system function demonstrates the suitability of the conformal differentially fed antenna in biomedical applications.

ABSTRACT: A mathematically accurate method of analysis of a spheri - cal-disk antenna conformally printed on a dielectric-co ¤ ered metallicsphere is presented. The antenna is fed by a radial coaxial probesimulated by an electric dipole. The solution consists of reducing theboundary- ¤ alue problem to the dual-series equations, and further to aregularized infinite-matrix equation. This procedure is based on theanalytical in ¤ ersion of the static part of the problem of a disk in freespace, and results in a stable and fast algorithm with a guaranteedcon ¤ ergence. Numerical data on the basic antenna characteristics arepresented. Q 2000 John Wiley & Sons, Inc. Microwave Opt TechnolLett 26: 176]182, 2000. Key words: spherical disk; conformal antenna; dual-series equations;analytical regularization; directi ¤ ity 1. INTRODUCTION Metallic circular disks printed on dielectric substrates areused frequently in patch antenna technology. Conformalprinted antennas are necessary in automotive and airbornecommunications and radar due to their low profile and lightweight. In this paper, the problem of modeling of aspherical-disk conformal printed antenna is considered as-suming an excitation by a coaxial probe. The probe is mod-eled by a radial electric dipole RED located at the surface.of the metal sphere covered with dielectric. From a theoreti-cal point of view, such a geometry is a canonical one for awide class of conformal patch antennas. Previously, similarproblems have been analyzed by direct applications of themethod of moments 1, 2 . However, convergence of thesewxnumerical approximations is not uniformly guaranteed, espe-cially if narrow resonances are present 3 . Patch antennaswxare essentially resonant devices; hence, this must be kept inmind when developing an accurate simulation software. Wepropose an exact mathematical method based on the analyti-cal inversion of the free-space static problem for a sphericaldisk 4, 5 that has been used previously in the analysis ofwxcavity-backed apertures and reflector antennas 6wx]8 . Thismethod belongs to the broad family of techniques collectivelycalled the method of analytical regularization 9 that arewxremarkable for stable and fast numerical solutions.

In this paper, the field distribution in the upper half space is divided into two regions: the fields in the upper hemisphere with r <;a <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> and the fields in the exterior region r > a <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> , where a <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> is a scale dependent on the geometry of the patch and the permittivity of the substrate. By employing dyadic Green's functions expanded in these two regions, an exact solution is obtained to both near and far fields of circular patch antennas.

To characterize electromagnetic waves in complex media has been an important topic because of the useful applications and the scientific significance of the physical mechanism. Dyadic Green's functions, as a mathematical kernel or a dielectric medium response, relate directly the radiated electromagnetic fields and the source distribution. In terms of the vector wave functions in cylindrical coordinates, dyadic Green's functions in an unbounded and a planar, multilayered gyroelectric chiral media are formulated. After a general representation of the Green's dyadics is obtained, the scattering coefficients of the Green's dyadics are determined from the boundary conditions at each interface and are expressed in a greatly compact form of recurrence matrices. In the formulation of the Green's dyadics and their scattering coefficients, three cases are considered, i.e. the current source is impressed in (1) the first, (2) the intermediate, and (3) the last regions, respectively. Although the dyadic Green's functions for an unbounded gyroelectric chiral medium have been reported in the literature, the results are either incorrect or suspicious. As compared to the existing results, the current work basically contributes (1) a correct form of the dyadic Green's function for a unbounded gyroelectric chiral medium, (2) the general representation of the dyadic Green's functions for a multi-layered gyroelectric chiral medium, and (3) a convincing and direct derivation of the irrotational Green's dyadic.

The dyadic Green's functions of the cylindrical chirowaveguide are derived by modal expansion. Bohren's decomposition of the electromagnetic field is used to obtain the vector wave functions. The magnetic dyadic Green's function that is purely solenoidal is first derived and the electric dyadic Green's function is then obtained by manipulating the magnetic dyadic Green's function. The singular term in the expression of the electric dyadic Green's function is reinstated through the manipulation procedure.

This paper presents an approach to analyze the microstrip lines using Vector Dyadic Green's function. The vector Dyadic spectral Green's function is obtained directly from the Spectral domain immitance approach thus leading to a discretized system of equations which can be utilized in the semi analytical analysis of the planar microwave structures and resonators. Finally, the equations so derived have been used to analyze the characteristics of microstrip line in simple and suspended configurations. The current distribution on the strip is also calculated. The results thus obtained were found to be in good agreement with results using Spectral Domain Approach (SDA). Ill. 5, bibl. 9 (in English; summaries in Lithuanian, English and Russian).

This paper presents a systematic and unified formulation of the dyadic Green's functions for multilayered biisotropic media. The media are stratified in a general direction which includes the canonical cases of planar, cylindrical and spherical geometries. Both electric and magnetic dyadic Green's functions are derived simultaneously based on the principle of scattering superposition. For the scattered dyadic Green's functions, their scattering coefficients are determined using the effective reflection and transmission concepts. This approach has avoided cumbersome operations and has also provided good physical insights to the scattering mechanism. The resulting general expressions are written in very compact and convenient forms. These expressions have been applied explicitly to the three canonical cases. For some common sets of biisotropic constitutive relations, their dyadic Green's functions are discussed and compared. The special case of multilayered isotropic media are considered as well.