Two alternative methods of aperture antenna analysis are described in this book.
Inspec keywords: antenna radiation patterns; approximation theory; Fourier transforms; geometrical theory of diffraction; aperture antennas; antenna theory
Other keywords: Kirchhoff approximation method; Fourier transform; geometrical theory of diffraction; antenna radiation pattern; asymptotic approximation; paraboloidal reflectors; plane wave spectrum representation; aperture edge diffraction; aperture antenna analysis; Fresnel transforms; aperture field radiation pattern; near-field measurements; diffraction theory; reflection coefficient; far-field radiation pattern
Subjects: Single antennas; Integral transforms in numerical analysis; Interpolation and function approximation (numerical analysis); Antenna theory
An aperture antenna may be described in two ways. First, as an area of a surface with a radiating field distribution across it, the field being negligible on the surface outside the area. Second, as an area bounded by edges and excited by a source. Examples are radiating slots, horns and reflectors. These two descriptions characterise the two alternative methods of aperture antenna analysis used in this book. One is based on aperture field radiation, the other on aperture edge diffraction. Both apply strictly to large apertures so slots are generally excluded, but they are also useful for apertures with dimensions comparable to a wavelength. They tend to be complementary in that where one fails the other may succeed.
In this chapter, plane wave aperture in antennas use the Maxwell's equation which relate spatial and time variations of the electric and magnetic field.
The Fourier transform relationship between an aperture distribution and its radiation pattern is exact, but its application involves an approximation at once for the field is never known over the entire aperture plane. Usually it is known approximately only within the aperture and is assumed to vanish in the rest of the aperture plane. Suppose a field exists in an aperture S in the plane z = 0 and is negligible outside S. The tangential electric field in S is resolved into appropriate components, usually Cartesian if the aperture shape is rectangular.
the radiation patterns considered were at distances from the aperture sufficiently large that all ray paths from the aperture to the field point are essentially parallel, i.e. r>a,b in Fig. 3.1 Here this assumption is removed and the radiation field in what is known in optics as the Fresnel zone of the aperture is examined. With the condition r > λ maintained, the reactive near fields of the aper ture are excluded from consideration.
The results of this Section are for point measuring probes in the near-field. If the measuring probe directivity is significant axial near-field gain can be specified only for identical antennas. Near-field gain reduction factors for identical circular and square apertures with uniform and tapered distributions have been derived.
A few examples of the application of Fourier transform theory to the calculation of the radiation properties of some practical antennas are given here. These examples are chosen to illustrate the method and nature of the approximations necessary in its application. The major approximation of the Kirchhoff or Fourier transform method is the assumed form of the field in the aperture plane both inside and out side the aperture. Usually the tangential electric field is assumed zero outside the aperture and the incident field in the aperture.
The preceding chapters use the approximate Kirchhoff theory of diffraction. As indicated in Sections 2.6 and 6.1 it does not, in general, satisfy the boundary con ditions. This chapter gives a few elementary diffraction solutions for conductors with edges in which boundary conditions are rigorously satisfied. These exact solutions are the basis of the newer approximate method of aperture antenna analysis used in the remaining chapters.
The geometrical theory of diffraction is Keller's (1953) name for an approximate method of solving diffraction problems which combines the principles of geometrical optics with asymptotic diffraction theory. The method is an improvement over the Kirchhoff theory in dealing with aperture antennas in that it admits edge diffraction and interaction and allows fields in and behind the aperture plane to be calculated. Although not rigorous, it provides approximate solutions to problems for which rigorous solutions are unavailable. It also gives the correct asymptotic form in situations where there is an exact solution. For diffraction by plane con ducting screens we begin with the asymptotic solution for diffraction by a conduct ing half-plane.
In antenna analysis the geometrical theory of diffraction is particularly useful in obtaining the radiation field at angles well off the beam axis or in the rear direction where the Kirchhoff method either fails or cannot be applied. On or near the beam axis geometrical diffraction theory may fail, as in the case of a paraboloidal reflector. There the Kirchhoff method is both applicable and accurate and should be used. In this sense the two methods are complementary.
The appendixes contain a brief exposition of some mathematical techniques used together with details of the half-plane diffraction solution and a derivation of the transmission cross-section of an aperture.