Certain Factors Affecting the Gain of Directive Antennas* 



By G. C. SOUTHWORTH 



This paper analyzes the performance of antenna arrays as influenced by 

 certain variables within the control of the designing engineer. It starts with 

 an extremely simple analysis of the interfering effects produced by two 

 sources of waves of the same amplitude. This is followed by a short dis- 

 cussion of a paper by Ronald Foster, which considers two antennas and also 

 16 antennas when arranged in linear array. Two antennas separated in 

 space by J^ wave-length and in phase by i^ period give sensibly more 

 radiation in one direction than in the opposite. This, for convenience, has 

 been called a unidirectional couplet. A number of these couplets may be 

 arranged in linear array, thereby giving an extremely useful directive 

 system. Diagrams are shown for such arrays as affected by the number and 

 spacings of the indi\'idual couplets. The gains from such arrays are 

 calculated and data are given showing fair agreement between calculation 

 and observation. 



Directional diagrams for arrays of coaxial antennas indicate that some- 

 wliat less gain may be expected from this form than when the elements are 

 spaced laterally. Combinations of tliese two types of arrays give marked 

 directional ]3ro])ertios in both their horizontal and vertical planes of refer- 

 ence. This principle lias been used ratiier generally in short-wave coni- 

 nmnication. This paper also discusses effects resulting from combining 

 two or more arrays. In one case the sjiace between two arrays tends to 

 emphasize sjiurious lobes. The directional diagram of such a combination 

 may be rotated within limits by changing tlie phasing between adjacent 

 arrays or sections of an array. In all of the above cases the influence of 

 the earth is ignored. 



A mathematical appendix gives general equations for calculating di- 

 rectional diagrams of linear arrays. Special cases of these equations apply 

 to the figures included in the main part of the text. General equations are 

 also given for calculating the gains of arrays. Similar equations permit the 

 areas of diagrams to be calculated. An extended bibliography on antenna 

 arrays is appended. 



Introduction 



THROUGHOUT the development of radio communication the 

 engineer has aspired to a directive system whereby radiation 

 might be projected from one point to another with a maximum 

 of efficiency and a minimum of interference with adjacent stations. 

 Also, he has aimed at similar directivity at the receiver to improve 

 the signal-to-noise ratio and otherwise discriminate against un- 

 desirable signals. It was recognized at a very early date that directive 

 radio based on wave interference was feasible provided sufficiently 

 short waves could be utilized, and as a result many interesting sug- 

 gestions to this end were made. However, as is well known, the early 

 development of the radio spectrum proceeded in the direction of long 



* Presented at Convention of I. R. E., Toronto, Ont., Canada, Aug. 19, 1930. 

 Proc, I. R. E., Sept. 1930. 



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