A Theoretical investigation of the phase relations in beam systems

In most problems on antenna systems the field at any point is assumed to be one or other of the so-called induction and radiation fields. Actually it is a combination of the two and in some cases the ¿ static ¿ electric field has to be considered. All antenna systems are designed to give a specific radiation field in certain directions. It would simplify problems connected with antenna systems and, in particular, beam systems, if the total field at any point in space were expressed in the form of a radiation field. In order to take account of the apparent change in type of field as we recede from the antennae, the equation for such a field must contain two variable factors depending on the distance. One of these governs the phase and the other the amplitude of the total field. In this paper these factors are calculated and curves are plotted giving their values for different distances. The best position for a reflector is then considered and it is found not necessarily to be at a ¿ wave-length behind the transmitter, as is commonly supposed. The method of calculating from the curves the required positions of antennae in a system for any given purpose is shown. Two specific cases are considered. One corresponds to the parabolic reflector and the other to the linear curtain system. It is shown that the envelope of the reflecting antennae when these are tuned is not quite a parabola. In a beam system with a linear antenna array, it is found that good conditions are obtainable if the transmitting antennae are spaced 0.72 wave-length apart and the reflector is in line 1/4 wave-length behind, with the individual antennae midway between the two corresponding antennae of the transmitter. The experimental results of Tatarinoff appear to confirm the theoretical results obtained.