Hallen-type Integral Equations Research Articles

Faster convergence for MoM analysis of resonant circular arrays of cylindrical dipoles

Method-of-moments analyses of resonant circular arrays of cylindrical dipoles present unique and particular difficulties. A previous publication overcame the major difficulties by using a set of improved kernels in the usual Hallen-type integral equations and by applying an appropriate convergence acceleration method. Based on previous works dealing with the isolated cylindrical dipole, proposed is a better method of calculating the constant C (m) appearing in the aforementioned equations; this results both in improved accuracy and in faster overall convergence of the authors' moment method.

Method-of-Moments Analysis of Resonant Circular Arrays of Cylindrical Dipoles

We perform a method-of-moments (MoM) analysis of a circular array of cylindrical dipoles. The array is known from earlier theoretical and experimental studies to possess very narrow resonances. The earlier theoretical studies were carried out using the “two-term theory.” The present paper is a direct continuation of a recent work showing that the problem possesses unique and particular difficulties. The main difficulties are overcome herein using a set of improved kernels in the usual Hallen-type integral equations (these kernels had been developed in previous works, and were successfully incorporated into the aforementioned two-term theory analyses). We make a detailed comparison of our MoM results to two-term theory results and, also, to the earlier experimental results.

Original and Modified Kernels in Method-of-Moments Analyses of Resonant Circular Arrays of Cylindrical Dipoles

Properly dimensioned circular arrays of cylindrical dipoles are known to possess very narrow resonances. It is also known that analyzing such arrays using moment methods presents unique and particular difficulties, as application of such methods to the usual Hallen-type integral equations can yield meaningless results from which no further conclusions should be drawn. In the present paper, we apply moment methods to properly modified integral equations and obtain much more reliable results. We also observe that certain difficulties still remain, and discuss them in detail.

Fundamental transmitting properties of carbon nanotube antennas

Fundamental properties of dipole transmitting antennas formed by carbon nanotubes are investigated. Since carbon nanotubes can be grown to centimeter lengths, and since they can be metallic, the properties of carbon nanotubes as antenna elements are of fundamental interest. In this paper, dipole carbon nanotube antennas are investigated via a classical Hallen's-type integral equation, based on a quantum mechanical conductivity. The input impedance, current profile, and efficiency are presented, and the radiation pattern is discussed, as are possible applications.

Entire-domain analysis of thin-wire antennas near or in lossy ground

An entire-domain method is proposed for the analysis of thin-wire antennas assembled from arbitrarily interconnected straight segments placed on one or both sides of the interface air/lossy ground. The approach is based on an exact Sommerfeld-type formulation combined with the Hallen-type integral equations for current distribution, polynomial approximation of current and point matching. Limitations on the antenna position with respect to the interface and on the value of the ground parameters seem to be less than in other available methods, and accuracy of the results depends principally on available CPU time.

A Hallen-type integral equation for symmetric scattering from lossy circular disks

A rigorous technique is presented for calculating the current induced on a thin lossy disk by rotationally symmetric sources, and the resulting scattered field. A Hallen-type integral equation is developed for the current using the magnetic vector potential, and it is solved by the method of moments. It is shown that the diffraction lobes usually associated with radiation above a finite circular ground plane can be reduced dramatically by the addition of loss. Application to a quarter-wave monopole radiating above a finite circular perfectly conducting ground plane shows good agreement with experiment. >

Hallen-type integral equation to a system composed of wires with dielectric coating

The Hallen-type integral equation for an arbitrary wire antenna with dielectric coating is formulated. The numerical results for a dipole and a helical antenna are found to be in very good agreement with the results obtained from the reaction integral.

Analysis of Umbrella antenna at the Omega navigation station

The characteristics of the electrically very small umbrella antenna used for the Omega navigation system are examined by the numerical analysis. The transmitting antenna of height about 0.02 \lambda with 16 inclined elements at the Tsushima station is analyzed as an example of electrically very small umbrella antenna. In the analysis the ground is assumed to be a perfectly conducting plane and the Hallen-type integral equation is used. The difference between the calculated input resistance and the measured one is estimated as the earthing resistance. The approximate equation of radiation resistance is derived and the relation between the inclined elements and the antenna characteristics is discussed.

Analysis of an antenna composed of arbitrarily located slots and wires

A technique of analyzing an antenna composed of arbitrarily oriented thin wires and slots in a planar conducting screen is presented. The analysis is based on the generalized Hallen's type integral equation with closed form kernel. A parametric evaluation is done for a configuration of slot and two bending wires (Clavin element). The results obtained are shown to be in close agreement with the experimental ones obtained by Clavin et al.

On the integral equation of piecewise linear antennas

An efficient computation technique for obtaining the current distribution on a piecewise linear antenna is presented. The generalized Hallen's type integral equation with closed form kernel is formulated and then solved numerically by the collocation method. Numerical and experimental results for the gull shape and the trapezoidal tooth wire antennas are included.

On the analysis of the umbrella antennas using the Hallen-type integral equation

Umbrella antennas of heights 0.125\lambda and 0.5141\lambda are numerically and experimentally analyzed, and the effect of the junction on the current distribution is discussed. A simplified Hallen-type integral equation and an integral equation for the scalar potential of the antenna composed of straight wires are formulated and applied to umbrella antennas. The integral terms in these equations are analytically reduced to single integrals, and the extended boundary condition that the electric field vanishes on the axis of the antenna is used.

Current distribution and impedance of monopole antenna on lossy ground

A Hallen's type integral equation is solved by the method of moments with sub-sectional basis and parabolic expansion functions. The effect of the ground is taken into account by reflection-coefficient approximation. A variational expression is derived for the impedance changes resulting from the presence of a lossy ground. Numerical results are presented for the current distribution and impedance changes of quarter-wave vertical antennas on an inhomogeneous wet ground at 1 MHz and 5 MHz as a function of thickness and elevation of antennas.

Currents induced on a pair of skew crossed wires

Hallen-type integral equations are formulated for skew crossed wires and, by numerical solution techniques, current distributions are obtained. The coupled integral equations are founded entirely upon the familiar electric scalar potential and magnetic vector potential whereas, in the past, similar analyses have been based upon an auxiliary scalar function. Numerical results are presented for several cases, including different skew angles, and are compared with available data for the special case of perpendicular wires.

Mutual coupling in linear dipole arrays

A Hallen's type integral equation is formulated for the current distribution on a dipole which can assume an arbitrary tilt angle in an infinite periodic phased array. The active impedance of the dipole is calculated for various combinations of spacing, tilt angle, scan angle, and frequency.