Multiple reflections between two tuned receiving antennae

A consideration of previous work on the reflecting action an idle or parasitic receiving antenna suggested the desirability of investigating the extent to which multiple to-and-fro reflections between parallel receiving antennae affect the currents produced in them. In order to avoid the possible errors arising from the assumption that tuned half-wave antennae act as Hertzian dipoles, the values of the mutual impedances and phase differences deduced by Carter and tabulated Tani are used in the present work. By considering the effects of multiple reflections between two tuned receiving antennae, formulae for the antenna currents are obtained in terms of the currents produced in the antennae when isolated, the distance between the antennae, the wavelength, and the orientation of the plane containing the antennae to the direction of wave propagation. The validity of these formulae was tested by experiments with electromagnetic waves 80 cm. in length, The experimental results are compared with the graphical representations of the formulae, and for antenna spacings greater than about one-quarter of the wavelength, it is concluded that (i) the effects of multiple reflections do not appreciably affect the optimum or critical spacings between the antennae, but must be taken into account when determining the antenna currents, and (ii) tuned antennae may be considered to act as Hertzian dipoles. With parallel tuned antennae oriented with the line joining them parallel to the direction of wavepropagation, the optimum distances between them for maximum current in the leading antenna are 0.31?, 0.85?, 1.36?, 1.87?, etc. In the trailing antenna the current gradually increases as the antenna, spacing increases above a value somewhat less than 0.2? For maximum current in either antenna when oriented with the line joining them perpendicular to the direction of wave propagation, the optimum spacings are 0.67?, 1.71?, etc., and for other orientations the current variations with antenn- a spacing are determined by equations (4) and (6) when the field is uniform, and by equations (5) and (7) when the field not uniform.