Piecewise Sinusoidal Basis Functions Research Articles

An Efficient Method of Moments for Thick-Wire Antennas

Detailed formulation of a simple Galerkin method of moments (MoM) is presented. It is based on compact closed-form expressions of mutual impedance among filamentary sinusoidal monopoles. Using piecewise sinusoidal basis functions, the mutual impedance of thick-wire sections can be computed through an azimuthal integration of the mutual impedance between filamentary dipoles. Each element of impedance matrix is calculated through a rapidly convergent single integral only. This is unlike other MoM techniques, where double or triple integrals are needed to evaluate impedance matrix. In our formulation, it has been assumed that the wire current is uniform in azimuth, and changes along the axial direction only. No approximation on the segment length or radius of the thick-wire is made, and hence our formulation remains efficient for arbitrarily long/thick antennas.

Chiral frequency selective surfaces comprised of multiple conducting strips per unit cell

The periodic structure based on an array of multiple conducting strips per unit cell on a chiral slab is investigated in this letter. Instead of a single strip, a unit cell is constructed by equal and unequal lengths of double or triple strips. In this case, the array is periodic, as opposed to the traditional individual elements. The co-polarised reflectance, co-polarised transmittance and cross-polarised transmittance of new types of frequency selective surfaces (FSS) comprised of perfectly conducting double or triple strips on a chiral slab are analysed theoretically for a plane wave at normal incidence. The analysis is based on the modal expansions and moment methods together with the Floquet theorem. The unknown current coefficients induced on the conducting elements are computed by using the subdomain overlapping piecewise sinusoidal basis functions. By using two or three conducting strips per unit cell, FSS can be operated in different frequency bands. The double and triple strips per unit cell on chiral slab produce double and triple resonances, respectively. The structure can be used in band-stop filter, multiband antenna applications and subreflector systems as well as the polarisation rotator. The computed result of free-standing strip FSS is compatible with the measured and calculated results in literature.

Zigzag metallic conductors as frequency selective surfaces

Reflection and transmission properties of a new type of frequency selective surface (FSS) made of zigzag metallic elements placed periodically on a dielectric substrate are investigated theoretically for arbitrary polarisation. The electric field integral equation technique with the subdomain overlapping piecewise sinusoidal basis functions are employed to compute the unknown current coefficients induced on the metallic elements. The zigzag FSS arrays act as a low-pass filter in S -(1-5 GHz), X -(8-12 GHz) and K u -(12-18 GHz) bands. Owing to multiple resonances the zigzag FSS arrays can be used in multiband frequency applications. Between the resonances there exist transmission windows that allow full energy transfer. By removing the first and third arms, the power reflection coefficient of three-arm zigzag FSS is compared with a freestanding strip FSS, and it is compatible with the measured and calculated results found in the literature.

ACCURACY AND COMPLEXITY ASSESSMENT OF SUB-DOMAIN MOMENT METHODS FOR ARRAYS OF THIN-WIRE LOOPS

A direct sub-domain moment-method formulation is presented for the analysis of arrays of thin-wire loops. Curved piecewise sinusoidal basis functions are used for the description of the currents on the loops, while both point matching and reaction matching are examined as testing schemes. Numerical results are provided for representative array structures with the intention to delve into the behavior of the solutions as the number of basis/testing functions grows, but also for the purpose of comparison with well-documented results. Finally, the complexity of the developed codes is estimated and general guidelines are provided for the efficient and accurate analysis of multi-element arrays.

Complete surface current distribution in a normal-mode helical antenna using a Galerkin solution with sinusoidal basis functions

An investigation of the surface current distribution in a normal-mode helical antenna (NMHA) is reported. This enables precise prediction of the performance of NMHAs, since traditional wire-antenna simulations ignore important details, such as non-uniform and transverse current distributions. A moment-method formulation is developed, using two-dimensional basis functions to represent the total non-uniform surface current distribution over the surface of the wire of the helix. Piecewise-sinusoidal basis functions are employed in two normal directions, with an exact kernel formulation and application of Galerkin's solution method. The numerical solution of the singular integrals associated with self-impedance terms was computed with a very low relative error. The surface current distribution was computed for different helix geometries. It was found that the axially-directed component of the current distribution around the surface of the wire was highly non-uniform and that there was also a significant circumferential current flow due to inter-turn capacitance, both effects that are overlooked by standard filamentary current representations.

Characterization of cylindrical microstrip gap discontinuities

AbstractA rigorous full‐wave analysis of microstrip gap discontinuities on cylindrical surfaces is presented. Numerical results for the frequency‐dependent reflection and transmission coefficients and the gap capacitance and conductance are calculated using a moment‐method calculation, in which a combination of entire‐domain sinusoidal and piecewise sinusoidal basis functions is used to represent the currents on the microstrip line. The characteristics of cylindrical microstrip gap discontinuities for various curvatures and gap spacings are analyzed. © 1995 John Wiley & Sons, Inc.

Moment method analysis of linearly tapered slot antennas

AbstractAn accurate Method of Moments (MoM) model is developed and implemented for the analysis of the linearly tapered slot antenna (LTSA). The model employs an unequal size reactangular sectioning for conducting parts of the antenna. Piecewise sinusoidal basis functions are used for the expansion of conductor current. The effect of the dielectric is incorporated in the model by using equivalent volume polarization current density and solving the equivalent problem in free space. The feed section of the antenna including the micro‐stripline is handled rigorously in the MoM model by including slotline short‐circuit and microstripline currents among the unknowns. Comparison with measurements is made to demonstrate the validity of the model for both the air case and the dielectric case. Numerical results for the effect of the dielectric permittivity are presented.

Numerical computation of 2D sommerfeld integrals— A novel asymptotic extraction technique

The accurate and efficient computation of the elements in the impedance matrix is a crucial step in the application of Galerkin's method to the analysis of planar structures. As was demonstrated in a previous paper, it is possible to decompose the angular integral, in the polar representation for the 2D Sommerfeld integrals, in terms of incomplete Lipschitz-Hankel integrals (ILHIs) when piecewise sinusoidal basis functions are employed. Since Bessel series expansions can be used to compute these ILHIs, a numerical integration of the inner angular integral is not required. This technique provides an efficient method for the computation of the inner angular integral; however, the outer semi-infinite integral still converges very slowly when a real axis integration is applied. Therefore, it is very difficult to compute the impedance elements accurately and efficiently. In this paper, it is shown that this problem can be overcome by using the ILHI representation for the angular integral to develop a novel asymptotic extraction technique for the outer semi-infinite integral. The usefulness of this asymptotic extraction technique is demonstrated by applying it to the analysis of a printed strip dipole antenna in a layered medium.

Numerical computation of 2D sommerfeld integrals— Deccomposition of the angular integral

Spectral domain techniques are frequently used in conjunction with Galerkin's method to obtain the current distribution on planar structures. When this technique is employed, a large percentage of the computation time is spent filling the impedance matrix. Therefore, it is important to develop accurate and efficient numerical techniques for the computation of the impedance elements, which can be written as two-dimensional (2D) Sommerfeld integrals. Once the current distribution has been found, then the near-zone electric field distribution can be obtained by computing another set of 2D Sommerfeld integrals. The computational efficiency of the 2D Sommerfeld integrals can be improved in two ways. The first method, which is discussed in this paper, involves finding a new way to compute the inner angular integral in the polar representation of these integrals. It turns out that the angular integral can be decomposed into a finite number of incomplete Lipschitz-Hankel integrals, which in turn can be calculated using series expansions. Therefore, the angular integral can be computed by summing a series instead of applying a standard numerical integration algorithm. This new technique is found to be more accurate and efficient when piecewise-sinusoidal basis functions are used to analyze a printed strip dipole antenna in a layered medium. The incomplete Lipschitz-Hankel integral representation for the angular integral is then used in another paper to develop a novel asymptotic extraction technique for the outer semi-infinite integral.

Analyse von planaren Schaltungen mit eingebauten passiven oder aktiven konzentrierten Bauelementen

A method for the investigation of planar microstrip circuits embedded in layered media is presented. The circuit consisting of active and passive lumped elements is fed by a various number of microstrip lines. The current on the metallic structure is described by asymmetric piecewise sinusoidal basis functions. The integral equation is formulated in the spectral domain and solved with the method of moments.

Equivalent antenna radius for narrow slot apertures having depth

The problem of electromagnetic penetration of a narrow slot aperture in a thick perfectly conducting plane is reduced to the solution of Hallen's integral equation with an equivalent antenna radius. The depth and width of the slot are assumed to be small compared to both the length of the slot and the wavelength. The equivalent radius is evaluated in terms of the solution to the transverse static problem. Simple approximations for the equivalent radius is also given. Hallen's integral equation is solved by the Galerkin method with piecewise sinusoidal basis functions. Large slot depth-to-width ratios give rise to vanishingly small equivalent radii and thus large antenna resonance quality factors. A simple correction to the static field distribution in the slot is also given. This correction allows the depth to become somewhat larger relative to the wavelength. >

A hybrid technique for wire antennas in a cavity

Two numerical techniques for solving the current distribution on wire antennas, namely point matching and reaction matching, have been combined in a particular fashion to yield a new technique termed the "hybrid method." The hybrid method is well suited for a wire antenna mounted in a cavity. Over the antenna, piecewise sinusoidal basis functions with reaction matching are used, and on the support structure, point matching is used with pulse basis functions. The hybrid method has been applied to calculate the input impedance and the radiation efficiency of the three-turn loop antenna in an open circular cavity. Calculated input resistance of the antenna is found to agree quite well with measured data. Effects of varying the extent of recession of the antenna and varying the radius and the material of the antenna wire on the bandwidth, the efficiency, the antiresonance frequencies, and the general input reactance level of the antenna have been examined for a specific antenna geometry. The results are considered to be indicative of the general characteristics of a multiturn loop antenna with nearby support structure. The computer program that has been developed may be applied to a systematic parametric study of this type of antenna in order to optimize it for a particular application.