GAIN OF DIRECTIVE ANTENNAS 81 



Stacked Antennas 



Thus far the discussion has centered mainly around directivity 

 produced by placing vertical antennas in horizontal array. Added 

 gain may be had also by incorporating directivity in a vertical plane.^ 

 This is frequently accomplished by arranging individual antennas one 

 above another with their axes coUinear, and is sometimes known 

 as stacking. The fundamental principles of analysis are the same as 

 those already utilized. However, an approximate correction must be 

 allowed to account for the fact that the radiation from a linear oscilla- 

 tor increases from zero along the axis to a maximum in a plane per- 

 pendicular to the axis. The directional characteristic in planes passed 

 through and parallel to such a radiator is approximated by two 

 tangent circles. 



Fig. 17 shows a series of directional diagrams indicating the re- 

 sults of stacking unidirectional couplets. The diagrams shown refer 

 to the plane passed through the axes of the two linear oscillators com- 

 prising the couplet. On each diagram is a unit circle corresponding to 

 a single point source. Inscribed are the two tangent circles, represent- 

 ing the vertical directional characteristic of a single linear source. 

 Inside one of the tangent circles is the final directional diagram of the 

 stacked array. The ratio of the area of the tangent circles to that of 

 the characteristic diagram is given under each figure. This may be 

 regarded as a rough measure of the relative gain. These diagrams are 

 arranged horizontally in order of increasing number of couplets and 

 vertically in order of separation. It frequently happens in practice 

 that each radiator is approximately >^ wave-length long so it is con- 

 venient to utilize a vertical spacing interval also of }4 wave-length. 

 Consequently the second row of diagrams is probably of greatest 

 practical interest. In calculating these diagrams earth efi"ects have 

 been ignored. 



In Figs. 18 and 19, the gain in decibels to be expected from stacking 

 couplets has been plotted against number of couplets and fractional 

 wave-length spacing. These values, like those for Figs. 7 and 8 above, 

 were calculated by integrating the equation of diagram over a sphere 

 of arbitrary radius. This was accomplished by use of equation (30) 

 below. On account of the limited data at hand, Figs. 18 and 19 

 should be regarded only as a convenient method of illustrating the 

 trend of the variables. These indicate that somewhat lower corre- 

 sponding improvements result from stacking than from increasing the 

 length of an array. 



8 U. S. Patent 1,683,739, John Stone Stone, September 11, 1928. 



