John D. Mahony

Approximations to the radiation resistance and directivity of circular-loop antennas

The purpose of this article is to derive approximate formulas for the radiation resistance (R), and the directivity (D) of circular loop antennas. It is shown that simple approximations to the Bessel functions can be employed, to accurately model the oscillatory behavior of the Bessel function integral for both small and intermediate-sized loop antennas. Furthermore, when these approximations are combined with the usual asymptotic contributions to the integral in the case of a large input parameter ka (a=loop radius, a=2/spl pi///spl lambda/) accurate and relatively simple results for R and D can be secured for all loop sizes. Numerical results can, if necessary, be obtained using a simple pocket calculator.<<ETX>>

Omnidirectional pattern directivity in the absence of minor lobes: revisited

The article presents a simple, approximate formula for the directivity of an omnidirectional antenna without minor lobes. This problem has been treated before by Monser (1954), and the results have been cited by Levine and Monser (1961). In this earlier work, an approximate formula, showing antenna directivity as a function of the half-power beamwidth (HPBW), was determined by fitting a curve to data that had been obtained previously by numerically integrating across the half-power beamwidth spectrum: a process involving many integrations. Notwithstanding the evident good agreement between the exact and curve-fitted data in that instance, it is equally possible to return to the supporting sums and determine directly a very simple, alternative approximation to the defining integral and, hence, to the directivity of such antennas.

On the relationship between the directivity and the half-power beamwidth in quasi-symmetric pencil-beam radiation patterns

In antenna theory, the formulae relating the directivity and the half-power beamwidth are reexamined in the case of pencil-beam radiation patterns from large grounded apertures, both square and circular. It is shown that the differences among them can be reconciled by taking into account, for example, effects due to sidelobes. Effects due to an aperture-edge taper are also addressed.

The Tapered Cosine Distribution on a Circular Aperture

It is shown how it is possible to obtain a closed-form expression for the radiation integral associated with a tapered cosine distribution on a circular aperture.

Alternative Approximate Methods for the Efficient Computation of the Half-Power Beamwidths of a

Values for the principal plane halfpower beamwidths (HPBWs) of a well-known aperture distribution are re-examined. This article illustrates how a solution to the governing transcendental equations that involve Bessel functions can be simplified without any significant loss in accuracy by employing useful approximations. Moreover, the argument can be extended to any two orthogonal planes.

TE_{11}

A method is proposed for the evaluation of the integrals Cin(z) and Si(z), using integer-order Bessel functions. The results add to the repertoire, and are well suited for use in Excel spreadsheet applications, where functions of the Bessel type are part of an easily accessible library.

Mode Distribution on a Grounded Circular Aperture [EM Programmer's Notebook]

A request was made in an earlier letter [1] for help in proving some trigonometric results arising in antenna theory. It is the purpose of this letter to show just how such results might indeed be established. Perhaps the most instructive way to establish them is to do so from first principles, using mathematics that might be familiar to graduates in mathematics or engineering.

On alternative evaluations of the integrals cin(z) and si(z) [em programmer's notebook]

An approximate expression for the directivity associated with a tapered-cosine distribution on a circular aperture is obtained. This is used in calculations to optimize directivity at EOC (edge of cover).

Establishing a ¿Pythagorean¿ Result [Letter to the Editor]

An integral commonly occurring in analyses associated with RCS calculations and directivity calculations for uniform arrays is re-examined. Typically, such integrals are evaluated either numerically (a tedious business) or approximately (using asymptotic methods for large arguments). It is shown here that by incorporating only the next higher-order term in the usual asymptotic development for such integrals, it is possible to secure a significant improvement in integral-estimation accuracy, at very little increase in computational effort.