140 BELL SYSTEM TECHNICAL JOURNAL 



when 



hiR 



dl 



I = -r— j -T- for the major ear of the directive ,,, 



2(1 — sin<^-cosA) ,. (4) 



diagram, 



•7 — = when 



tan c" (1 ~ sin <^-cos A) 



_ 27r/-cos^ 0-cos A(l — sin (/)-cos A) ,,, 

 X (sin — cos A) 



Substituting equation (4) into (5), it is found that, 



sin (f) = cos A. (6) 



This result determines the fact that, regardless of antenna height, 

 the best tilt-angle </> is the complement of the wave-angle A, where the 

 optimum element length is used. Taking this result and substituting 

 it back into either (4) or (5) results in 



The value of "/" in equation (7) together with the height given by 

 equation (3), and the tilt-angle given by equation (6) determine the 

 dimensions of the horizontal rhombic antenna with maximum output 

 for any given wave-angle A. 



As an example of the use of the above equations. Fig. 3 is the resulting 

 incident plane directive pattern with the antenna designed for the 

 given wave-angle of 17.5 degrees. Figure 4 is a plot of the antenna 

 output versus the azimuth angle for the fixed incident angle of 17.5 

 degrees as obtained by using these dimensions in the three-dimensional 

 directivity equation in the appendix. 



Note in Fig. 3 that the directive pattern does not have its maximum 

 radius at the line indicating the given wave-direction even though the 

 greatest possible amplitude for that wave-angle has been determined. 



It is believed that this method of design has a definite application 

 where over-riding set-noise by the largest possible signal output is 

 paramount. In cases where discrimination against random static is 

 desirable, or where the received wave-direction is unstable, an align- 

 ment of the mean wave-direction with the optimum radius of the 



