A need for precise measurement of the radiation from microwave antennas has arisen in connection with the development of advanced antenna design concepts and improved theoretical approaches for antenna analysis. The need has been felt in particular within space applications where antennas are being constructed to tight specifications, i.e. down to the order of one per cent in gain. Antenna testing has therefore attracted considerable interest in recent years where a large number of studies have been made and new developments effected. The oldest type of test range, the outdoor far-field range, has seen a few modern implementations. However, it is to the indoor test techniques that most of the efforts have been devoted. The compact range as well as near-field scanning ranges in planar, cylindrical and spherical geometries have all more or less reached mature states. They are now being installed at many places and seem to be the natural choice for contemporary antenna testing.

The scattering matrix theory for antennas is the obvious tool for analyzing the interaction between the test antenna and the probe in near field test ranges with spherical geometries. In particular, the theory forms a natural basis for a simple derivation of the transmission formula in spherical coordinates. This formula is fundamental to spherical near-field testing of antennas, and its derivation is the main subject of this chapter.

This chapter deals with the practical aspects of spherical near-field antenna testing. Section 5.2 on measurement probes provides a transition from the theoretical chapters to the experimental techniques beginning in Section 5.3. Section 5.3 on probe corrected measurements contains a section (5.3.2) where the spherical near-field test range is examined from a system point of view. In another section (5.3.3), the test range is described from the point of view of the various measurement procedures that can be carried out on the range and that constitute a complete measurement of a given test antenna. Some measurement results obtained at the TUD test range are also presented (Section 5.3.4). As was shown in Chapter 4, the basic spherical near-field measurement not only yields the radiation patterns of the test antenna but also its directivity. If the test antenna gain is wanted, some additional measurements must be carried out. These are dealt with in Section 5.4.

This chapter considers the general problem of far-field measurements from the point of view of plane-wave synthesis. This point of view is straightforward if we consider the measurement of the receiving characteristics of a test antenna. The far-field pattern can here be measured with the receiving test antenna rotated in an incident plane-wave field. Any deviation from plane-wave behaviour of the incident field in the volume occupied by the test antenna - caused, for example, by compromises in the design of the range, reflections from surroundings or multiple interaction - will cause errors in the measured far-field data. Arguments of this kind show that any far-field measurement technique must, in some way, realize or synthesize a quasi-plane wave field in the test zone. The creation of a plane-wave zone of sufficient quality can be achieved in a number of different ways which may be used to classify the various types of far-field measurement ranges. The quality of the plane-waves produced allows comparison of the different ranges.

Considers two right-handed rectangular coordinate systems, initially co incident. Let the first, the unprimed system (x, y, z), remain fixed in space while the other, the primed system (x', y', z'), is rotated about the origin from its initial orientation to some arbitrary orientation in space and kept there.

In antenna pattern measurements in general and in spherical near-field testing in particular extensive use is made of various forms of sampling and reconstruction schemes for band-limited, periodic functions. The purpose of this appendix is to provide an overview of these techniques.