530 ANTENNAS AND RF COMPONENTS 



most useful form as a constant beamwidth, circularly polarized, broadband 

 radiator, an engineering description of the antenna pictures a traveling 

 wave moving outward along the spiral to a diameter where the circum- 

 ference is 1 wavelength. Around this circumference, the waves on adjacent 

 turns are such as to reinforce one another, producing radiation in this ring; 

 whereas, in general, at other diameters, no reinforcement takes place and 

 radiation is small. Since most of the energy leaves the antenna at a 

 circumference on 1 wavelength, little is left at the next resonant circum- 

 ference of 2 wavelengths. 



A spiral so proportioned, fitting this engineering description and having 

 a circle-like turn in the radiating region, gives conductor sizes impractically 

 fine in the central driving point area. As a result, another type of spiral 

 has been studied at the Massachusetts Institute of Technology^^ and 

 elsewhere, which is similar in all respects except that it is defined by an 

 arithmetic growth, 



r = Cd. (10-14) 



This spiral, pictured in Fig. 10-9(b), has electrical characteristics similar to 

 the geometric spiral, including wide bandwidth and constant beamwidth. 

 Thus although the conductor width is a specifying linear dimension, the 

 antenna is a good approximation to the principle of description by angles 

 only when the conductor width is made small compared to a wavelength 

 everywhere in its radiating band. 



Analysis. With wirelike radiator elements such as have been described, 

 it is more satisfactory to consider the problem from antenna array theory 

 than from aperture consideration, because in small apertures of the order 

 of wavelength squared, the effective aperture cannot be determined by a 

 mere inspection of the physical aperture. The radiating ring of the spiral 

 can be reduced to an array in the following manner. 



The current in the radiating ring has been described as a traveling wave, 



/ = cos (co/ - ^Z) (10-15) 



where cot produces the uniform time variation of the current and j8Z 

 produces the linear space variation of the wave measured around the 

 circumference of the ring. To make the ring circumference 1 wavelength 

 and from definitions, 



X = 2xr, ,8 = ^, and Z ^ rS . (10-16) 



A 



The current may now be rewritten 



/ = cos CO/ cos d + sin w/ sin 6 . 



l»B. H. Burdine and R. M. McElvery, The Spiral Antenna, Massachusetts Institute of 

 Technology, Research Laboratory of Electronics, Report No. 1, March 15, 1955. 



