"Non-uniformly spaced arrays of directional elements"

Abstract

In February 1965, a research programme in radio astronomy was started by the Electrical Engineering Department of the University of Auckland. One of the main purposes of the programme was to provide a unified theme for post-graduate research in the department. The initial aim of the programme was to develop through graduate research, sufficient facilities for radio astronomy observations at frequencies below 100Mhz.

Being among the first group of graduate students in the programme, the author was given the problem of studying the antenna requirements for the programme. At the frequencies concerned, the antenna systems are often large and expensive. As the programme is supported at present, only by funds for ordinary graduate research, there is a great need for an antenna array with good performance at minimal cost. This has led the author into his main field of study, viz. the synthesis of arrays with non-uniformly spaced directional elements. The use of directional elements together with non-uniform spacing technique permits larger inter-element spacings in the array without resulting in large sidelobes in the response pattern.

Available synthesis methods are inadequate despite the large number of papers published on the subject since its introduction 7 years ago. The synthesis problem involves the determination of a set of element positions to give a desirable response pattern. Because the element position variables lie in the arguments of the cosine terms in the pattern function, the problem becomes highly non-linear. For simplicity, most of the published works have assumed isotropic elements. The methods proposed have been mainly centred on some form of linear approximations to the problem. Consequently, these methods are only effective over a limited region of space*. As a result of this limitation, good pattern characteristics can only be achieved with impractically small spacings.

For arrays with less than about 50 elements, the element spacings can best be determined by an optimisation procedure. This method involves the repeated application of small pertubations to the element positions of a starting array until maximum improvement to the sidelobe levels of the array is achieved. An efficient perturbation method has been proposed by Baklanov et al using a matrix approach. Because of the inherent limitation of this method, Baklanov’s arrays are mostly impractical due to the occurrence of small spacings. Such limitations are removed by the author through the use of a modified synthesis procedure. With this new procedure, the author was able to control the pattern over a considerably larger area in space. Thus arrays with average inter-element spacings up to two wavelengths can be synthesised with positive control over all sidelobes in the arrays. The sidelobe levels of the author’s arrays are, as a whole, bery close to the levels of the corresponding theoretically optimal patterns. The element directivities are taken into account in the synthesis process.

A total of 30 non-uniformly spaced arrays of varying sizes and sidelobe levels were synthesised using the method developed. Since all these arrays have near to optimal sidelobe characteristics, they provide a basis for a detailed study of the properties of non-uniformly spaced arrays as a whole. A number of interesting points are revealed when pattern parameters like gain, beamwidth, sidelobe level, etc., are studied in relation with the spacing characteristics of the arrays. A better understanding of the properties of non-uniformly spaced arrays is also gained by comparing the pattern characteristics of the synthesised arrays with that of current tapered arrays.

The design and testing of a 16-element non-uniformly spaced array of Yagi antennas is described in Chapter 4. This array demonstrates one practical application of the synthesis work reported in this thesis.

*The word ‘space’ used throughout the Introduction does not mean the physical space, which is defined, in a 2-D case, by the zenith angle θ. Here, the space is defined by the parameter χ=2πdavsinθ/λ. Thus with an average inter-element spacing dav= λ, the visible space is defined by χ=0 to π.