146 BELL SYSTEM TECHNICAL JOURNAL 



and 6 to determine what effect the sacrifice in height and the increased 

 length has had. 



The effect on the directive pattern of reducing the length can be 

 minimized by changing the tilt-angle 4>- When the height given by 

 equation (3) is used, the new tilt-angle can be obtained by writing 

 equation (10) as 



. ^ / - 0.371X .,., 



sm<^= — -. -— • (15) 



/ cos A ^ 



If it is desired to align the directive pattern with the wave-angle 

 when the height and length are both reduced from the recommended 

 values, equation (8) can be solved for the new tilt-angle. Any of these 

 compromise designs will, of course, reduce the antenna output. 



Limitations of Results 



The accuracy of the calculations in this paper is based on the 

 following assumptions : 



1. Negligible effect by wire attenuation. 



2. Negligible mutual coupling between elements. 



3. The rate of change of the effective voltage with var>-ing di- 



mensions is large as compared with the rate of change of 

 radiation resistance. 



The validity of the assumptions has been checked to engineering 

 accuracies in the ultra-short wave experiments to be described, where 

 the shape of the directivity predicted by these equations agreed well 

 with experiment. However, theory and experiment have both shown 

 that ordinary ground has an appreciable influence on the wire attenu- 

 ation when the antenna heights are of the order of only small fractions 

 of a wave-length. This effect increases as the antenna dimensions are 

 extended. In such unusual cases, this behavior should be carefully 

 investigated even though calculations including large wire attenuations 

 have shown surprisingly little effect upon the directive diagrams. 

 Approximate values for the variation of radiation resistance with 

 dimensions, for terminated rhombic antennas, indicate that assumption 

 3 is probably warranted provided that the antenna is not extraordi- 

 narily small. 



Finally, attention should be called to these important facts: 

 The suggested dimensions in this jiaper not only do not restrict the 

 broad frequency range of this type of antenna but arc in many cases 



